{"as_of":"2026-08-08T11:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:60c55b6d0e1dd19a69cc06b8ec6ff26854282c6eb88a88d4e25679d8b0a2dd29","coverage":[{"denominator":97,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":97,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T03:40:22.217092Z","state":"measured"},{"denominator":97,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":97,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.13886/citation-record","integrity":"/paper/2607.13886/integrity","json":"/paper/2607.13886/citation-record.json","paper":"/paper/2607.13886"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:12.363358Z","title":"Martingale property and moment explosions in signature volatility models.arXiv Preprint: 2503.17103, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.363358Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:bbf69903bdd297c1ac55010bfea141b82cae42faa4ec4cee9dcb97aa6c8aa217","observation_id":"5aa3c84b-88a9-48f1-8395-e3775d2fa3b9","resolution":{"observed_at":"2026-08-02T03:40:12.363358Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:12.466272Z","title":"Signature volatility models: pricing and hedging with Fourier.SIAM Journal on Financial Mathematics, 16(2):606–642, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.466272Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:2e1aa0a6819ef0fbdbf04c1d32505c696d7e99d0fceebadd38fafbdeb7763374","observation_id":"01105d8e-223b-4c97-8b8b-3ffa06a8824e","resolution":{"observed_at":"2026-08-02T03:40:12.466272Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.03700","last_updated":"2026-05-22T13:15:09Z","snapshot_observed_at":"2026-07-06T21:52:27.493261Z","submitted_at":"2025-07-04T16:30:59Z","title":"Exponentially Fading Memory Signature","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.03700","snapshot_observed_at":"2026-08-02T03:40:12.580101Z","title":"Exponentially fading memory signature.arXiv Preprint: 2507.03700, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.580101Z"},"links":{"cited_paper":"/paper/2507.03700","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:4e1156f561912d18d01ff49346856443dc00ed23e6fc7cede550d48ecdb30b69","observation_id":"1746e20f-0541-4cfc-a7f9-3fce6c43acd5","resolution":{"observed_at":"2026-08-02T03:40:12.580101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:12.722477Z","title":"Cambridge University Press, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.722477Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:21519ab5e598fb9d38ecf612ecd484d2be4d90029e144d586b921a6bb9d5dc98","observation_id":"b00ce402-0ac0-49cc-959e-fff0fd2f12ca","resolution":{"observed_at":"2026-08-02T03:40:12.722477Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:12.866089Z","title":"Agrachev and Yuri L","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.866089Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:7a53856d48db54fdda8714e412492edc6bf2b73167a1b01cca4a8671fd19936c","observation_id":"66cee82d-feb9-4050-bdf4-45a7630aef8d","resolution":{"observed_at":"2026-08-02T03:40:12.866089Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:12.930662Z","title":"Rough differential equations containing path-dependent bounded variation terms.Journal of Theoretical Probability, 37(3):2130–2183, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:12.930662Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:5c5e697c0644ddf39179e4d89acb2cac9b6c2ac9120c09a65db10b1ee4ca0229","observation_id":"c66586dc-7632-4180-a8c7-06ad6c13afc0","resolution":{"observed_at":"2026-08-02T03:40:12.930662Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.007783Z","title":"Aliprantis and Kim C","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.007783Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:632e44045f4945fa662446ab2695a4a5d3e6d0818305c59556b54557d4c1a27a","observation_id":"c8a6fb6e-5073-4650-8265-442ffb7f8765","resolution":{"observed_at":"2026-08-02T03:40:13.007783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.107569Z","title":"Rough differential equations with path-dependent coefficients.Annales Henri Lebesgue, 6:1–29, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.107569Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:6c765976bb7a192f19bedc103ddd6d737bb303b820450e7aa29da2105754864f","observation_id":"a698c8b5-45a8-47c6-9f49-40d848f63b59","resolution":{"observed_at":"2026-08-02T03:40:13.107569Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.226155Z","title":"Path dependent equations driven by H¨ older processes.Stochastic Analysis and Applications, 37(3):480–498, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.226155Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:1f5f3d584335caa0083eaa1b73c44477d988d0a97527fb6d74e2c7cbc9734377","observation_id":"4e9bee99-cdb6-46ac-9dfc-ecba662e25ad","resolution":{"observed_at":"2026-08-02T03:40:13.226155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.355744Z","title":"Sig-SDEs model for quantitative finance","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.355744Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:3bd2a654975511402c1e7509f886a61457e7b50423cd6d0ca13340b5c6d4eb17","observation_id":"452360b9-a65f-45ca-91df-95d7ad139f5d","resolution":{"observed_at":"2026-08-02T03:40:13.355744Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.488421Z","title":"Asmar and Loukas Grafakos.Complex Analysis with Applications","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.488421Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:6b20f2f7b04b9d978748ee909d69ff22e96d1f2286a0ce8678393370d0e5b6ed","observation_id":"37e5f422-8d35-4e92-a864-4cd8dcb69525","resolution":{"observed_at":"2026-08-02T03:40:13.488421Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.626443Z","title":"Baum and Ted Petrie","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.626443Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:cb09ccfc9c1eb36aa2dfef3660163f49a93084923fd12b12b4eb1125147fa500","observation_id":"05e32e50-8357-479a-bdcd-7ee4dc756bd4","resolution":{"observed_at":"2026-08-02T03:40:13.626443Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:13.781821Z","title":"Hager, Sebastian Riedel, and John Schoenmakers","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.781821Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:64f2c4ec1ea97c0c8cf57d16b13345c0a5bf597ea465e328f607865b6403cb95","observation_id":"92ad23dd-ba37-4402-805f-0da4c01c24da","resolution":{"observed_at":"2026-08-02T03:40:13.781821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15703","last_updated":"2025-02-25T08:48:12Z","snapshot_observed_at":"2026-07-06T20:40:39.302105Z","submitted_at":"2025-01-15T17:40:42Z","title":"An introduction to tensors for path signatures","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.15703","snapshot_observed_at":"2026-08-02T03:40:13.936260Z","title":"An introduction to tensors for path signatures.arXiv preprint arXiv:2502.15703, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:13.936260Z"},"links":{"cited_paper":"/paper/2502.15703","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:b31009dfae1a8bd497f2001dd757692f6827ca19e80ab3afa93be4eeff3ab7c5","observation_id":"72deafde-c704-4ed2-8c26-d27986bf23b6","resolution":{"observed_at":"2026-08-02T03:40:13.936260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.017335Z","title":"Friz, Sylvie Paycha, and Rosa Preiß","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.017335Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:8fecae83377ff6438338edb53dc3a35c137a08f9ac88bcf58d1bdb03aa3234b7","observation_id":"e4f30556-0cab-4e96-8055-87b28cd6ac7f","resolution":{"observed_at":"2026-08-02T03:40:14.017335Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.181088Z","title":"Delfour, and Sanjoy K","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.181088Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:36ee73bfb75afa0355239693a1cef8d8d7bc8d10549d0d56df5a14583e650d97","observation_id":"454b91a2-83e2-4e69-b226-4c5d928f975b","resolution":{"observed_at":"2026-08-02T03:40:14.181088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.294647Z","title":"A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations.Acta Mathematica Hungarica, 7(1):81–94, 1956","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.294647Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:d6c9579922fa65e9f693eaa81c2b8c4c5b97fd6dcea51084eba2f1ee0f579c19","observation_id":"22e6d94b-a0f5-45c6-9a84-6e5b921891cc","resolution":{"observed_at":"2026-08-02T03:40:14.294647Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.390545Z","title":"SL2(R)-developments and signature asymptotics for planar paths with bounded variation.Rev","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.390545Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:c5b13d53c6944abf645034ae6ced0b5d1e5d1d47143837afd41101e7203deb6c","observation_id":"1be4623c-7978-4df9-b2e3-c7e14795e5e9","resolution":{"observed_at":"2026-08-02T03:40:14.390545Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.507750Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.507750Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:c92f1a96d6634cd87eae7fa0991e3e287dec30872cb372aa2b74e665c9af7686","observation_id":"9bd719d3-a9fc-4552-a100-8e635f730bca","resolution":{"observed_at":"2026-08-02T03:40:14.507750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.614854Z","title":"Zur Theorie der elastischen Nachwirkung.Sitzungsberichte der Kaiser- lichen Akademie der Wissenschaften, 70:275–306, 1874","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.614854Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:7fd8f09b0a0aa83e980ceef988a662f8af440784e982a71acf502f857de9bb13","observation_id":"7486f98e-b85d-4eec-8c72-6042dfac38c7","resolution":{"observed_at":"2026-08-02T03:40:14.614854Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.723459Z","title":"Brockett","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.723459Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:91cbb33c07b904a7ddb49a484756bdee4337d099391205e5a939ccd26cdbd8b2","observation_id":"41b6ccb5-e9e6-48f7-a30b-0e7df1d9434b","resolution":{"observed_at":"2026-08-02T03:40:14.723459Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.811793Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.811793Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:010ec26bd6102004bf78f96e0ace8069afa859edc7ff8d4a531176548bcd6e08","observation_id":"a7984069-2624-4bff-9bd9-cbd903c25734","resolution":{"observed_at":"2026-08-02T03:40:14.811793Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:14.920671Z","title":"Iterated integrals and exponential homomorphisms.Proceedings of the London Mathematical Society, 3(1):502–512, 1954","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:14.920671Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:fbb75af4ad00cb77706b289856186e73a334515d13ab52e95350d5dd29159851","observation_id":"a2b3cf5a-0b67-4725-901f-0da3c91b9e3d","resolution":{"observed_at":"2026-08-02T03:40:14.920671Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.039497Z","title":"Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula.Annals of Mathematics, 65(1):163–178, 1957","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.039497Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:6eccfa07a1373a02c1a367d1fb83bfbbec1425849142718d7e17ec3ad3138b32","observation_id":"c8ee0381-87e3-4d95-8f38-fd555a4afc7a","resolution":{"observed_at":"2026-08-02T03:40:15.039497Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.124469Z","title":"Iterated path integrals.Bulletin of the American Mathematical Society, 83(5):831–879, 1977","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.124469Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:4278776963983a79b3530ea7448a89046fffe8554018b3471f41bb1e5a9fa98a","observation_id":"0247519a-5fc5-44fb-b08a-d82731013c0e","resolution":{"observed_at":"2026-08-02T03:40:15.124469Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.241891Z","title":"A primer on the signature method in machine learning.arXiv preprint arXiv:1603.03788, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.241891Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:e70f14ebe424c7a2303d09ab54a66884b12abcf617ff5b702a6b2e07d442b977","observation_id":"93a1f7e2-9c3a-41bd-9edf-7f9756784dae","resolution":{"observed_at":"2026-08-02T03:40:15.241891Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.364747Z","title":"Characteristic functions of measures on geometric rough paths.Ann","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.364747Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:0b0941b2a6cbb0aa2add186ce279edb3a6b1d0070aa86d46d44ac4df2b8c4df0","observation_id":"c8b93e86-da37-4a83-8e9e-4346a2eec6af","resolution":{"observed_at":"2026-08-02T03:40:15.364747Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.469199Z","title":"Functional Itˆ o calculus and stochastic integral representation of martingales.Ann","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.469199Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:0bed2aed9fde8ffa47d81d635c1b277b4ac32e0e58641649db14cdff9ae2a849","observation_id":"f0bc6b32-a349-41e0-a69e-f8202708d0d0","resolution":{"observed_at":"2026-08-02T03:40:15.469199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.610606Z","title":"On the support of solutions to stochastic differential equations with path-dependent coefficients.Stochastic Processes Appl., 130(5):2639–2674, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.610606Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:cdd61de23843fe4c5f1327f79bac12cf14f2d1be89c736f81cb1fb6f7a4806c8","observation_id":"c0827b1e-7ef4-4071-b232-8a856fb07b68","resolution":{"observed_at":"2026-08-02T03:40:15.610606Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.715994Z","title":"Sur certaines ´ equations fonctionnelles de Volterra.Funkc","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.715994Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:10264b5e0680a5135b8e7dbbe03ff256bfbaae9b84e924d5fd0106f441dd4722","observation_id":"e41d44d1-2710-48e3-ad11-7be646c8afff","resolution":{"observed_at":"2026-08-02T03:40:15.715994Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.824803Z","title":"Joint calibration to SPX and VIX options with signature-based models.Mathematical Finance, 35(1):161–213, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.824803Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:ecac7ee26b613d4ef4c88f2251e50695faec3fcf6828e0dbd29a8b63070f2c0e","observation_id":"e1173459-60ab-4027-8ef2-391a92137835","resolution":{"observed_at":"2026-08-02T03:40:15.824803Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:15.953333Z","title":"Signature-based models: theory and calibration.SIAM Journal on Financial Mathematics, 14(3):910–957, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:15.953333Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f19de48c671b9dff073029bcd995aa87e53f7544716c9aaf224f80581fd0f799","observation_id":"0e13a27d-e5b1-4504-87f1-68a5146c7bad","resolution":{"observed_at":"2026-08-02T03:40:15.953333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:16.070398Z","title":"Signature methods in stochastic portfolio theory.SIAM Journal on Financial Mathematics, 16(4):1239–1303, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:16.070398Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:2564c0e31d5332bfe7659324629e8cbf621f4211ff0372eeeea21743cd40909d","observation_id":"909d9757-4cb9-46a7-97b0-e4d8d39fc8f1","resolution":{"observed_at":"2026-08-02T03:40:16.070398Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:16.199215Z","title":"Universal approximation theorems for continuous functions of c` adl` ag paths and L´ evy-type signature models.Finance and Stochastics, 29(2):289–342, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:16.199215Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:7108740158158d8222431fc85266ef11a8ef3c6341d0076e2dfbdb3cc8ddd5f7","observation_id":"d6b7ce73-c55e-4fcf-90e2-f8453f0be2e1","resolution":{"observed_at":"2026-08-02T03:40:16.199215Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:16.356544Z","title":"Global universal approximation of functional input maps on weighted spaces.Constructive Approximation, pages 1–76, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:16.356544Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:2b423c17e5a1358f2de031572b86d089d9cf86e4175e087fe032af2b6b8d2575","observation_id":"eaf23109-01d8-4e5a-885c-c0debb76afe0","resolution":{"observed_at":"2026-08-02T03:40:16.356544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:16.639741Z","title":"Signature SDEs from an affine and polynomial perspective.forthcoming in the Electronic Journal of Probability, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:16.639741Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:366ec43236285409e92c264852514c09877cd1a455867f1519262b164ca4f432","observation_id":"c3df1d73-01dd-4f53-87f8-46537c892e44","resolution":{"observed_at":"2026-08-02T03:40:16.639741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1011.2651","last_updated":"2010-11-11T13:40:14Z","snapshot_observed_at":"2026-07-06T02:19:03.905500Z","submitted_at":"2010-11-11T13:40:14Z","title":"A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1011.2651","snapshot_observed_at":"2026-08-02T03:40:16.958581Z","title":"A semigroup point of view on splitting schemes for stochastic (partial) differential equations.arXiv preprint arXiv:1011.2651, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:16.958581Z"},"links":{"cited_paper":"/paper/1011.2651","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:6183adb0c7dd54a9d109fda9db5f96da797d601eb95c0850d949209dbceecf00","observation_id":"c2fd927e-9cf1-4b20-99b1-117a4467a26a","resolution":{"observed_at":"2026-08-02T03:40:16.958581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:17.160658Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:17.160658Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:d9bbff85e08c26d11dcc8f51e0d7885ca9dc4c55f2d44fa65d9b62f34302743d","observation_id":"f2cdd95b-2e4f-4aae-a583-18a822988d42","resolution":{"observed_at":"2026-08-02T03:40:17.160658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:17.376564Z","title":"Duffaut Espinosa, Kurusch Ebrahimi-Fard, W","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:17.376564Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:54132646dd14b606ed1b2b76fa2622bc20ef5b6f4e0411d8ac19f4ee86d5b29a","observation_id":"265495df-3784-4259-8c99-922261695b50","resolution":{"observed_at":"2026-08-02T03:40:17.376564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:17.519977Z","title":"Functional Itˆ o calculus.Quantitative Finance, 19(5):721–729, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:17.519977Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:477f94ce35134cfcbd15c281e58f3e902fedc71449a8f2de806a6b31d68b3d1f","observation_id":"15ee8bcb-e13f-4ff5-8040-fe477572fc4f","resolution":{"observed_at":"2026-08-02T03:40:17.519977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:17.720289Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:17.720289Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:076be0c22c1100d1f5edbe94a93c0f701593017f8a75b71680cf80e58267deab","observation_id":"a098e32d-f050-4303-a281-50a321726c63","resolution":{"observed_at":"2026-08-02T03:40:17.720289Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:17.852229Z","title":"Fonctionnelles causales non lin´ eaires et ind´ etermin´ ees non commutatives","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:17.852229Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f1780cc6d5f4839263d553321fdd7703ab15cd026e42a7fd0498cc748e95054a","observation_id":"27f76106-e9aa-4923-be9b-0c37e5ded7ab","resolution":{"observed_at":"2026-08-02T03:40:17.852229Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.005807Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.005807Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:c8c4a31cc53abda09d670bd520fddef3d5e060ea48da588ba3b8060cdb6c4830","observation_id":"0effed3d-2f29-4265-8471-d55f0dc71f45","resolution":{"observed_at":"2026-08-02T03:40:18.005807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.120178Z","title":"Columbia University, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.120178Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:308ce5021482acc997ffb9667db6ace321d36af3d2ecc2986bcf329d8d755053","observation_id":"741b0d47-b197-47cd-82fa-cfe578d3d11c","resolution":{"observed_at":"2026-08-02T03:40:18.120178Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2509.07893","last_updated":"2025-09-09T16:23:29Z","snapshot_observed_at":"2026-08-05T14:29:00.877411Z","submitted_at":"2025-09-09T16:23:29Z","title":"Expected Signature Kernels for L\\'evy Rough Paths","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.07893","snapshot_observed_at":"2026-08-02T03:40:18.244485Z","title":"Friz and Paul P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.244485Z"},"links":{"cited_paper":"/paper/2509.07893","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:cc9f8a24076e553c76f7cd90afd448dcab7410acd1b0ed0d4f53e18d311f1dad","observation_id":"823ebe88-1494-4a00-bc7d-b2843e064e56","resolution":{"observed_at":"2026-08-02T03:40:18.244485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.356784Z","title":"Friz and Martin Hairer.A Course on Rough Paths","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.356784Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:47d772218bc8c4fcba4c40265c9c5b645518f33caded32d12f8f4537068c04da","observation_id":"5bc7efcf-a3e4-4067-a3c9-fe22de5d1f1c","resolution":{"observed_at":"2026-08-02T03:40:18.356784Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.467805Z","title":"Friz and Nicolas B","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.467805Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:5f9cdf4538ecff99cdf489d1482fe9ed458a87aef18a6a9af5f06c5d9004745f","observation_id":"0dfb97a2-9f35-4ec1-a959-59112f813477","resolution":{"observed_at":"2026-08-02T03:40:18.467805Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.577777Z","title":"Kilbas, Francesco Mainardi, and Sergei V","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.577777Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:1c94c730a16a62d7d83a7244d63df291a7b94ce215fa6420968b1ca545638015","observation_id":"235152b4-5ee1-48fe-a37c-b478654c8acf","resolution":{"observed_at":"2026-08-02T03:40:18.577777Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.662783Z","title":"Hale and M.A","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.662783Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:97d5728cd4530ad3e5eebee117c45d4749695a83aac0c33e7192e45f54aec5e0","observation_id":"7cf7b7ec-d616-4dd2-8788-3214e94d6b40","resolution":{"observed_at":"2026-08-02T03:40:18.662783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.760059Z","title":"Hale and Sjoerd M","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.760059Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f62b959a5d3a8bc98f40bbeacf404f49e7f0aa12a3df75fe91426706252bf59d","observation_id":"bce4b5f0-53ef-4914-b671-fd257f502197","resolution":{"observed_at":"2026-08-02T03:40:18.760059Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.855957Z","title":"A neural RDE approach for continuous- time non-Markovian stochastic control problems","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.855957Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:58566bd4e26e4759bf121e6bc866b55252b4c4ce172c07adefbc7cafed0dd72c","observation_id":"75186a4c-bf41-464a-a01c-c8728b5a8038","resolution":{"observed_at":"2026-08-02T03:40:18.855957Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:18.982165Z","title":"Evelyn Hutchinson","venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:18.982165Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:9fc70f96bb1abff658066a97186739bcd12dd45848b8c4b59f2685af1f02f536","observation_id":"60c65ff7-9a1d-446a-8b1b-9a041eed2beb","resolution":{"observed_at":"2026-08-02T03:40:18.982165Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.122037Z","title":"Generalized ordinary differential equations in Banach spaces and applications to functional equations.Bol","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.122037Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:fa7873ff5f924451bd2fad32277eb36022c29d3e05b1e6c846ea6e34cf62b076","observation_id":"41b5584a-0aeb-47d5-804c-4885c2c3fc3e","resolution":{"observed_at":"2026-08-02T03:40:19.122037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.262430Z","title":"A uniformly differentiable approximation scheme for delay systems using splines.Applied Mathematics and Optimization, 23(3):217–262, 1991","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.262430Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:168866ecfad0017cbf2f90b104431d4b931fc9cde3d0f69ea9865fa9cf516816","observation_id":"7ee268b5-15fc-4f98-9f01-788d3a09e293","resolution":{"observed_at":"2026-08-02T03:40:19.262430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.400985Z","title":"Stephen Jones","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.400985Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:741e1ef6e8a542ddff76bfc3721be1401bf1e7f5332f63d2548c8d41c1c039ad","observation_id":"b99e6ba1-8a30-45a6-a1f6-ce0c429cac57","resolution":{"observed_at":"2026-08-02T03:40:19.400985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.554703Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.554703Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:612623db3457c676222b3594bf396da6d2f5efa608522201a040bfe0acd38e35","observation_id":"adfc534c-c0a5-41b3-9441-5b2c60c4e43c","resolution":{"observed_at":"2026-08-02T03:40:19.554703Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.706517Z","title":"Sussmann","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.706517Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:cf04bfe4a5473d8d6d1fa6e91731fb0f730e1fae2e537271149571ce5ac7cba0","observation_id":"45020cfa-364a-48ed-b984-e82bc9c12499","resolution":{"observed_at":"2026-08-02T03:40:19.706517Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.756825Z","title":"Littman, and Anthony R","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.756825Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:3720a57a8d6fb9db431cfccbfed4b1c3aed7f0728dfe29724100a3984446324e","observation_id":"cd3929b3-f8ba-4373-b8b2-44d37d6cbc87","resolution":{"observed_at":"2026-08-02T03:40:19.756825Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:19.915235Z","title":null,"venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:19.915235Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:230c7fb6aff493f2fc3fc5bc87e6d3964fa91fe4dd94c6a69cda78deee6717f7","observation_id":"6e659d7b-777d-4a84-9b3b-e0edfefb0f8e","resolution":{"observed_at":"2026-08-02T03:40:19.915235Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.020637Z","title":"Optimal execution with rough path signatures.SIAM Journal on Financial Mathematics, 11(2):470–493, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.020637Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:9ce3789f2684e074e6d57fe4eb841aa018921ac2ad4d9533a6c98c83b2926825","observation_id":"e61f23e8-51b7-46db-aba8-eefa2f906815","resolution":{"observed_at":"2026-08-02T03:40:20.020637Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.099253Z","title":"Spline approximation for retarded systems and the Riccati equation.SIAM Journal on Control and Optimization, 25(4):1082–1117, 1987","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.099253Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:ae8e795b18ad8e2fcfdf79319bbc532b0718080746ce1fa3b06b2ee59059b325","observation_id":"90ac025e-9ac2-430d-8868-64f3d3c8732e","resolution":{"observed_at":"2026-08-02T03:40:20.099253Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.216267Z","title":"On the stability properties of spline approximations for retarded systems.SIAM Journal on Control and Optimization, 27(2):407–431, 1989","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.216267Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:0bc8f7ab830b70ca611bdc276fcc9167e97abe47dac7bc33b51f7ab5d4b1c3b5","observation_id":"fe06d9f8-717e-49be-925f-f2bccfc34a05","resolution":{"observed_at":"2026-08-02T03:40:20.216267Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.272238Z","title":"McKendrick","venue":null,"work_id":null,"year":1927},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.272238Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:0f52ac27bfe473df257c97ffc79c9669eac232a53a0ab9e6367f5b64617fea18","observation_id":"610e71d4-e24a-4b76-8037-8cdf429014ef","resolution":{"observed_at":"2026-08-02T03:40:20.272238Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.355184Z","title":"Neural controlled differential equations for irregular time series","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.355184Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:1c591050332948ecc3ae162f571937167776082f2c86cc39b46050bd86786c2a","observation_id":"b59b1351-bbb6-45fc-941f-4d9c79e843b5","resolution":{"observed_at":"2026-08-02T03:40:20.355184Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.509419Z","title":"I., volume 159 ofGrundlehren Math","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.509419Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:d0faa889275be2bd58d7f91e981e2569646b9685ce47dea4310431390bf39664","observation_id":"b139e409-5e77-41f8-a8c2-fddfa597ff50","resolution":{"observed_at":"2026-08-02T03:40:20.509419Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.14284","last_updated":"2024-07-04T16:02:36Z","snapshot_observed_at":"2026-07-06T13:25:43.254971Z","submitted_at":"2022-06-28T20:50:14Z","title":"Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.14284","snapshot_observed_at":"2026-08-02T03:40:20.637484Z","title":"Optimal estimation of generic dynamics by path-dependent neural jump ODEs.arXiv Preprint: 2206.14284, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.637484Z"},"links":{"cited_paper":"/paper/2206.14284","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:0da106f2c82f139c4865c221cbc98c28bd0499549c7b808fa6608811f77c33da","observation_id":"301b6dd9-c28c-406a-9147-848a0b5223da","resolution":{"observed_at":"2026-08-02T03:40:20.637484Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.697344Z","title":"Kwossek, Andreas Neuenkirch, and David J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.697344Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:c0fc48d55315e3e50e574de85c83ff4a1861af3616438395fdc9eb15666489f5","observation_id":"2982686d-d3e8-4b17-8249-05524c33e7ce","resolution":{"observed_at":"2026-08-02T03:40:20.697344Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.734717Z","title":null,"venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.734717Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f5d9baf58bc164d5f6216c2097d5432abab484b198c129867c76829c812c56a7","observation_id":"65c34b0c-9891-474a-b6be-62b8b16d54c0","resolution":{"observed_at":"2026-08-02T03:40:20.734717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.782406Z","title":"Space of signatures as inverse limits of Carnot groups","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.782406Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:8a7fd4191a1496d46b6234e22dcff54ca9e636cc1f474850e5c6f5803bb07064","observation_id":"1e997122-da66-474d-9183-d9efc4bd1d6d","resolution":{"observed_at":"2026-08-02T03:40:20.782406Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.830635Z","title":"Lee.Introduction to Smooth Manifolds, volume 218 ofGraduate Texts in Mathe- matics","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.830635Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:7564d181b599069ba84c3f531d23f61e02e8311307589d4358220a7f3a018fb9","observation_id":"832ee50c-00b0-4510-af21-dab24741f03d","resolution":{"observed_at":"2026-08-02T03:40:20.830635Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.866232Z","title":"Oxford University Press, 2002","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.866232Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f0ade4c95bb902fc66562b85f8e4e043d2bf1d5f6432eaf0e4208822baf0a8bd","observation_id":"3891eb61-b530-4802-8469-f828535fdd7a","resolution":{"observed_at":"2026-08-02T03:40:20.866232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.900013Z","title":"Differential equations driven by rough signals.Revista Matem´ atica Iberoamer- icana, 14(2):215–310, 1998","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.900013Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:4f5ea5608df3c1e2324acb08360fae6dc000ddf7b66cffb7a6c214ad00098cd7","observation_id":"46a81efb-3f70-4743-934d-c01f88f4aa7a","resolution":{"observed_at":"2026-08-02T03:40:20.900013Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.936869Z","title":"Lyons, Michael J","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.936869Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:f4e733b17fd6e4505e55439f899ff13928dfbb70048226d0bd2deb161582fae4","observation_id":"147d57a8-abbc-4378-a1cd-b6f06d7b607e","resolution":{"observed_at":"2026-08-02T03:40:20.936869Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:20.992767Z","title":"On Lipschitz vector fields and the Cauchy problem in homogeneous groups.Communications in Contemporary Mathematics, 20(05):1750057, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:20.992767Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:556601f49034c3cdb2a6063d3d4c065539dce2d17e7a36df21877126d5d3203f","observation_id":"ff16e974-0ddd-428d-85a5-15a692fdb60a","resolution":{"observed_at":"2026-08-02T03:40:20.992767Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.021313Z","title":"edition, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.021313Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:98647525eca97aae29d20351d514cf66374d6b71a72431e0955d028d4b29cd73","observation_id":"5e6545f4-4d02-4c5f-bd0c-d40e0cc1740d","resolution":{"observed_at":"2026-08-02T03:40:21.021313Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.043141Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.043141Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:9369b9b93e95dde5e4add8724002b33eec86764216c60b81f3de73939402aaf4","observation_id":"0d814fc5-8e05-4a09-b63a-645bfc1a7d62","resolution":{"observed_at":"2026-08-02T03:40:21.043141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.069349Z","title":"Directional stability of automatically steered bodies.Journal of the American Society for Naval Engineers, 34(2):280–309, 1922","venue":null,"work_id":null,"year":1922},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.069349Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:5b9ba3f07cc3416a17e392184a8752311028a04a1cd5b438edd6bc4574840e83","observation_id":"234f5da5-856d-4b61-b2e8-fb5a042ed278","resolution":{"observed_at":"2026-08-02T03:40:21.069349Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.123346Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.123346Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:eaade3c5c6d182ab0304c850df904957ae1bd6c9f1f0e9c76b218639e2438c7d","observation_id":"60c32850-12d5-4b63-b96f-00dfa26d680d","resolution":{"observed_at":"2026-08-02T03:40:21.123346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.137418Z","title":"Neural rough differential equations for long time series","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.137418Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:ced681b40a928f6a3dde5efd4b8817ad3663eaaedeac6884c7f18f5075079531","observation_id":"8b1f3931-becf-4198-8a82-36817fd868f1","resolution":{"observed_at":"2026-08-02T03:40:21.137418Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.173112Z","title":"Munkres.Topology.Upper Saddle River, NJ: Prentice Hall, 2nd edition, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.173112Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:3b761d063080e9468e0f7e47f281faed24c3fd86db77c0daf2bfdb7d1996af2c","observation_id":"85418bc3-b22e-4811-b725-85ca821bcf58","resolution":{"observed_at":"2026-08-02T03:40:21.173112Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.201020Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.201020Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:71b0e9eb7690fdb94ab47b28d2d48a6ec574e226ca37c4a734feaef47a6a8659","observation_id":"619ca9c5-db23-4e22-bcf1-7cc107d8955a","resolution":{"observed_at":"2026-08-02T03:40:21.201020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.237144Z","title":"Parameter estimation for rough differential equations.Ann","venue":null,"work_id":null,"year":2047},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.237144Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:bd09499fecf8a4125e9947af6fa8babdfc030c01700f67d61194a3f7756d34ec","observation_id":"e62e94fe-0b5d-41bb-a85a-86e6df5d4756","resolution":{"observed_at":"2026-08-02T03:40:21.237144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.275369Z","title":"Learning non-Markovian dynamical systems with signature-based encoders","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.275369Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:8913913a9a000f493daa50f462b7b5482307a133f98e2a1b50225d63411d312c","observation_id":"f642c91e-9114-4e49-bfaf-466498c748a8","resolution":{"observed_at":"2026-08-02T03:40:21.275369Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.312470Z","title":"Protter.Stochastic Integration and Differential Equations, volume 21 ofAppl","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.312470Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:2ab4f154a6a81841634cd432a14c53a4910fccd02840ce95417663cf8c3d8ed9","observation_id":"123e492a-79e3-4d15-a8ab-f0403dba20e2","resolution":{"observed_at":"2026-08-02T03:40:21.312470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.358442Z","title":"Lie elements and an algebra associated with shuffles.Annals of Mathematics, 68(2):210–220, 1958","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.358442Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:cd7beafc588c8b9c1840a3acd85cf1fa79d480b115022ff9e0d9dffdd20b0279","observation_id":"139ab887-35ae-48ce-b621-8f2222a78aeb","resolution":{"observed_at":"2026-08-02T03:40:21.358442Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.399633Z","title":"Oxford University Press, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.399633Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:33bdfa263d2ffc9d5832147068b30043a69ebaf7ca104e59e4ae128c2923e229","observation_id":"ce7bd7cf-36ea-4a16-911f-e69b39d0064e","resolution":{"observed_at":"2026-08-02T03:40:21.399633Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.426101Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.426101Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:22e1164c068a9d0ffde303f703e6cb3858e31d5f38c8e0e4e6a15f980b52387d","observation_id":"96164e7e-58a6-413d-95fc-559d0fb2595e","resolution":{"observed_at":"2026-08-02T03:40:21.426101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.466001Z","title":"Der Fixpunktsatz in Funktionalra¨ umen.Studia Mathematica, 2(1):171–180, 1930","venue":null,"work_id":null,"year":1930},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.466001Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:edfedfbb24a57eb39e5fca8e305ffe92760c8a585de4d6b02000ff4782dfb40d","observation_id":"c1d931ee-0072-4b10-91d6-8bff747c7f12","resolution":{"observed_at":"2026-08-02T03:40:21.466001Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.522029Z","title":"Cambridge University Press, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.522029Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:4a41ad372420e111bfbfd2d2385d8917856b1d2520690b586f2cf57a4a1fb53d","observation_id":"03e38489-70b3-4268-a661-0990993e5a2c","resolution":{"observed_at":"2026-08-02T03:40:21.522029Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.22646","last_updated":"2025-05-28T17:56:53Z","snapshot_observed_at":"2026-08-08T08:37:13.225473Z","submitted_at":"2025-05-28T17:56:53Z","title":"Path-Dependent SDEs: Solutions and Parameter Estimation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.22646","snapshot_observed_at":"2026-08-02T03:40:21.607130Z","title":"Path-dependent SDEs: solutions and parameter estimation.arXiv preprint arXiv:2505.22646, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.607130Z"},"links":{"cited_paper":"/paper/2505.22646","citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:09f126fb74671c21bf58d3be2444c7cac2dfc06c67a07938ff3805583adc90d4","observation_id":"90e32072-6a4e-4c83-bc3f-f7126d44eb16","resolution":{"observed_at":"2026-08-02T03:40:21.607130Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.696427Z","title":"Sussmann","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.696427Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:c4fe428c83640b84833032ab67b9d5a3e749d7a416d8cfbbca9d7c877b21d17d","observation_id":"190c77df-45ba-4d63-8903-0ddaae462f6e","resolution":{"observed_at":"2026-08-02T03:40:21.696427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.762700Z","title":"Sutton and Andrew G","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.762700Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:56563f90b390ec584a690729018dbd5f24ec200e0cc70639f69c4643a316f7b4","observation_id":"0028be5f-be89-45a3-a007-badc6e624c3c","resolution":{"observed_at":"2026-08-02T03:40:21.762700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.858095Z","title":"Cambridge University Press, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.858095Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:69a3eb1f6d230ffd6b78938b34e9f446726949f3ec37a0fa94ff49f7225ef14e","observation_id":"d35c8a3d-b6f9-4397-86b4-88c94f8dc90b","resolution":{"observed_at":"2026-08-02T03:40:21.858095Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:21.951225Z","title":"Sulle equazioni integro-differenziali della theoria dell’elasticit` a.Atti Reale Accad","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:21.951225Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:ae7ee87bf3667630774cd9567ac1d46b583ad1ee17db0f63c29f18c4de3a3478","observation_id":"3fa41243-5ff4-404f-ad25-318569fde2d9","resolution":{"observed_at":"2026-08-02T03:40:21.951225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:22.021303Z","title":"Gauthier-Villars, 1913","venue":null,"work_id":null,"year":1910},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:22.021303Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:2a87cef5ba76d09352311666787411032e7209b96e52b00a30c1a19ab275e070","observation_id":"b745219a-cb40-44a2-908b-20afffd2a0b5","resolution":{"observed_at":"2026-08-02T03:40:22.021303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:22.120634Z","title":"Sur la th´ eorie math´ ematique des ph´ enom` enes h´ er´ editaires.Journal de math´ ematiques pures et appliqu´ ees, 7:249–298, 1928","venue":null,"work_id":null,"year":1928},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:22.120634Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:9854ea771cd18127f21bd7c0224fe031121a415bcf2e32f661be153e081badae","observation_id":"8b85650a-da76-430c-9c1f-f7afd2929d93","resolution":{"observed_at":"2026-08-02T03:40:22.120634Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T03:40:22.217092Z","title":"Log neural controlled differential equations: The Lie brackets make a difference","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-02T03:40:22.217092Z"},"links":{"citing_paper":"/paper/2607.13886"},"observation_digest":"sha256:09fc1f0922f234b40de9032bc8e100acb06f8ca6fe91a2c1f7b4e959a5ea3469","observation_id":"1ebbf110-0983-4a21-8894-d8f7a6882994","resolution":{"observed_at":"2026-08-02T03:40:22.217092Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.13886","last_updated":"2026-07-15T14:34:08Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-02T03:40:09.290443Z","submitted_at":"2026-07-15T14:34:08Z","title":"Dynamic Universal Approximation via Signature Controlled Differential Equations"},"reference_resolution":{"displayed":97,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":97,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":97},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 97 of 97 outbound references and 0 inbound Pith citation observations for arXiv:2607.13886."}