{"as_of":"2026-08-14T02:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5301dcc6dedbce712bf865b0d40290dc94be61db7fdc68ddc30939bd4f2150df","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T06:05:07.708827Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2607.13191/citation-record","integrity":"/paper/2607.13191/integrity","json":"/paper/2607.13191/citation-record.json","paper":"/paper/2607.13191"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T06:05:04.986981Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:04.986981Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:d2036798f89862e3e0beef6823e0e84760abb862aa6075768b71de2bc58631db","observation_id":"5c190eee-4748-4bc8-83a9-92a1c2b73c74","resolution":{"observed_at":"2026-08-02T06:05:04.986981Z","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":"2026-08-02T06:05:05.027375Z","title":"Biamonte, P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.027375Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:b19bdbf79b1e2caf7591d5e608f9c97bf23f2e2ef78b97979231c6d000705f63","observation_id":"c36c14e9-8cb7-4c73-a594-dd7e1b892984","resolution":{"observed_at":"2026-08-02T06:05:05.027375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0610235","last_updated":"2006-10-28T07:29:53Z","snapshot_observed_at":"2026-07-07T07:24:11.364656Z","submitted_at":"2006-10-27T10:44:55Z","title":"BQP-complete Problems Concerning Mixing Properties of Classical Random Walks on Sparse Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0610235","snapshot_observed_at":"2026-08-02T06:05:05.104432Z","title":"Janzing, P","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.104432Z"},"links":{"cited_paper":"/paper/quant-ph/0610235","citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:b9b221f3530323badd97926efeda9fcfc41843a9481c3000fff9ee83a3ddc9fd","observation_id":"19489ba0-d097-4b46-9d07-0c9d0e496ee6","resolution":{"observed_at":"2026-08-02T06:05:05.104432Z","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":"2026-08-02T06:05:05.197335Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.197335Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:4f444b099025d815034e0af1519ffd605a8ebc75f03b5ade37990d7f3889a9ec","observation_id":"7de79ebd-9ae9-4dac-983f-48ea54140bba","resolution":{"observed_at":"2026-08-02T06:05:05.197335Z","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":"2026-08-02T06:05:05.286381Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.286381Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:6a4887104be335136731b384063bd4bf802293e2075b76f497edfe49b71e2c77","observation_id":"6dbac485-a263-4879-b4a8-357aad1b28d8","resolution":{"observed_at":"2026-08-02T06:05:05.286381Z","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":"2026-08-02T06:05:05.454730Z","title":"Alman, V","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.454730Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:8a912f3f0ce94f75cdf9733a96af71a74f4ea7a8f7b3b7190a322f8859f7fc73","observation_id":"ca112c37-1cde-444d-9253-b835b79fa828","resolution":{"observed_at":"2026-08-02T06:05:05.454730Z","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":"2026-08-02T06:05:05.573823Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.573823Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:3dadaa561cc5590d8efd20d47d1dd79ee5b6b92052afc99d61360ed4654f41dc","observation_id":"ae8777d0-9f20-47eb-8472-81f637573112","resolution":{"observed_at":"2026-08-02T06:05:05.573823Z","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":"2026-08-02T06:05:05.657439Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.657439Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:74f4592638f987061eac588c89149ebc73ee4bf1ca1985a8348137e454471591","observation_id":"790bc4ff-7ecc-49a4-93b6-6219d256b2ab","resolution":{"observed_at":"2026-08-02T06:05:05.657439Z","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":"2026-08-02T06:05:05.787019Z","title":"Wossnig, Z","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.787019Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:fb2addb383a849460dcf51dab37aa15b5259d08e98477172a6e63ea1e1a8c29b","observation_id":"906b8a01-bfd9-4230-a31c-a1a31f215c39","resolution":{"observed_at":"2026-08-02T06:05:05.787019Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-02T06:05:05.911496Z","title":"Chakraborty, A","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:05.911496Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:71892d2db0049b0bafe26aee5b78117a73e13fa5c985d80466f98056339ee332","observation_id":"f5f4b329-6264-4a39-a2ff-48e4ea50bea8","resolution":{"observed_at":"2026-08-02T06:05:05.911496Z","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":"2026-08-02T06:05:06.034744Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.034744Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:5b1305604f5978ee1a96da2562beea9be7799ed9935d40f3ab9e87fa956e4894","observation_id":"65351a2c-361b-4dab-a666-4d0d6d75f6a1","resolution":{"observed_at":"2026-08-02T06:05:06.034744Z","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":"2026-08-02T06:05:06.145698Z","title":"Li, P.-L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.145698Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:b2b1068cb80644a32cb834bcc0768287958fd96cbbdd1eee1f00d991c19621ad","observation_id":"4bfd50f4-6de3-4132-8b93-8dccd54f6774","resolution":{"observed_at":"2026-08-02T06:05:06.145698Z","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":"2026-08-02T06:05:06.251541Z","title":"Gilyén, Y","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.251541Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:8bf1b63175137cd935e39ab2a238042e9324d1409ff0e05efc5a2d1f86f1300f","observation_id":"9743deee-8a74-4977-9bdb-b42ead64cdde","resolution":{"observed_at":"2026-08-02T06:05:06.251541Z","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":"2026-08-02T06:05:06.350440Z","title":"Montanaro, C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.350440Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:c789a53e3adee788341c15b235f25d697124aa264e21e9a2000c507820e3ca69","observation_id":"ae779e5e-67c2-47a7-9d6b-f999d3010879","resolution":{"observed_at":"2026-08-02T06:05:06.350440Z","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":"2026-08-02T06:05:06.421344Z","title":"Bernasconi, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.421344Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:6f84acda06dc0198745890816db75391cfeab1b2a968a3c62367faf01ebebbea","observation_id":"a607d93b-74d2-4473-8055-b8cf47ff1f1b","resolution":{"observed_at":"2026-08-02T06:05:06.421344Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-02T06:05:06.514621Z","title":"Giovannetti, S","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.514621Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:32a2030218b1b80ad5696c1b1de06d6b6a254a8f1b5a97b02023b4db3a3978cb","observation_id":"df0606b3-3306-40d5-b428-f8decc490449","resolution":{"observed_at":"2026-08-02T06:05:06.514621Z","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":"2026-08-02T06:05:06.611949Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.611949Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:758217a92298a2fe04eeecde802e7152cbb1b3836d5111228302e7339807a9fc","observation_id":"5c6e638e-5451-48be-a56a-72a4e1d1cd26","resolution":{"observed_at":"2026-08-02T06:05:06.611949Z","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":"2026-08-02T06:05:06.707457Z","title":"Antonioli, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.707457Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:ecb3f0be78eb05007ecdeb22407dcf8e1bf411877b7873e7ec8ded09e64f834b","observation_id":"e56a471b-189f-438f-8a99-2376b77f006e","resolution":{"observed_at":"2026-08-02T06:05:06.707457Z","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":"2026-08-02T06:05:06.834609Z","title":"Bernasconi, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.834609Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:99e00c170d0335ee240371cf5b8fad66a5ec48abd8b0dc53a2276a19c2f39afc","observation_id":"e32b36a7-e6b7-493b-a006-504f8a8ce137","resolution":{"observed_at":"2026-08-02T06:05:06.834609Z","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":"2026-08-02T06:05:06.919348Z","title":"Poggiali, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:06.919348Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:d1daac81e5d39867b68fd95e7a51df255cc487da01dad27a85bc64d95e588970","observation_id":"335c1dac-4027-4e6f-95f0-df6fbae66a06","resolution":{"observed_at":"2026-08-02T06:05:06.919348Z","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":"2026-08-02T06:05:07.015072Z","title":"Poggiali, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.015072Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:adb0b5901c2cfdff2c92302df241a2022626c77143525629f5c747dc860d1c49","observation_id":"ab8551ab-5ed4-435a-ba25-98dbb5d5ad4b","resolution":{"observed_at":"2026-08-02T06:05:07.015072Z","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":"2026-08-02T06:05:07.123943Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.123943Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:043d2abf3d89d958357fc094f7f23e7a7a73b336a02122dee16869eb52b1491b","observation_id":"e110b0e5-7340-49ee-9cf8-a498697e5556","resolution":{"observed_at":"2026-08-02T06:05:07.123943Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.08810","last_updated":"2024-06-19T01:39:44Z","snapshot_observed_at":"2026-08-13T08:14:01.293513Z","submitted_at":"2024-05-14T17:55:32Z","title":"Quantum computing with Qiskit","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.08810","snapshot_observed_at":"2026-08-02T06:05:07.176216Z","title":"Javadi-Abhari, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.176216Z"},"links":{"cited_paper":"/paper/2405.08810","citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:4c719c6e2c77e895ab2bb130192a5611fcea59defb750d8370f927cdff8bd25e","observation_id":"6740a12d-9133-4d99-86e0-03493e62af6a","resolution":{"observed_at":"2026-08-02T06:05:07.176216Z","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":"2026-08-02T06:05:07.261063Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.261063Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:562e2d697cc8da2f2d00795c2d4e7013717ee6a256e320e2d8d09bf84c156923","observation_id":"368f75b7-ff20-466f-ba28-f9ebed7b1740","resolution":{"observed_at":"2026-08-02T06:05:07.261063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.16149","last_updated":"2026-04-09T07:36:43Z","snapshot_observed_at":"2026-08-12T16:32:13.047537Z","submitted_at":"2025-10-17T18:50:07Z","title":"Efficient Quantum State Preparation with Bucket Brigade QRAM","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.16149","snapshot_observed_at":"2026-08-02T06:05:07.351794Z","title":"Berti, F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.351794Z"},"links":{"cited_paper":"/paper/2510.16149","citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:c3bb4b3670896cf2b3e27783b729ed1e2ba02f5fd3a8b90640bdf44dbbbdb879","observation_id":"c52e3734-aeb4-4874-bd6c-926862a58962","resolution":{"observed_at":"2026-08-02T06:05:07.351794Z","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":"2026-08-02T06:05:07.424427Z","title":"Kerenidis, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.424427Z"},"links":{"citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:7488fe34cdfee7405a2d0d04157fa95fb6562832ff07cf96a55f17be27bfa516","observation_id":"a13e5d14-1e0c-4a0a-b1dd-411b066750e3","resolution":{"observed_at":"2026-08-02T06:05:07.424427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0005055","last_updated":"2000-05-15T18:19:59Z","snapshot_observed_at":"2026-07-07T07:03:25.387553Z","submitted_at":"2000-05-15T18:19:59Z","title":"Quantum Amplitude Amplification and Estimation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0005055","snapshot_observed_at":"2026-08-02T06:05:07.567967Z","title":"Brassard, P","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.567967Z"},"links":{"cited_paper":"/paper/quant-ph/0005055","citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:965cfa369fd253b04778cb5a0d44d92ad8b21d0e852d02913feb0813454e7cac","observation_id":"fdef4928-26c2-4b3e-9d26-cd275cd7fa9c","resolution":{"observed_at":"2026-08-02T06:05:07.567967Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1706.09279","last_updated":"2017-06-28T13:27:00Z","snapshot_observed_at":"2026-07-06T05:48:51.172872Z","submitted_at":"2017-06-28T13:27:00Z","title":"The Quantum Complexity of Computing Schatten $p$-norms","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1706.09279","snapshot_observed_at":"2026-08-02T06:05:07.708827Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T06:05:07.708827Z"},"links":{"cited_paper":"/paper/1706.09279","citing_paper":"/paper/2607.13191"},"observation_digest":"sha256:505c034268d8cc0adf000687bb5a46c30738a2da14867b2a069c7870d1af6475","observation_id":"34bea48c-1367-4b42-a90b-2edb5e9b0390","resolution":{"observed_at":"2026-08-02T06:05:07.708827Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.13191","last_updated":"2026-07-14T18:42:40Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-09T04:33:41.219801Z","submitted_at":"2026-07-14T18:42:40Z","title":"Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":28},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.13191."}