{"as_of":"2026-08-09T13:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:338e08341c2f5f264894a3fbb30c70758925ac429e72098f2e8c5f7fb80a3909","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T14:42:44.844239Z","state":"measured"},{"denominator":16,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":16,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2606.20473/citation-record","integrity":"/paper/2606.20473/integrity","json":"/paper/2606.20473/citation-record.json","paper":"/paper/2606.20473"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:42:44.844239Z","title":"Aurenhammer, R","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:97619ae5b05a1fe6deab60a0bbdeab3f131921f6eec716bca50db09fb2bd1cae","observation_id":"d7145647-fdee-4e91-9e11-fbb46d348951","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"Manturov,Knot Theory, Second Edition, CRC Press, 2018, 580 pp","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:7e77be7388918cc048cecf6e6ec55b83b399cd524c6d07703efcb71a9e3ce287","observation_id":"94c8af42-1d7b-4293-b4ea-40adedf1896e","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:399d460fe60fedc05051b750cff6c4cd342cc974b0778cc969012c49d40dcd67","observation_id":"bbdae43a-d6b6-471b-81b3-a85a18dc6697","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"слипаться","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:33c700f09ce9d3a43943098f8008645aea8dbc524fc4808d37e3dc724ca1a216","observation_id":"544ac3db-ce8b-491f-8ff9-165bd9d8f657","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:b16563d86b05935a25c6b3b69309001e3a1ff65f55d6bf7e1496586cccd79ba4","observation_id":"e8fff11c-96de-416f-9bbc-c3f60b18f095","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"Из определения триангуляции Делоне следует, что ее внешняя грань не всегда треугольная, поэтому триангуляция Делоне не всегда являет- ся триангуляцией в строгом понимании","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:c9dc024cb1d99ca811a08e2ce49f6ad77417cdf76f90b05fe0c2a486e28bf338","observation_id":"c4836ade-861a-4bcb-be1e-f0e30cbf8780","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"Aurenhammer, R","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:215a106b5b688b322f384a0e88acfae391af8c68fffa57409c47965de4b7ee5d","observation_id":"0b59712f-4a11-403d-a741-12bb0852d6d6","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.02695","last_updated":"2020-12-21T15:04:24Z","snapshot_observed_at":"2026-08-09T10:34:19.632349Z","submitted_at":"2019-12-04T14:54:08Z","title":"Manifolds of Triangulations, braid groups of manifolds and the groups $\\Gamma_{n}^{k}$","version":2},"cited_work":{"arxiv_id":"1912.02695","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1912.02695","snapshot_observed_at":"2026-07-04T06:09:38.103841Z","title":null,"venue":null,"work_id":"6aef3fbc-21fa-4336-b7f0-8fe79914ca99","year":2020},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"cited_paper":"/paper/1912.02695","citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:cccebad1a290968929ac054cd170f915ce0a5e91680bffa4579d862cbd6c596c","observation_id":"46ac4bad-7e24-446a-bbce-cc4f5c7f8885","resolution":{"observed_at":"2026-07-04T06:09:38.105435Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:42:44.844239Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:a704622be4e194db674d3d42552b26929c11a54ea549087d7b33da95fbad20d1","observation_id":"63055dbb-7ec1-42cd-9492-cbdfd15d13a9","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.05146","last_updated":"2025-08-07T08:31:18Z","snapshot_observed_at":"2026-08-05T23:37:06.763669Z","submitted_at":"2025-08-07T08:31:18Z","title":"Liftable braids and the coloured braid groupoid","version":1},"cited_work":{"arxiv_id":"2508.05146","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.05146","snapshot_observed_at":"2026-07-04T06:09:38.101050Z","title":"Licata and V","venue":null,"work_id":"cbd69a38-6829-4f9e-a137-fac0f5599ab9","year":2025},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"cited_paper":"/paper/2508.05146","citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:09b59056743058ba3419964003426c48641d008e784a2c226f99a543a1135f7d","observation_id":"2c469ecf-e614-4b58-82dc-320cadb0f713","resolution":{"observed_at":"2026-07-04T06:09:38.102588Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1501.05208","last_updated":"2015-01-21T15:58:20Z","snapshot_observed_at":"2026-07-06T04:06:50.815584Z","submitted_at":"2015-01-21T15:58:20Z","title":"Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems, Geometry, and Topology","version":1},"cited_work":{"arxiv_id":"1501.05208","doi":null,"metadata_source":"pith","pith_arxiv_id":"1501.05208","snapshot_observed_at":"2026-07-04T06:09:38.098299Z","title":"Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems, Geometry, and Topology","venue":"math.GT","work_id":"b6ba34fd-32f7-4941-9cee-49f892980051","year":2015},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"cited_paper":"/paper/1501.05208","citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:c2a5e1ff2f8dd4d922e00e695827fa29e91086f93f45903b70d70b4dd4a901f3","observation_id":"b352f96d-e1fd-48aa-b44e-2d5b15510f67","resolution":{"observed_at":"2026-07-04T06:09:38.099720Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:42:44.844239Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:8d4719050836d98f627bc7aceb8368b2db4b6121c00b7d75565b3280967da549","observation_id":"d4874383-d8b4-4075-b2a7-c55b83fd79a5","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"Manturov, D","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:bcb0e5c3d32582f25c8f95ac639c2f70571ad92241ee1da21cf5d2066581ea87","observation_id":"663037a8-21f6-4e3b-8c68-a82fcfe75558","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.06316","last_updated":"2023-05-10T17:08:51Z","snapshot_observed_at":"2026-08-03T02:13:10.394243Z","submitted_at":"2023-05-10T17:08:51Z","title":"The groups $\\Gamma_{n}^{4}$, braids, and $3$-manifolds","version":1},"cited_work":{"arxiv_id":"2305.06316","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2305.06316","snapshot_observed_at":"2026-07-04T06:09:38.098054Z","title":null,"venue":null,"work_id":"e0507738-4da4-465c-8a99-f538ee980f11","year":2023},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"cited_paper":"/paper/2305.06316","citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:a48b5e08301c17cfc8e5196a5b3ab0b344e9762ce809dd70dacf8bf43d909083","observation_id":"2e0858d1-15be-4928-a9f1-47bda0129a87","resolution":{"observed_at":"2026-07-04T06:09:38.099849Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:42:44.844239Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:d5cf46d2869113daa44d457a94bc8e2c5042be3a458cf016bba74d3b91c1e94b","observation_id":"154ccb13-bf16-4df0-bb48-4100a681f2a7","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","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":"2026-06-26T14:42:44.844239Z","title":"Ohtsuki,Quantum Invariants: A Study of Knots, 3-Manifolds, and Their Sets, World Scientific Publishing, 2002, 508 pp","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-26T14:42:44.844239Z"},"links":{"citing_paper":"/paper/2606.20473"},"observation_digest":"sha256:e484adae0cb275acb30d8f493d7f0042d5ed52b9a97c111e5089cbd30042d565","observation_id":"e03e08ac-d458-46de-9df0-7bba8d7d07eb","resolution":{"observed_at":"2026-06-26T14:42:44.844239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.20473","last_updated":"2026-06-18T16:52:40Z","latest_version":1,"primary_category":"math.GN","snapshot_observed_at":"2026-08-05T02:27:18.224139Z","submitted_at":"2026-06-18T16:52:40Z","title":"Invariants of the Colored Braid Groupoid"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":4,"verified_fuzzy":0},"total_outbound_references":16},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2606.20473."}