{"as_of":"2026-08-05T00:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cda4617b801e69e3f431b365a643c7ca6ef9a047ff0ae36f938eb6b189e687e1","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T04:00:08.473630Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+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/2606.29865/citation-record","integrity":"/paper/2606.29865/integrity","json":"/paper/2606.29865/citation-record.json","paper":"/paper/2606.29865"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T04:00:08.473630Z","title":"Artin: Theorie der z¨ opfe","venue":null,"work_id":null,"year":1926},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:1bfd304d9a8c097e5d1bd4701b6f16cdaeba66247e5dddd09b2fb3e091ba3e46","observation_id":"47be661f-ff59-482d-8075-2720510e6f81","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Artin: Theory of braids","venue":null,"work_id":null,"year":1947},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:00a64843f8f05ee328a15f7164dc1a82ac5f8ec11ac0715196372bfccefed44d","observation_id":"b3cc662b-90ef-48b9-87e3-2806075186a2","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Baez: Link invariants of finite type and perturbation theory","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:e0b322e16d521df28ec847b10c311e41f4240ab8ec5767be99d73ac0c5b96b05","observation_id":"1efdc1ea-bca7-40f1-9022-28c7a7ad0d29","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Bardakov, N","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:2e5281a2060f8d25179e7ac258631046415835ffa3d57fa294c84d0182a5cc40","observation_id":"b61636df-dfe4-4320-a8f7-63bc094d0439","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Birman: New points of view in knot theory","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:eb2be9e311dd9ecf67178bab65982a0d6c929d01840d2e46f3ad057a50395ec4","observation_id":"2fe28cd4-a5f4-4d01-a8c1-5495110bb7bc","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Caprau, A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:9a526d6f8bf29fa34b24ee54b14ad6d9be9eabf8decb0134ec2f3c992b37fe30","observation_id":"96032458-c2a3-42c1-9f4f-bbaba5a7113e","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Caprau, S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:9e738f6a77a7bdca739516b2f2d63c0f20ec9ec016219c2b131d63644650683e","observation_id":"3e2f2a2c-eda7-480e-9fc7-e46c6ff7875a","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Caprau, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:572af2613557eb9154b5977d0462a448a3421800e07c4208c8e859fee0c8d61e","observation_id":"f0e6080e-fa2a-4d7d-a2c8-64e8ea184912","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2601.01707","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-01T15:15:48.050706Z","title":"Caprau and M","venue":null,"work_id":"9de54cbc-a1a3-4e0c-8b7b-e12d6f2a786c","year":2026},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:f9faffea512d3754df0c76bdcc5ad05d94ac8acdc4a0511308d035468a1a4e28","observation_id":"978a21c4-99b3-4cde-a1be-c80317317d94","resolution":{"observed_at":"2026-07-01T15:15:48.052009Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-30T04:00:08.473630Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:2694f919b8c85dceec80a033f134ca75ec8c77932b2d8142330e2f74ca7d275a","observation_id":"55b6108c-dfa6-4a3c-928b-8c2e8b271871","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Khovanov: RealK(π,1) arrangements from finite root systems","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:8fcc263ac9b848edbff507e13da6f486e269f61ab848c57de5fbc3e3963a2ceb","observation_id":"059a86c6-f5d1-4ff9-9c2f-3a9dbb05e742","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Khovanov: Doodle groups","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:2de3adde378d42b6c27c609c8d70c0769fc0bb5bae6ebb470a518043a36d4daa","observation_id":"dea0d3d0-01eb-4225-a1e0-df96636407a8","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2026-06-30T04:00:08.473630Z","title":"Nasser: Local extensions and Φ-type extensions of some local representations of the braid groupB n to the singular braid monoidSM n","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:780a8586d4dd9c9612468c1b15b1b780779babbf2404a63cc88c9f2dca390834","observation_id":"a6a4ee01-a223-4857-ae9f-a472d7372919","resolution":{"observed_at":"2026-06-30T04:00:08.473630Z","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":"2510.04075","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-01T15:15:48.053251Z","title":"Nasser and N","venue":null,"work_id":"9975ea01-d21d-4128-a294-f3bd96508fa1","year":2025},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:c77fe5248084f066f723a4c75c9493b261e48a1d0282cb8701714cde4cef5ef3","observation_id":"978e18bd-1dac-4a40-b952-5782c2cefefd","resolution":{"observed_at":"2026-07-01T15:15:48.054621Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.07863","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-01T15:15:48.055729Z","title":"Nasser, N","venue":null,"work_id":"3d530712-7b1f-44a0-99a4-44357b7c7119","year":2026},"citing_paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-30T04:00:08.473630Z"},"links":{"citing_paper":"/paper/2606.29865"},"observation_digest":"sha256:f4902c74a286ce4421319b015d6a86c6e0b345c1681400212a5281d0809bd829","observation_id":"92ff7cab-0cae-482f-bc2a-a6c06d38e5c9","resolution":{"observed_at":"2026-07-01T15:15:48.057299Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.29865","last_updated":"2026-06-29T06:59:17Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-07-07T00:03:45.783349Z","submitted_at":"2026-06-29T06:59:17Z","title":"On the structure of the singular triplet monoid and its virtual extension"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":15},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2606.29865."}