{"as_of":"2026-08-23T08:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:29ecea6f8b6567a97348aa204a4cbceded3a808d21175da78173fea32fb25d98","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T22:33:37.525234Z","state":"measured"},{"denominator":53,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":53,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T03:26:57.925455Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-29T10:03:17.221053Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.07221","snapshot_observed_at":"2026-08-03T03:26:57.925455Z","title":"Hirose, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.08176","last_updated":"2026-07-13T07:43:39Z","snapshot_observed_at":"2026-08-23T07:10:05.649051Z","submitted_at":"2026-02-09T00:37:22Z","title":"Relations and Derivatives of Multiple Eisenstein Series","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T03:26:57.925455Z"},"links":{"cited_paper":"/paper/2505.07221","citing_paper":"/paper/2602.08176"},"observation_digest":"sha256:a063fe3a96638ff7d6be27a6dee0761db477d5a182f7c1a0038f8a2267a35ef4","observation_id":"9959a4ec-df89-45ed-8be1-d32ae7315298","resolution":{"observed_at":"2026-08-03T03:26:57.925455Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"cited_work":{"arxiv_id":"2505.07221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.07221","snapshot_observed_at":"2026-06-29T10:03:17.221053Z","title":"Hirose, T","venue":null,"work_id":"6e9a649e-5841-44ee-8dca-03e9bb24179f","year":2025},"citing_paper":{"arxiv_id":"2604.25451","last_updated":"2026-04-28T10:00:16Z","snapshot_observed_at":"2026-08-05T20:10:17.818345Z","submitted_at":"2026-04-28T10:00:16Z","title":"The threshold for linear independence of multiple zeta values in positive characteristic","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-07T14:53:13.577674Z"},"links":{"cited_paper":"/paper/2505.07221","citing_paper":"/paper/2604.25451"},"observation_digest":"sha256:cde58143f713ef5888f0f7f8e8c67800c9a988b89b68efb07456d22571e498fa","observation_id":"999feb79-9779-428b-96bb-51a58682b088","resolution":{"observed_at":"2026-05-12T00:36:17.358176Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"cited_work":{"arxiv_id":"2505.07221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.07221","snapshot_observed_at":"2026-06-29T10:03:17.221053Z","title":"Hirose, T","venue":null,"work_id":"6e9a649e-5841-44ee-8dca-03e9bb24179f","year":2025},"citing_paper":{"arxiv_id":"2605.28584","last_updated":"2026-05-27T15:06:48Z","snapshot_observed_at":"2026-08-15T02:35:25.228113Z","submitted_at":"2026-05-27T15:06:48Z","title":"A unified proof of conjectures on the spaces of multiple $q$-zeta values","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-29T09:56:27.021374Z"},"links":{"cited_paper":"/paper/2505.07221","citing_paper":"/paper/2605.28584"},"observation_digest":"sha256:d03b29565bd513fdd5fb5e223d3c39a399e3ee32eaaf32a7558cc398addac986","observation_id":"d5eea9ef-ef6f-4f0c-94aa-2e6a1bbabb67","resolution":{"observed_at":"2026-06-29T10:03:17.222773Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.07221/citation-record","integrity":"/paper/2505.07221/integrity","json":"/paper/2505.07221/citation-record.json","paper":"/paper/2505.07221"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:39.068875Z","title":"Bachmann, T","venue":null,"work_id":"6b10e57e-913a-4cfb-9dc1-12e30cb2456a","year":2020},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.334364Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:712a4ace1ffb413be2027708228087f28e948e07dfda0941cf744fb61b684982","observation_id":"ced02da8-69f9-4da3-9796-071f2e32ae18","resolution":{"observed_at":"2026-08-15T22:33:39.072284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:39.058729Z","title":"Brindle,A unified approach toqMZVs, INTEGERS24(2024), Paper No","venue":null,"work_id":"9c8671b3-0ccb-48de-994d-0fb5b728d9f6","year":2024},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.398250Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:eb761f6b8444eb53072ae0880394cf8a817f1f5bba9273209923991e372e692a","observation_id":"a769a5f8-0c84-49b5-933a-0406d51bb878","resolution":{"observed_at":"2026-08-15T22:33:39.062522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:39.014416Z","title":null,"venue":null,"work_id":"573c0246-36eb-411c-9a72-4dccaac780af","year":2006},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.402858Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:408e89cd88eddc4e5dfb0a29b03ceb2a9e1a76ae00b1cb9268b8064a29133ca2","observation_id":"d053ae0e-a2d4-4577-8a8d-d57c89031e9f","resolution":{"observed_at":"2026-08-15T22:33:39.049018Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.920119Z","title":null,"venue":null,"work_id":"adbb8186-1a8f-4ce5-9c7b-78ae4594271f","year":2009},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.406649Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:54e54ad1ca3eefb7c906e84013e0d40d41a0f96248f1d6625453243ed93d00de","observation_id":"5f5164a7-d609-4f70-b39e-c937a0766973","resolution":{"observed_at":"2026-08-15T22:33:38.969446Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.885810Z","title":null,"venue":null,"work_id":"5ee39292-8ad2-4856-8150-118f0cd7d758","year":2012},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.410625Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:5601d9d824ad4ab74173437bcfa3fb41523bc6b511c77eacb1ccacaceae0f05c","observation_id":"b66351c6-038f-4633-b13a-efc2f28b7cb6","resolution":{"observed_at":"2026-08-15T22:33:38.889133Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.876145Z","title":null,"venue":null,"work_id":"0902d1ae-16ad-4b50-ad9d-68a4f30baa38","year":2012},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.414132Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:82af89f1419bae96d3c470b3873a49a1cbf509bd8e8f5c0debe1f18b557b6c55","observation_id":"4529755e-aa23-4a4f-a391-2af2a7fef3cc","resolution":{"observed_at":"2026-08-15T22:33:38.879663Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.866699Z","title":"Chang, Y.-T","venue":null,"work_id":"79e38e20-efec-470c-9ab9-a9b37b9f492a","year":2023},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.418190Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:4e3d056ac9e7028f67fe7c9012b9098561667507cd2b3b6e1c2ce940fdf74ed9","observation_id":"432f34a0-d72b-4c38-a97c-fb8644aa2172","resolution":{"observed_at":"2026-08-15T22:33:38.869943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.857021Z","title":"Deligne,Le groupe fondamental unipotent motivique deG m−µ N, pourN= 2,3,4,6ou8, Publ","venue":null,"work_id":"a42bed80-5e29-48e8-963c-cbb136811fe5","year":2010},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.421217Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:0cfc214590ee08025603e129dfa2675544a0b284f844cdb65036cc24c34640f0","observation_id":"3c99cd2e-62bb-45d9-8f28-8432ae90b32a","resolution":{"observed_at":"2026-08-15T22:33:38.860520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.847215Z","title":"Deligne, A","venue":null,"work_id":"9aaf018f-37a1-4e6b-a54c-e130c0e1fad3","year":2005},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.424629Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:12fe3c616111c65b4f7f47ff1699d0efff72cab8bcfe9570352b2455c40ae9ae","observation_id":"360da36f-54ff-4cf5-bf31-5701e491517e","resolution":{"observed_at":"2026-08-15T22:33:38.851011Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.807813Z","title":"Ecalle,The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducibles, With computational assistance from S","venue":null,"work_id":"be0ddd57-e5ff-4e8d-aad2-0751d4045bd9","year":2011},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.459056Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:684ea9096b0ac96b9cb2981a5b12b9ae4932cfc779b4063c1f51f91c9d1af621","observation_id":"48661e35-7236-49a2-9993-715875ec40a7","resolution":{"observed_at":"2026-08-15T22:33:38.840810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.736614Z","title":"Furusho,Double shuffle relation for associators, Ann","venue":null,"work_id":"4f66fb0c-217b-46d3-9abf-e513ffa4f676","year":2011},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.531081Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:c49d0fa9876aac62e0a9ee8a31a5b7e5b237824bf4a3c00be068569f1bca4baa","observation_id":"d6f2cb8c-245f-4ecc-887d-b65a5e49db0c","resolution":{"observed_at":"2026-08-15T22:33:38.770718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.673032Z","title":"Furusho,The pentagon equation and the confluence relations, Amer","venue":null,"work_id":"6622b253-1ed6-4e42-93ee-86ea660ca535","year":2022},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.627844Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:798e987e27bdc351768ffa8273011ad51b6703ad162f44fd854a2dbd3eaf35d2","observation_id":"42daff70-2a30-485e-b849-b547b9be2c09","resolution":{"observed_at":"2026-08-15T22:33:38.705095Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1603.05178","last_updated":"2016-03-16T17:01:04Z","snapshot_observed_at":"2026-08-14T22:05:45.270652Z","submitted_at":"2016-03-16T17:01:04Z","title":"Unramified Euler sums and Hoffman $\\star$ basis","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1603.05178","snapshot_observed_at":"2026-08-15T22:33:36.682078Z","title":"Glanois,Unramified Euler sums and Hoffman⋆basis, preprint, arXiv:1603.05178","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.682078Z"},"links":{"cited_paper":"/paper/1603.05178","citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:f2a922d61c79004fbcad5b49363322d33f99975e8369595edcccfe76199aab81","observation_id":"6986a442-2870-453c-b518-612c58fbe358","resolution":{"observed_at":"2026-08-15T22:33:36.682078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.15210","last_updated":"2024-04-23T16:44:46Z","snapshot_observed_at":"2026-08-20T19:11:48.485172Z","submitted_at":"2024-04-23T16:44:46Z","title":"A discretization of the iterated integral expression of the multiple polylogarithm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.15210","snapshot_observed_at":"2026-08-15T22:33:36.686161Z","title":"Hirose, T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.686161Z"},"links":{"cited_paper":"/paper/2404.15210","citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:dc7bb757b73e7ca4ba767b2e0f076b6b7dce8516385772a6ad0e6996bbb97809","observation_id":"e6cce67f-f849-4be1-b49a-b97140a28a0e","resolution":{"observed_at":"2026-08-15T22:33:36.686161Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.664130Z","title":"Hirose, H","venue":null,"work_id":"25db9fb2-dd4f-484e-9b83-1097016c6cc9","year":2021},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.690017Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:f78ff250c0531eda43b5ce631f5f3d593ec65801b09a5d42870f9bc6952729f6","observation_id":"7e4093f9-2a8b-41b6-9613-1b0dd252c4be","resolution":{"observed_at":"2026-08-15T22:33:38.667243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.654760Z","title":"Hirose, H","venue":null,"work_id":"00050bd0-8140-4754-a4a7-f69aa74d72ca","year":2023},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.694267Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:c537adc52541bc2f12e7f258a69f9b8ea882bc2d0c6233c7bc998a20371c912e","observation_id":"f75c8949-9cdd-42f5-a7a1-d4f615118021","resolution":{"observed_at":"2026-08-15T22:33:38.658333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.645250Z","title":"Hirose, N","venue":null,"work_id":"fbdbed5c-183a-4e67-8ab6-1cc3ce858f56","year":2019},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.697604Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:a4d9bd4547bf51dbb1b2ba5a50f2e619da3a2ca169f8d1dd9295663b934ef098","observation_id":"c6f3eb9d-145a-4765-9cd3-b88e277a7973","resolution":{"observed_at":"2026-08-15T22:33:38.648382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.04288","last_updated":"2022-02-10T09:55:32Z","snapshot_observed_at":"2026-08-10T04:04:13.492615Z","submitted_at":"2020-07-08T17:35:10Z","title":"The motivic Galois group of mixed Tate motives over $\\mathbb{Z}[1/2]$ and its action on the fundamental group of $\\mathbb{P}^{1}\\setminus\\{0,\\pm1,\\infty\\}$","version":2},"cited_work":{"arxiv_id":"2007.04288","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.04288","snapshot_observed_at":"2026-08-15T22:33:37.579469Z","title":"The motivic Galois group of mixed Tate motives over $\\mathbb{Z}[1/2]$ and its action on the fundamental group of $\\mathbb{P}^{1}\\setminus\\{0,\\pm1,\\infty\\}$","venue":"math.NT","work_id":"37b844ee-ec44-4959-b925-7c103aabd5cf","year":2020},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.700952Z"},"links":{"cited_paper":"/paper/2007.04288","citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:3fa5e79952b0b10d279ca3d9d32c09c7e5592eacac68a82408f3cd9694563006","observation_id":"76cc63ba-070a-47d8-b000-c2d1f40a56fb","resolution":{"observed_at":"2026-08-15T22:33:37.623569Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.03458","last_updated":"2022-06-07T17:24:27Z","snapshot_observed_at":"2026-08-16T16:54:40.135515Z","submitted_at":"2022-06-07T17:24:27Z","title":"Block shuffle identities for multiple zeta values","version":1},"cited_work":{"arxiv_id":"2206.03458","doi":null,"metadata_source":"pith","pith_arxiv_id":"2206.03458","snapshot_observed_at":"2026-08-15T22:33:37.564213Z","title":"Block shuffle identities for multiple zeta values","venue":"math.NT","work_id":"ca509323-41aa-489c-9abb-fe2f8c59cfa9","year":2022},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.704734Z"},"links":{"cited_paper":"/paper/2206.03458","citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:496fac408c6c113523743d438df1e27a17957a5f5dcf2ff70ff4f74fa88d3170","observation_id":"4ae01cb3-5e5b-4b38-b95f-ab91ced5fcdc","resolution":{"observed_at":"2026-08-15T22:33:37.569254Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.635813Z","title":null,"venue":null,"work_id":"71bc19b9-fc4c-40fe-b48f-9f8f1c281358","year":1997},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.708621Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:92253d8f7690f82a5b86cb219d609f92ab609cf3950c479c0fcfa0228e60f986","observation_id":"d9aefe60-91c0-4950-be71-a68819072488","resolution":{"observed_at":"2026-08-15T22:33:38.639086Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.626380Z","title":null,"venue":null,"work_id":"e234fe92-dd03-4fa9-bcb4-ba7c8d005001","year":2015},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.712251Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:535d12d5d144aa74b978313adf6ff8f7331945efbf463532156f3b2487b5519f","observation_id":"a3def2af-168d-4856-846b-cbed22fc6def","resolution":{"observed_at":"2026-08-15T22:33:38.629587Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.617057Z","title":"Hoffman, Y","venue":null,"work_id":"e3cafd41-318f-4e23-81db-cc810c81b8a3","year":2003},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.715660Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:d3350a24c4e189292e30b7bd6a2d3b61c134810f7c4cd3e30bc4b97d9e16d730","observation_id":"c2719b31-dfe0-4e56-a625-7d841b1b5e1b","resolution":{"observed_at":"2026-08-15T22:33:38.620340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.607688Z","title":"Ihara, J","venue":null,"work_id":"2b0149bb-19c4-4066-b299-2ba419046288","year":2011},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.733024Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:00a9749f0f4326d440d662d71ed59bbbd97789b9e80ab5d579d0c2aea2ff3bb9","observation_id":"10754d7c-40ec-4616-adb9-39d3424e79cb","resolution":{"observed_at":"2026-08-15T22:33:38.611218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.598192Z","title":"Ihara, M","venue":null,"work_id":"3403627f-b854-404f-bbcc-ecfd8139f1c9","year":2006},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.800020Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:b82609d770629debdeb8e6bf0eb54d6e5bb23cb0aabbfc6fe03c22a552097e67","observation_id":"65f3cd95-a5d4-4c33-bdd1-6f786b18ec73","resolution":{"observed_at":"2026-08-15T22:33:38.601335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.494443Z","title":null,"venue":null,"work_id":"8bc53b83-6c06-4a08-b4d6-50d8864a67ae","year":2024},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.865652Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:a39b5459c81532a98da6ece7ed84ac199d8dc20fdb20d20d30db9711b2b57307","observation_id":"b5fdd153-e8a1-42be-9eb2-ad97fbd071ce","resolution":{"observed_at":"2026-08-15T22:33:38.562204Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.424842Z","title":"Kaneko, M","venue":null,"work_id":"f062993f-f14d-4131-a171-23bd2ff1572f","year":2016},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.959804Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:0f2e051057fb156a8e6459b6805c71247d20d0a55ca6ac960590f837679d2fc3","observation_id":"93f33b82-9a4a-4229-be47-378666eeddc6","resolution":{"observed_at":"2026-08-15T22:33:38.466189Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.379159Z","title":"Kaneko, C","venue":null,"work_id":"a53a2e10-d533-458d-99c3-66211ffdb475","year":2021},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.963832Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:8f1e3c0733de31a86585ec3240b0731b3f36861b77b0a8a173fdaa9889930293","observation_id":"89c5f865-15bf-483d-8fa8-a959ea832a2e","resolution":{"observed_at":"2026-08-15T22:33:38.382369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.369931Z","title":"Kaneko, S","venue":null,"work_id":"9106dc8e-e80f-494d-8566-9928bab1c631","year":2018},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.966597Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:1b94fb4695df213fb371150b6fb6e202afa95eef6d69ff0b3b1086aa5119acba","observation_id":"43dce2cc-08e0-4482-8a13-2b83a4322f60","resolution":{"observed_at":"2026-08-15T22:33:38.373020Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.359208Z","title":"Kawashima,A class of relations among multiple zeta values, J","venue":null,"work_id":"6506e990-6600-4b03-98eb-db169b7e4c13","year":2009},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.970211Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:078e008131eadc95c3094deb2d2336a01e020a960615d17114c35b91bf55d0a3","observation_id":"d3db6956-77d9-4fb3-8450-1be04cb139a0","resolution":{"observed_at":"2026-08-15T22:33:38.362426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.350244Z","title":"Kimura,Intersection of duality and derivation relations for multiple zeta values, J","venue":null,"work_id":"97e9e677-6219-4a49-af7d-07d1ef74da39","year":2024},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.973554Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:8dcae01a95b764fd31a5c30ba2704101d484d24b11421298dfd49ed489ce9d63","observation_id":"bc8b14f2-7613-46ed-8964-8d6bec597d45","resolution":{"observed_at":"2026-08-15T22:33:38.353236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.339848Z","title":"Linebarger, J","venue":null,"work_id":"1bd9da56-02eb-40e7-a943-289798979abb","year":2015},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.976797Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:1ab5f5d1ee811005647be5471ac981160c60f46bea7eebc4003d1a9592137bba","observation_id":"d5bdea6f-5c39-4ed3-a5f0-9560d3ff0930","resolution":{"observed_at":"2026-08-15T22:33:38.343619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.05730","last_updated":"2024-02-29T11:26:09Z","snapshot_observed_at":"2026-08-22T02:25:36.674570Z","submitted_at":"2024-02-08T15:05:49Z","title":"Deriving two dualities simultaneously from a family of identities for multiple harmonic sums","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.05730","snapshot_observed_at":"2026-08-15T22:33:36.979601Z","title":"Maesaka, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.979601Z"},"links":{"cited_paper":"/paper/2402.05730","citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:981f4005570a994e89303f82ba3b29b67f5ac834bab4c6c6f4c9e2711b29a83a","observation_id":"f9c941ca-766b-4585-80d8-637339ac73ff","resolution":{"observed_at":"2026-08-15T22:33:36.979601Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.263047Z","title":"Murahara, M","venue":null,"work_id":"43735e31-8724-4422-9a26-2efb1f2133c4","year":2018},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.983340Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:d2ddcd7983af75e98b07ff823838092417e06f3bbb7616fb0b72b710d57672a7","observation_id":"30644154-3217-409f-91bb-29846f5078e9","resolution":{"observed_at":"2026-08-15T22:33:38.324553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.118874Z","title":"Ngo Dac,On Zagier–Hoffman’s conjectures in positive characteristic, Ann","venue":null,"work_id":"9845c590-f6b3-4922-8d43-45008437f131","year":2021},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.986870Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:ce06327b2cc597244d358ec41d9c839ccc71806422429ecb43c0aba0b85d05d7","observation_id":"5e279bef-dd6b-4da3-8792-40629d1c44a9","resolution":{"observed_at":"2026-08-15T22:33:38.192473Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.108381Z","title":"Ohno,A generalization of the duality and sum formulas on the multiple zeta values, J","venue":null,"work_id":"ef4f4dd7-5ff0-4146-86fd-165f06e89576","year":1999},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.990997Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:2a8d66b375a9f0d90bc0fc4b6d0c656c4db74ed585f617f203dda8081be23b91","observation_id":"9a26a036-dbf0-4dcc-9db5-957d32b27977","resolution":{"observed_at":"2026-08-15T22:33:38.112853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.099124Z","title":"Seki,Connectors, RIMS Kˆ okyˆ uroku2160(2020), 15–27","venue":null,"work_id":"84afc77a-4333-4d10-8ac7-1b97ada5ff75","year":2020},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.994952Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:63190cb57e5083b768f9b9e2e207108deef951b81bcc6c38899e6e13c87c3d09","observation_id":"4b4ba904-093c-47e4-939f-5b5dc13bf00c","resolution":{"observed_at":"2026-08-15T22:33:38.102145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.089986Z","title":"Seki,A proof of the extended double shuffle relation without using integrals, Kyushu J","venue":null,"work_id":"0b561123-d966-4c47-86e4-bf2ea73fd666","year":2025},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:36.997711Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:ad22e87f4c1c854e3aa2b7cfa1b26caa62857f85303c99fc36bf3b83a062e9f7","observation_id":"2b4836fe-1f28-4dda-a477-5a45b7670941","resolution":{"observed_at":"2026-08-15T22:33:38.092881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.080121Z","title":null,"venue":null,"work_id":"8ee6e3ab-a768-4673-a972-dbdcd31d2cb9","year":2019},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.053972Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:fe307e39a9f8a972a29cc38e95b2af7d7a6f1953f2fd3397292b12ebb9f00454","observation_id":"32d7c4a6-1e3b-4205-add6-6fd027904a86","resolution":{"observed_at":"2026-08-15T22:33:38.083431Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.071393Z","title":null,"venue":null,"work_id":"9aa5ff93-d330-4243-b28c-26b3d8c07cfe","year":2020},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.142498Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:0bf0ea063613d9c0d933414f092dc3420c9bf92ac0b1876f69f4c636bba8ae17","observation_id":"afb8fab8-ff67-4bf8-9344-4844681cfc25","resolution":{"observed_at":"2026-08-15T22:33:38.074152Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.061637Z","title":null,"venue":null,"work_id":"49b030a2-c911-49b7-b2b4-adac6b4cee65","year":null},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.238218Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:839f262c36e6837edca098be83a6aa58208f05b9f7714a93571fca8f1a0edef9","observation_id":"18aa897c-de05-48f3-941a-38c97fb51377","resolution":{"observed_at":"2026-08-15T22:33:38.065237Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:38.029213Z","title":"Tanaka,On the quasi-derivation relation for multiple zeta values, J","venue":null,"work_id":"c5e3ee3d-0c1e-455f-aea6-7d67575ceada","year":2009},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.295316Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:475b7a814f00573bee964d5751e62c27ce06becf42c73f3b231640f778a15a76","observation_id":"873bc82b-5a0e-4cfa-b68c-e984cb8fc101","resolution":{"observed_at":"2026-08-15T22:33:38.054534Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.896029Z","title":"Tanaka, N","venue":null,"work_id":"75359eec-0f78-404a-96ba-c4465e001627","year":2010},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.376220Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:bfc25617cf36706de54059a2332e55c8068218b8bd1410dcd7add16453ae41e5","observation_id":"289ff08c-5b0c-41ce-b430-75be90321c1e","resolution":{"observed_at":"2026-08-15T22:33:37.956900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.876311Z","title":"Terasoma,Mixed Tate motives and multiple zeta values, Invent","venue":null,"work_id":"bdcabbeb-2d9c-43ac-87ab-6aea94d1108d","year":2002},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.485991Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:bd596101a32eb71a5d1675977c26276f5c159d92a61229ecece61e9f033fd1f4","observation_id":"608a6cda-cc20-4733-9c84-71667201df2e","resolution":{"observed_at":"2026-08-15T22:33:37.879596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.866889Z","title":null,"venue":null,"work_id":"a6353684-6b05-458e-8502-a2535f837d67","year":2017},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.504432Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:cb616e232884033960e667f436132b9798a629f2e8e78535281ec756599434cd","observation_id":"94176b8f-bc8a-487d-b77e-4f2b98e037c1","resolution":{"observed_at":"2026-08-15T22:33:37.869928Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.856700Z","title":"Todd,A conjectural characterization forF q(t)-linear relations between multizeta values, J","venue":null,"work_id":"feb55d68-b9e3-41f4-85a2-84f244276d4a","year":2018},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.507404Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:6030eb31ad402b3261991171b12832c3ff5279606f3ee9fa9e37a266fc847deb","observation_id":"0762accc-6c6e-461b-88cb-e959175b9620","resolution":{"observed_at":"2026-08-15T22:33:37.860332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.845467Z","title":"Yamamoto,Explicit evaluation of certain sums of multiple zeta-star values, Funct","venue":null,"work_id":"56d4e846-c979-4261-b23c-887df38c29dc","year":2013},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.510870Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:bd2f0d0370fd35c12a07a29ac3c32d1f0978cd4de8f76421ff4fdf35e86166d4","observation_id":"9950d66c-579f-4637-b7a1-ce11d21c6db5","resolution":{"observed_at":"2026-08-15T22:33:37.849272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.835545Z","title":"Yamamoto,Interpolation of multiple zeta and zeta-star values, J","venue":null,"work_id":"e79e15f6-54f3-4f3f-8f88-726fdf638f63","year":2013},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.514058Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:336be8dfb63088783d3d2e63c23b7bba06b3826ee1ce87eafe3c0ac512ee9d93","observation_id":"1f597b61-4c03-4bb5-9643-601dcc04ba9b","resolution":{"observed_at":"2026-08-15T22:33:37.839204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.825155Z","title":"Yamamoto,A note on Kawashima functions, Publ","venue":null,"work_id":"cc6ffed9-6b28-4fa8-ac5d-5014ff9e8e83","year":2019},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.517302Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:773e9e36d33bbfeb55f3641c5e22f625ece07359fd1c905944ba6507d23e7b6f","observation_id":"db350135-1288-48f2-8b27-e96ada271e43","resolution":{"observed_at":"2026-08-15T22:33:37.828410Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.813580Z","title":null,"venue":null,"work_id":"62cdc374-852f-44ef-81f2-e3a3810c872f","year":1992},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.521664Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:411ae0dda0698e221b83d592c734095a73758220c022de3aa02a8d37fac4d034","observation_id":"bc4bb50c-79f7-4953-9029-79b79dde4e69","resolution":{"observed_at":"2026-08-15T22:33:37.817807Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T22:33:37.728418Z","title":null,"venue":null,"work_id":"2b63e6f3-77e3-4e4b-9e04-947ff8da5677","year":2012},"citing_paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-15T22:33:37.525234Z"},"links":{"citing_paper":"/paper/2505.07221"},"observation_digest":"sha256:96da3e345aa2ba620cf59ba0a98af7f45d9c1aea8397455c7b2f2bb0e03e6932","observation_id":"59e69041-1a37-4701-a19d-2381871f51ea","resolution":{"observed_at":"2026-08-15T22:33:37.784302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.07221","last_updated":"2025-05-25T15:26:10Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-15T22:19:45.794490Z","submitted_at":"2025-05-12T04:26:07Z","title":"The $\\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":2,"verified_fuzzy":32},"total_outbound_references":50},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 3 inbound Pith citation observations for arXiv:2505.07221."}