{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XYTA2ATI5EVLCLS2MTAEFFTUXD","short_pith_number":"pith:XYTA2ATI","schema_version":"1.0","canonical_sha256":"be260d0268e92ab12e5a64c0429674b8daedf48a960f1586046ba7dc46892bb8","source":{"kind":"arxiv","id":"2607.16334","version":1},"attestation_state":"computed","paper":{"title":"A Hypergraph Tutte Polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joanna A. Ellis-Monaghan, Khallil Berrekkal, Merijn Moody","submitted_at":"2026-07-16T07:32:48Z","abstract_excerpt":"We introduce a Tutte polynomial for hypergraphs, $T_{\\mathrm{HG}}$, together with $T_k$, a related Tutte polynomial for $k$-polymatroids. Both invariants admit deletion--contraction recursions that remain within their respective classes, and they are linked by the fact that $T_{\\mathrm{HG}}$ specializes to $T_k$ on the associated polymatroid of any $(k+1)$-uniform hypergraph. We show that $T_{\\mathrm{HG}}$ satisfies several desirable Tutte type properties, including multiplicativity and duality, while $T_k$ further admits a universality theorem, as well as a convolution product formula. In the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.16334","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-16T07:32:48Z","cross_cats_sorted":[],"title_canon_sha256":"226932038b9c36c584172ade9bb4ef30adb7eae0feb2238f9a766dc0a86cd265","abstract_canon_sha256":"9e39c9787d0ad0699868b33b44024eb3d4d57ebbb83d3db45591d648e8fc6fcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:12.875385Z","signature_b64":"/T1/wlWHleM1S+nbxtDmZAC6eiI4FRabj/if1PJyXU1kC9lzRqlZ1wIZ2uOpX/+Eg7YrYUbau7OKAqBi2DqaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be260d0268e92ab12e5a64c0429674b8daedf48a960f1586046ba7dc46892bb8","last_reissued_at":"2026-07-21T00:20:12.874521Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:12.874521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Hypergraph Tutte Polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joanna A. Ellis-Monaghan, Khallil Berrekkal, Merijn Moody","submitted_at":"2026-07-16T07:32:48Z","abstract_excerpt":"We introduce a Tutte polynomial for hypergraphs, $T_{\\mathrm{HG}}$, together with $T_k$, a related Tutte polynomial for $k$-polymatroids. Both invariants admit deletion--contraction recursions that remain within their respective classes, and they are linked by the fact that $T_{\\mathrm{HG}}$ specializes to $T_k$ on the associated polymatroid of any $(k+1)$-uniform hypergraph. We show that $T_{\\mathrm{HG}}$ satisfies several desirable Tutte type properties, including multiplicativity and duality, while $T_k$ further admits a universality theorem, as well as a convolution product formula. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16334","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.16334","created_at":"2026-07-21T00:20:12.874967+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.16334v1","created_at":"2026-07-21T00:20:12.874967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16334","created_at":"2026-07-21T00:20:12.874967+00:00"},{"alias_kind":"pith_short_12","alias_value":"XYTA2ATI5EVL","created_at":"2026-07-21T00:20:12.874967+00:00"},{"alias_kind":"pith_short_16","alias_value":"XYTA2ATI5EVLCLS2","created_at":"2026-07-21T00:20:12.874967+00:00"},{"alias_kind":"pith_short_8","alias_value":"XYTA2ATI","created_at":"2026-07-21T00:20:12.874967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD","json":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD.json","graph_json":"https://pith.science/api/pith-number/XYTA2ATI5EVLCLS2MTAEFFTUXD/graph.json","events_json":"https://pith.science/api/pith-number/XYTA2ATI5EVLCLS2MTAEFFTUXD/events.json","paper":"https://pith.science/paper/XYTA2ATI"},"agent_actions":{"view_html":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD","download_json":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD.json","view_paper":"https://pith.science/paper/XYTA2ATI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.16334&json=true","fetch_graph":"https://pith.science/api/pith-number/XYTA2ATI5EVLCLS2MTAEFFTUXD/graph.json","fetch_events":"https://pith.science/api/pith-number/XYTA2ATI5EVLCLS2MTAEFFTUXD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD/action/storage_attestation","attest_author":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD/action/author_attestation","sign_citation":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD/action/citation_signature","submit_replication":"https://pith.science/pith/XYTA2ATI5EVLCLS2MTAEFFTUXD/action/replication_record"}},"created_at":"2026-07-21T00:20:12.874967+00:00","updated_at":"2026-07-21T00:20:12.874967+00:00"}