{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:XNNZEWO6PSNXX5XRJNX6YH2PQQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"78c2d47236b6814185545d7123e2bae1fc3a06cfba0edfe773fb2a5e5c552cd4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-24T13:43:24Z","title_canon_sha256":"06d20990ad27c904250d39f6f292dc5f568312309f3d904294e31b5863171d56"},"schema_version":"1.0","source":{"id":"2309.13639","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.13639","created_at":"2026-06-23T02:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"2309.13639v2","created_at":"2026-06-23T02:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.13639","created_at":"2026-06-23T02:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"XNNZEWO6PSNX","created_at":"2026-06-23T02:13:58Z"},{"alias_kind":"pith_short_16","alias_value":"XNNZEWO6PSNXX5XR","created_at":"2026-06-23T02:13:58Z"},{"alias_kind":"pith_short_8","alias_value":"XNNZEWO6","created_at":"2026-06-23T02:13:58Z"}],"graph_snapshots":[{"event_id":"sha256:e336fd70f4c21c441ab0755d4590f86e00bbd613e8fb30f505b3ae7b881f2f05","target":"graph","created_at":"2026-06-23T02:13:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.13639/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Tutte polynomial is a fundamental invariant of matroids. The polymatroid Tutte polynomial $\\mathscr{T}_{P}(x,y)$, introduced by Bernardi, K\\'{a}lm\\'{a}n, and Postnikov, is an extension of the classical Tutte polynomial from matroids to polymatroids $P$. In this paper, we first obtain a deletion-contraction formula for $\\mathscr{T}_{P}(x,y)$. Then we prove two natural properties of coefficientwise monotonicity, one for containment and one for minors, both for the interior polynomial $x^{n}\\mathscr{T}_{P}(x^{-1},1)$ and the exterior polynomial $y^{n}\\mathscr{T}_{P}(1,y^{-1})$, where $P$ is a","authors_text":"Tam\\'as K\\'alm\\'an, Xian'an Jin, Xiaxia Guan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-24T13:43:24Z","title":"A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.13639","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0985511d68c15a42d30fa13df9b9e449e2d625e2f660f88ad26a0e97cfbc6314","target":"record","created_at":"2026-06-23T02:13:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"78c2d47236b6814185545d7123e2bae1fc3a06cfba0edfe773fb2a5e5c552cd4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-24T13:43:24Z","title_canon_sha256":"06d20990ad27c904250d39f6f292dc5f568312309f3d904294e31b5863171d56"},"schema_version":"1.0","source":{"id":"2309.13639","kind":"arxiv","version":2}},"canonical_sha256":"bb5b9259de7c9b7bf6f14b6fec1f4f8408e006f29645e447984164fa7672310f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb5b9259de7c9b7bf6f14b6fec1f4f8408e006f29645e447984164fa7672310f","first_computed_at":"2026-06-23T02:13:58.217919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:58.217919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BugK7bHONQ7Zwv3Cgg9Qee4GgUqoRdNRemwV25XN/DGEERgmZJIOwigRo9gOvwKkJ0D0rXd7l3PCt/uN/WLhDA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:58.218348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.13639","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0985511d68c15a42d30fa13df9b9e449e2d625e2f660f88ad26a0e97cfbc6314","sha256:e336fd70f4c21c441ab0755d4590f86e00bbd613e8fb30f505b3ae7b881f2f05"],"state_sha256":"6f452c67272cea2fb0a128304c25442b16577cb89a4a4751e601069062cb532f"}