{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XDOGEWIGGWDKP22PO2GMVSXRWD","short_pith_number":"pith:XDOGEWIG","schema_version":"1.0","canonical_sha256":"b8dc6259063586a7eb4f768ccacaf1b0ca8fce345666d9682c61cc4fe5bbce4f","source":{"kind":"arxiv","id":"1306.6132","version":3},"attestation_state":"computed","paper":{"title":"Lattice Points in Orthotopes and a Huge Polynomial Tutte Invariant of Weighted Gain Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Forge, Thomas Zaslavsky","submitted_at":"2013-06-26T05:10:34Z","abstract_excerpt":"A gain graph is a graph whose edges are orientably labelled from a group. A weighted gain graph is a gain graph with vertex weights from an abelian semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and forest-expansion polynomials that are Tutte invariants (they satisfy Tutte's deletion-contraction and multiplicative identities). Our dichromatic polynomial includes the classical graph one by Tutte, Zaslavsky's two for gain graphs, Noble and Welsh's for graphs with positi"},"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":"1306.6132","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-26T05:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"9e80a77533cef32f736e848f8eb4d70b8707394fd35291c1d6f516636f41a389","abstract_canon_sha256":"a1e7f70cc07a4bb4586470080c26ab869ebc6540c3594e366d336601da942cf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:14.332502Z","signature_b64":"rweITH+CHdc2xKyj6oMrEoM+QlYCV8BNfgNOjCKlHaRERhv6jjGFq76DPV6QCB1zmyUzWd1r1XJjZ6nNZZw8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8dc6259063586a7eb4f768ccacaf1b0ca8fce345666d9682c61cc4fe5bbce4f","last_reissued_at":"2026-05-18T01:02:14.332027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:14.332027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice Points in Orthotopes and a Huge Polynomial Tutte Invariant of Weighted Gain Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Forge, Thomas Zaslavsky","submitted_at":"2013-06-26T05:10:34Z","abstract_excerpt":"A gain graph is a graph whose edges are orientably labelled from a group. A weighted gain graph is a gain graph with vertex weights from an abelian semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and forest-expansion polynomials that are Tutte invariants (they satisfy Tutte's deletion-contraction and multiplicative identities). Our dichromatic polynomial includes the classical graph one by Tutte, Zaslavsky's two for gain graphs, Noble and Welsh's for graphs with positi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6132","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1306.6132","created_at":"2026-05-18T01:02:14.332093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.6132v3","created_at":"2026-05-18T01:02:14.332093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6132","created_at":"2026-05-18T01:02:14.332093+00:00"},{"alias_kind":"pith_short_12","alias_value":"XDOGEWIGGWDK","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XDOGEWIGGWDKP22P","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XDOGEWIG","created_at":"2026-05-18T12:28:06.772260+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/XDOGEWIGGWDKP22PO2GMVSXRWD","json":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD.json","graph_json":"https://pith.science/api/pith-number/XDOGEWIGGWDKP22PO2GMVSXRWD/graph.json","events_json":"https://pith.science/api/pith-number/XDOGEWIGGWDKP22PO2GMVSXRWD/events.json","paper":"https://pith.science/paper/XDOGEWIG"},"agent_actions":{"view_html":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD","download_json":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD.json","view_paper":"https://pith.science/paper/XDOGEWIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.6132&json=true","fetch_graph":"https://pith.science/api/pith-number/XDOGEWIGGWDKP22PO2GMVSXRWD/graph.json","fetch_events":"https://pith.science/api/pith-number/XDOGEWIGGWDKP22PO2GMVSXRWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD/action/storage_attestation","attest_author":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD/action/author_attestation","sign_citation":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD/action/citation_signature","submit_replication":"https://pith.science/pith/XDOGEWIGGWDKP22PO2GMVSXRWD/action/replication_record"}},"created_at":"2026-05-18T01:02:14.332093+00:00","updated_at":"2026-05-18T01:02:14.332093+00:00"}