{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HX2LAVOZ56VTAG6EPJAYG47ZTK","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":"43897e17570a9c77305c4905d511d74a151cc65aa7813a6af57790b5f94f442c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-15T11:44:26Z","title_canon_sha256":"68a429d54b0607f4513dd4e5c296f8c82e468b7aa75ab34ce0cad52985c3b0f0"},"schema_version":"1.0","source":{"id":"1404.3876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3876","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3876v2","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3876","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"HX2LAVOZ56VT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HX2LAVOZ56VTAG6E","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HX2LAVOZ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:dc8450f64b5e59dec0800d9cb9a8019de3edc9528e116cf4eeed79c890c4dd07","target":"graph","created_at":"2026-05-18T02:52:13Z","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"},"paper":{"abstract_excerpt":"The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a generalization of the matrix tree theorem holds for this wider class.\n  We give a new, geometric proof of this fact by showing via a dissect-and-rearrange argument that two combinatorially distinct zonotopes associated to a regular matroid have the same volume. Along the way we prove that for a regular oriented matroid represented by a unimodular matrix, the la","authors_text":"Aaron Dall, Julian Pfeifle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-15T11:44:26Z","title":"A Polyhedral Proof of the Matrix Tree Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3876","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":"sha256:8a02c931aa5ffef8a6f9a4871c0ca311ba4a05598073cf090d8625f200633d46","target":"record","created_at":"2026-05-18T02:52:13Z","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":"43897e17570a9c77305c4905d511d74a151cc65aa7813a6af57790b5f94f442c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-15T11:44:26Z","title_canon_sha256":"68a429d54b0607f4513dd4e5c296f8c82e468b7aa75ab34ce0cad52985c3b0f0"},"schema_version":"1.0","source":{"id":"1404.3876","kind":"arxiv","version":2}},"canonical_sha256":"3df4b055d9efab301bc47a418373f99a83c8e250855bb048bc72f16fc5872d6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3df4b055d9efab301bc47a418373f99a83c8e250855bb048bc72f16fc5872d6a","first_computed_at":"2026-05-18T02:52:13.869538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.869538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aeVdlZIFbLfyPccFW/ujhw82+BQ0R7Qys8xHS7ZVz8IZx0Cz85Gt6Hakf8O/wsBcCKxnRikzQIgNejJU+M1iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.870216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a02c931aa5ffef8a6f9a4871c0ca311ba4a05598073cf090d8625f200633d46","sha256:dc8450f64b5e59dec0800d9cb9a8019de3edc9528e116cf4eeed79c890c4dd07"],"state_sha256":"d1e315bf41b788812b9e10d57af359bbf747e9dbff5178044bd37fa11617d7a4"}