{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RDXTSFQ25P562EBO5HNACBL7VM","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":"74881cf2d828cfea051c409ebdedd8bd78e5802f6542d4fb838df321014e5f69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-10T13:48:25Z","title_canon_sha256":"62868d0fcaae30e1fb3a7ae5e4ee2c33197aaa94bf404170b53432162f8c3a60"},"schema_version":"1.0","source":{"id":"1508.02245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02245","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02245v2","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02245","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"RDXTSFQ25P56","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RDXTSFQ25P562EBO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RDXTSFQ2","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:6663a0bf032827de718b91382e3d2d53485f947c43d67ce78f193b0a25680285","target":"graph","created_at":"2026-05-18T00:55:14Z","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 was discovered by G.~Kirchhoff in 1847. It relates the principal minor of the Laplace (nxn)-matrix to a particular sum of monomials indexed by the set of trees with n vertices. The aim of this paper is to present a generalization of the (nonsymmetric) matrix-tree theorem containing no trees and essentially no matrices. Instead of trees we consider acyclic directed graphs with a prescribed set of sinks, and instead of determinant, a polynomial invariant of the matrix determined by directed graph such that any two vertices of the same connected component are mut","authors_text":"Yurii Burman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-10T13:48:25Z","title":"Higher determinants and the matrix-tree theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02245","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:ec9cf2b50bbed737e3ef4913d6354feac894884e99eba7d452b75e3f9f7578ec","target":"record","created_at":"2026-05-18T00:55:14Z","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":"74881cf2d828cfea051c409ebdedd8bd78e5802f6542d4fb838df321014e5f69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-10T13:48:25Z","title_canon_sha256":"62868d0fcaae30e1fb3a7ae5e4ee2c33197aaa94bf404170b53432162f8c3a60"},"schema_version":"1.0","source":{"id":"1508.02245","kind":"arxiv","version":2}},"canonical_sha256":"88ef39161aebfbed102ee9da01057fab350a19c28b4d9ddb82863e3d82264ff8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88ef39161aebfbed102ee9da01057fab350a19c28b4d9ddb82863e3d82264ff8","first_computed_at":"2026-05-18T00:55:14.499431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:14.499431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLRe2lBq+WwtMoIKkrbz8HxNV5ssThrpRXlZz5tE6WXaiMeuk9vT5RTuGv2Yl6yRggJuAaCjMA1nRRA2HHB8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:14.499899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec9cf2b50bbed737e3ef4913d6354feac894884e99eba7d452b75e3f9f7578ec","sha256:6663a0bf032827de718b91382e3d2d53485f947c43d67ce78f193b0a25680285"],"state_sha256":"0d3dbe02186fa124470525521ec2d2e420a54289121012ae8c30c5b5c89315a3"}