{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KVO6ZM7V6XMMFGWA5T6E7D63ZS","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":"16ca4d3a95069d92f6e3c147a19d31c545bd3c0375b9ec0f10e48cebf498c367","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AT","submitted_at":"2022-11-11T13:52:31Z","title_canon_sha256":"dd732d0a4f2dc9220b7330a36e8e6f10cb66d8992347d1e4d511e726542fee5d"},"schema_version":"1.0","source":{"id":"2211.06202","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.06202","created_at":"2026-07-05T07:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"2211.06202v3","created_at":"2026-07-05T07:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.06202","created_at":"2026-07-05T07:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"KVO6ZM7V6XMM","created_at":"2026-07-05T07:46:59Z"},{"alias_kind":"pith_short_16","alias_value":"KVO6ZM7V6XMMFGWA","created_at":"2026-07-05T07:46:59Z"},{"alias_kind":"pith_short_8","alias_value":"KVO6ZM7V","created_at":"2026-07-05T07:46:59Z"}],"graph_snapshots":[{"event_id":"sha256:7f17a7d30ca27909abf0b82c5f5f76f4197ac40f3884a3853d5d7be87a65a48a","target":"graph","created_at":"2026-07-05T07:46:59Z","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/2211.06202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY-theory) in a general simplicial setting. The new theory includes as particular cases the GLMY-theory for path complexes and new homology theories: path homology of categories with a chosen set of morphisms (marked categories) groups with a chosen subset (marked groups) and path Hochschild homology of algebras with chosen vector subspaces (marked algebras). Using our general machinery, we also introduce a new homology theory for quivers that we call square-commutative homology of quivers","authors_text":"Fedor Pavutnitskiy, Sergei O. Ivanov","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AT","submitted_at":"2022-11-11T13:52:31Z","title":"Simplicial approach to path homology of quivers, marked categories, groups and algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.06202","kind":"arxiv","version":3},"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":"sha256:43b1789aeb6bc58ba4854c5aa103b2c3d95262472ba0ceaad24023fd5ecb8dbe","target":"record","created_at":"2026-07-05T07:46:59Z","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":"16ca4d3a95069d92f6e3c147a19d31c545bd3c0375b9ec0f10e48cebf498c367","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AT","submitted_at":"2022-11-11T13:52:31Z","title_canon_sha256":"dd732d0a4f2dc9220b7330a36e8e6f10cb66d8992347d1e4d511e726542fee5d"},"schema_version":"1.0","source":{"id":"2211.06202","kind":"arxiv","version":3}},"canonical_sha256":"555decb3f5f5d8c29ac0ecfc4f8fdbccbad69888da6737e246990e3dc891ce3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"555decb3f5f5d8c29ac0ecfc4f8fdbccbad69888da6737e246990e3dc891ce3c","first_computed_at":"2026-07-05T07:46:59.673061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:46:59.673061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"506wDeVBugNv1WnZu78lkp3AmrlcreChh7XZIzJk5plo9Ty7ffEBWMtu3SyA30r8fdXLr7yI5JYAxXlZAaPfAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:46:59.673522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.06202","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43b1789aeb6bc58ba4854c5aa103b2c3d95262472ba0ceaad24023fd5ecb8dbe","sha256:7f17a7d30ca27909abf0b82c5f5f76f4197ac40f3884a3853d5d7be87a65a48a"],"state_sha256":"e2c8f2d113100363de6e49aa207b0b80f844b134f64db5924ba2d30430243a9c"}