{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AHHB7HSQWOAIRORYFFYXXQCME2","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":"44b7e2428899623bc4d51915695d07422c0a85304e87fe3e896d3ee8ee5e26da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-08-28T20:17:48Z","title_canon_sha256":"7614519d5efe3b8d00f6e055a92b11841a5a94802b180477daa82c6da11a82d6"},"schema_version":"1.0","source":{"id":"1208.5781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5781","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5781v1","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5781","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"AHHB7HSQWOAI","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHHB7HSQWOAIRORY","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHHB7HSQ","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:e78ad99b7dea6b25c5825cd72acfaa845a50ebcdbd14ff216f8432e4e723a298","target":"graph","created_at":"2026-05-18T03:46:48Z","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":"If $R$ is a commutative ring, $M$ a compact $R$-oriented manifold and $G$ a finite graph without loops or multiple edges, we consider the graph configuration space $M^G$ and a Bendersky-Gitler type spectral sequence converging to the homology $H_*(M^G, R)$. We show that its $E_1$ term is given by the graph cohomology complex $C_A(G)$ of the graded commutative algebra $A = H^*(M, R)$ and its higher differentials are obtained from the Massey products of $A$, as conjectured by Bendersky and Gitler for the case of a complete graph $G$. Similar results apply to the spectral sequence constructed fro","authors_text":"Radmila Sazdanovic, Vladimir Baranovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-08-28T20:17:48Z","title":"Graph homology and graph configuration spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5781","kind":"arxiv","version":1},"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:e3d194b51f81054067390f9046b4c43288888a19245f27d7cca219f0a025122a","target":"record","created_at":"2026-05-18T03:46:48Z","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":"44b7e2428899623bc4d51915695d07422c0a85304e87fe3e896d3ee8ee5e26da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-08-28T20:17:48Z","title_canon_sha256":"7614519d5efe3b8d00f6e055a92b11841a5a94802b180477daa82c6da11a82d6"},"schema_version":"1.0","source":{"id":"1208.5781","kind":"arxiv","version":1}},"canonical_sha256":"01ce1f9e50b38088ba3829717bc04c26b317e85f121ddc75e4bc90c37edafa65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01ce1f9e50b38088ba3829717bc04c26b317e85f121ddc75e4bc90c37edafa65","first_computed_at":"2026-05-18T03:46:48.723664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:48.723664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U6OOAO0B8ZD9tZz9f/un1/M3l6cMrmB+eGSi0CsZL0H9a4Ghq3L4m+yjg4LXyKn8znXTrkPbdwyBxf/4d1TXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:48.724436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3d194b51f81054067390f9046b4c43288888a19245f27d7cca219f0a025122a","sha256:e78ad99b7dea6b25c5825cd72acfaa845a50ebcdbd14ff216f8432e4e723a298"],"state_sha256":"e16c31cfd8814cc68422f2f013b8d7a40f6bf2ec4f3af07a2759817e5f050dea"}