{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JO55VYEU3PRQGKEJWVIPZYOOSM","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":"9f5898b5401c4186773e3ab0d3fd6a16de0da3a8e3ef1829b930863f6928ee1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-07-16T07:36:11Z","title_canon_sha256":"f37002b3b3a333b14e29ae76908c188666b663bf3eb0f528ae12732305ce8d6d"},"schema_version":"1.0","source":{"id":"0707.2165","kind":"arxiv","version":12}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2165","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2165v12","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2165","created_at":"2026-05-18T01:15:39Z"},{"alias_kind":"pith_short_12","alias_value":"JO55VYEU3PRQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JO55VYEU3PRQGKEJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JO55VYEU","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:5b81a7489c5b9bd3191a5f34456ba4442ef94fdca9541fce74fc53ee65d40317","target":"graph","created_at":"2026-05-18T01:15:39Z","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":"Motivated by the cohomology theory of loop spaces, we consider a special class of higher order homotopy commutative differential graded algebras and construct the filtered Hirsch model for such an algebra $A$. When $x\\in H(A)$ with $\\mathbb{Z}$ coefficients and $x^{2}=0,$ the symmetric Massey products $% \\langle x\\rangle ^{n}$ with $n\\geq 3$ have a finite order (whenever defined). However, if $\\Bbbk $ is a field of characteristic zero, $\\langle x\\rangle ^{n}$ is defined and vanishes in $H(A\\otimes \\Bbbk )$ for all $n$. If $p$ is an odd prime, the Kraines formula $\\langle x\\rangle ^{p}=-\\beta \\","authors_text":"Samson Saneblidze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-07-16T07:36:11Z","title":"Filtered Hirsch Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2165","kind":"arxiv","version":12},"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":"sha256:5318b346b72607685b3eb74c1e53827b36648c50f74bb568afb044e279f7e790","target":"record","created_at":"2026-05-18T01:15:39Z","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":"9f5898b5401c4186773e3ab0d3fd6a16de0da3a8e3ef1829b930863f6928ee1c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2007-07-16T07:36:11Z","title_canon_sha256":"f37002b3b3a333b14e29ae76908c188666b663bf3eb0f528ae12732305ce8d6d"},"schema_version":"1.0","source":{"id":"0707.2165","kind":"arxiv","version":12}},"canonical_sha256":"4bbbdae094dbe3032889b550fce1ce9332070880f3146807548b4da24489cc32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bbbdae094dbe3032889b550fce1ce9332070880f3146807548b4da24489cc32","first_computed_at":"2026-05-18T01:15:39.314448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:39.314448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mtjP3wRPglIwA17UfZFPfDc0aJAKONMFQCgQ5UoSWz9JuCj52tjk50JW/nFGx1M3T3Pqc4TX23JL6W0cQNXcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:39.315175Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.2165","source_kind":"arxiv","source_version":12}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5318b346b72607685b3eb74c1e53827b36648c50f74bb568afb044e279f7e790","sha256:5b81a7489c5b9bd3191a5f34456ba4442ef94fdca9541fce74fc53ee65d40317"],"state_sha256":"ec95ea09db3d597fbbc31edb54e188e7c01caa7d04d2df01c7ba63596a4cb43b"}