{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5K56EN4MIDAPQYBRRIDSMTH4FV","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":"2d09c65cdb3a209e69f9fd6885ba7cf993d2f61ac08dd1d76a7656d13ce1d0b4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-24T13:31:53Z","title_canon_sha256":"476ec308fbf4888435931b52c3ffe08d365739f63075114c7b573cf9e04c0234"},"schema_version":"1.0","source":{"id":"0802.3507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3507","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3507v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3507","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"5K56EN4MIDAP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5K56EN4MIDAPQYBR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5K56EN4M","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:921a0317c98b4d643f7e4bbe5aede14fa6b947a6f82c98c510c1561ad195b1d2","target":"graph","created_at":"2026-05-18T02:58:11Z","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":"We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A-infinity algebras. Further, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced","authors_text":"Andrey Lazarev, Joseph Chuang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-24T13:31:53Z","title":"Feynman diagrams and minimal models for operadic algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3507","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":"sha256:46d33c236fe28d4bda3c41e1f3f589773af2c2f2fc899e104d867ac2bdd6da48","target":"record","created_at":"2026-05-18T02:58:11Z","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":"2d09c65cdb3a209e69f9fd6885ba7cf993d2f61ac08dd1d76a7656d13ce1d0b4","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-02-24T13:31:53Z","title_canon_sha256":"476ec308fbf4888435931b52c3ffe08d365739f63075114c7b573cf9e04c0234"},"schema_version":"1.0","source":{"id":"0802.3507","kind":"arxiv","version":1}},"canonical_sha256":"eabbe2378c40c0f860318a07264cfc2d77adcc1b087e4efb67d3d231a461e69d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eabbe2378c40c0f860318a07264cfc2d77adcc1b087e4efb67d3d231a461e69d","first_computed_at":"2026-05-18T02:58:11.775499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.775499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yK1ZMAdh9PiHX9h8fcfqihFOdi6CfqdyJF/d8yNC3t2M21e1x+b13n1NkT0iGgq4JoKwyuVRweGo9x3Kr8fYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.776089Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.3507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46d33c236fe28d4bda3c41e1f3f589773af2c2f2fc899e104d867ac2bdd6da48","sha256:921a0317c98b4d643f7e4bbe5aede14fa6b947a6f82c98c510c1561ad195b1d2"],"state_sha256":"df1ad76d43d5e037e30df7f7d33553346ac6b9d80f7d8f5ef9ecf96a92a851c0"}