{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:X6WQ35TLJ37EEMTD42JH6TG2MC","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":"c5951b316b645fc0367421dcdfcf4cfd49b23559c17191af2c1e2b9aedc2d27c","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2011-06-22T13:58:58Z","title_canon_sha256":"f729fe14c9efbe319cfbfc902d69f49f097755d0f9a77cc06b8ee787106e2098"},"schema_version":"1.0","source":{"id":"1106.4448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4448","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4448v2","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4448","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"X6WQ35TLJ37E","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X6WQ35TLJ37EEMTD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X6WQ35TL","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:0fa7b0cc5cd1cc434b536fad243ae50bfb39a2b9eb46d214d92964e35dbbc019","target":"graph","created_at":"2026-05-18T03:31:43Z","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 present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which ","authors_text":"Damien Pous (LIG), Thomas Braibant (LIG)","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2011-06-22T13:58:58Z","title":"Tactics for Reasoning modulo AC in Coq"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4448","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:ed1f2ea2e2fd7f55310735342c07973dfe98582eceefa93b410f9a322e0d6aa8","target":"record","created_at":"2026-05-18T03:31:43Z","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":"c5951b316b645fc0367421dcdfcf4cfd49b23559c17191af2c1e2b9aedc2d27c","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2011-06-22T13:58:58Z","title_canon_sha256":"f729fe14c9efbe319cfbfc902d69f49f097755d0f9a77cc06b8ee787106e2098"},"schema_version":"1.0","source":{"id":"1106.4448","kind":"arxiv","version":2}},"canonical_sha256":"bfad0df66b4efe423263e6927f4cda609b193d9ab0a97898d5d8591ed5437d12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfad0df66b4efe423263e6927f4cda609b193d9ab0a97898d5d8591ed5437d12","first_computed_at":"2026-05-18T03:31:43.241733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:43.241733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HM1bSvNbgcvrB1cdHhlw6UPXEetuK8DludnTs2+5etBUmwEEhSU81wfalRETslBxNM/IYKdx3EcWi8E3sWfaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:43.242703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1f2ea2e2fd7f55310735342c07973dfe98582eceefa93b410f9a322e0d6aa8","sha256:0fa7b0cc5cd1cc434b536fad243ae50bfb39a2b9eb46d214d92964e35dbbc019"],"state_sha256":"4519165373b46e6237e2b31ac3e62127965e4d2ca9bd98fc1ab3483e75e9b816"}