{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:H4R2XNIIHPO5E7V2MJ53QDCSSY","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":"0bc41067a931642ea8bc922d9c3df4f819228df66c2add278253af26bb057b8f","cross_cats_sorted":[],"license":"","primary_cat":"cs.LO","submitted_at":"2006-10-12T11:47:54Z","title_canon_sha256":"821f673e708a31ba92e26db7dacad3414c0ca003bcc6d36ebb6d7ced79205ed7"},"schema_version":"1.0","source":{"id":"cs/0610072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0610072","created_at":"2026-05-18T01:08:54Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0610072v1","created_at":"2026-05-18T01:08:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0610072","created_at":"2026-05-18T01:08:54Z"},{"alias_kind":"pith_short_12","alias_value":"H4R2XNIIHPO5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"H4R2XNIIHPO5E7V2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"H4R2XNII","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:32aa5b7232845427adc8342215bbddd0bd2f228f8a40c29a1cb0070ab7257219","target":"graph","created_at":"2026-05-18T01:08:54Z","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":"This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. On the one hand, the Calculus of Constructions is a powerful type system in which one can formalize the propositions and natural deduction proofs of higher-order logic. On the other hand, rewriting is a simple and powerful computation paradigm. The combination of both allows, among other things, to develop formal proofs with a r","authors_text":"Fr\\'ed\\'eric Blanqui (INRIA Lorraine - LORIA, LIX)","cross_cats":[],"headline":"","license":"","primary_cat":"cs.LO","submitted_at":"2006-10-12T11:47:54Z","title":"Definitions by rewriting in the Calculus of Constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0610072","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":"sha256:41714ae2b524e3264ec2618179aff2c92bb18eaa2c619904f94a45273df5fd73","target":"record","created_at":"2026-05-18T01:08:54Z","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":"0bc41067a931642ea8bc922d9c3df4f819228df66c2add278253af26bb057b8f","cross_cats_sorted":[],"license":"","primary_cat":"cs.LO","submitted_at":"2006-10-12T11:47:54Z","title_canon_sha256":"821f673e708a31ba92e26db7dacad3414c0ca003bcc6d36ebb6d7ced79205ed7"},"schema_version":"1.0","source":{"id":"cs/0610072","kind":"arxiv","version":1}},"canonical_sha256":"3f23abb5083bddd27eba627bb80c52962143da45c4d472e11c63dffa075f8b7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f23abb5083bddd27eba627bb80c52962143da45c4d472e11c63dffa075f8b7e","first_computed_at":"2026-05-18T01:08:54.314191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:54.314191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J2dBsBNO753GGl5npmqZclxNNyGrlalGC/hWK82YeEsPapTW3/A6+6c9mPAAYadsUsu7ZoR0J+lUWdRx4Gl1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:54.314808Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0610072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41714ae2b524e3264ec2618179aff2c92bb18eaa2c619904f94a45273df5fd73","sha256:32aa5b7232845427adc8342215bbddd0bd2f228f8a40c29a1cb0070ab7257219"],"state_sha256":"8bd79b5ae40e30515ebe24f53814223a395e0506284c1318ac3961578b9e5977"}