{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CGTZYRP5EHEINNG4BYPX3EUY73","short_pith_number":"pith:CGTZYRP5","canonical_record":{"source":{"id":"1208.1597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-08-08T06:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"85d4555bf04756ef783473942a3d1ff10097a04736d2b336b41bd9f1ab0bc4f4","abstract_canon_sha256":"078a22b97a30a2e1cc42faf6ae8986bb4d963e6eb53ef3580d64eb4b5eff87b7"},"schema_version":"1.0"},"canonical_sha256":"11a79c45fd21c886b4dc0e1f7d9298fef3e5eee2d29d26991bcd288891dbb1f6","source":{"kind":"arxiv","id":"1208.1597","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1597","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1597v1","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1597","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"CGTZYRP5EHEI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CGTZYRP5EHEINNG4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CGTZYRP5","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CGTZYRP5EHEINNG4BYPX3EUY73","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-08-08T06:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"85d4555bf04756ef783473942a3d1ff10097a04736d2b336b41bd9f1ab0bc4f4","abstract_canon_sha256":"078a22b97a30a2e1cc42faf6ae8986bb4d963e6eb53ef3580d64eb4b5eff87b7"},"schema_version":"1.0"},"canonical_sha256":"11a79c45fd21c886b4dc0e1f7d9298fef3e5eee2d29d26991bcd288891dbb1f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:11.120066Z","signature_b64":"A8BjooUnNu5daG2WYEPSClqs+J1nn1ZeYqh/faq9OPwufJJvL3iefFXPKxGg+Fy6lGYnv/JjGGsD7PPrRqBSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11a79c45fd21c886b4dc0e1f7d9298fef3e5eee2d29d26991bcd288891dbb1f6","last_reissued_at":"2026-05-18T03:49:11.119479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:11.119479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1597","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SobZzER/rg63WzpbEUOQZkn35lPqqLQpnVp/VjkJIV/02qcEJxG+FwUg3kLFwN/tHV508x9P87a4nBm4rOCmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:00:47.291024Z"},"content_sha256":"227c66dd11c31ea59a153ef6c719b233c7486175291536c8ad91cac57649789e","schema_version":"1.0","event_id":"sha256:227c66dd11c31ea59a153ef6c719b233c7486175291536c8ad91cac57649789e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CGTZYRP5EHEINNG4BYPX3EUY73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recording Completion for Finding and Certifying Proofs in Equational Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Christian Sternagel, Harald Zankl, Ren\\'e Thiemann, Thomas Sternagel","submitted_at":"2012-08-08T06:47:28Z","abstract_excerpt":"When we want to answer/certify whether a given equation is entailed by an equational system we face the following problems: (1) It is hard to find a conversion (but easy to certify a given one). (2) Under the assumption that Knuth-Bendix completion is successful, it is easy to decide the existence of a conversion but hard to certify this decision. In this paper we introduce recording completion, which overcomes both problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1597","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwTvzVyFsoX2Mxw3mJQ+3wI/JijG2PW31Axiz6wSsU5yQawn107I6bNg7hZijye0uiXz9KVt8DROjWRG824gBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:00:47.291390Z"},"content_sha256":"5ed05ab898f4719fe9871ec8daf87f5e8dc0925aa8a0f9e2edc3bc8450dafa40","schema_version":"1.0","event_id":"sha256:5ed05ab898f4719fe9871ec8daf87f5e8dc0925aa8a0f9e2edc3bc8450dafa40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGTZYRP5EHEINNG4BYPX3EUY73/bundle.json","state_url":"https://pith.science/pith/CGTZYRP5EHEINNG4BYPX3EUY73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGTZYRP5EHEINNG4BYPX3EUY73/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T09:00:47Z","links":{"resolver":"https://pith.science/pith/CGTZYRP5EHEINNG4BYPX3EUY73","bundle":"https://pith.science/pith/CGTZYRP5EHEINNG4BYPX3EUY73/bundle.json","state":"https://pith.science/pith/CGTZYRP5EHEINNG4BYPX3EUY73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGTZYRP5EHEINNG4BYPX3EUY73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CGTZYRP5EHEINNG4BYPX3EUY73","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":"078a22b97a30a2e1cc42faf6ae8986bb4d963e6eb53ef3580d64eb4b5eff87b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-08-08T06:47:28Z","title_canon_sha256":"85d4555bf04756ef783473942a3d1ff10097a04736d2b336b41bd9f1ab0bc4f4"},"schema_version":"1.0","source":{"id":"1208.1597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1597","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1597v1","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1597","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"CGTZYRP5EHEI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CGTZYRP5EHEINNG4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CGTZYRP5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:5ed05ab898f4719fe9871ec8daf87f5e8dc0925aa8a0f9e2edc3bc8450dafa40","target":"graph","created_at":"2026-05-18T03:49:11Z","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":"When we want to answer/certify whether a given equation is entailed by an equational system we face the following problems: (1) It is hard to find a conversion (but easy to certify a given one). (2) Under the assumption that Knuth-Bendix completion is successful, it is easy to decide the existence of a conversion but hard to certify this decision. In this paper we introduce recording completion, which overcomes both problems.","authors_text":"Christian Sternagel, Harald Zankl, Ren\\'e Thiemann, Thomas Sternagel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-08-08T06:47:28Z","title":"Recording Completion for Finding and Certifying Proofs in Equational Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1597","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":"sha256:227c66dd11c31ea59a153ef6c719b233c7486175291536c8ad91cac57649789e","target":"record","created_at":"2026-05-18T03:49:11Z","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":"078a22b97a30a2e1cc42faf6ae8986bb4d963e6eb53ef3580d64eb4b5eff87b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-08-08T06:47:28Z","title_canon_sha256":"85d4555bf04756ef783473942a3d1ff10097a04736d2b336b41bd9f1ab0bc4f4"},"schema_version":"1.0","source":{"id":"1208.1597","kind":"arxiv","version":1}},"canonical_sha256":"11a79c45fd21c886b4dc0e1f7d9298fef3e5eee2d29d26991bcd288891dbb1f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a79c45fd21c886b4dc0e1f7d9298fef3e5eee2d29d26991bcd288891dbb1f6","first_computed_at":"2026-05-18T03:49:11.119479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:11.119479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A8BjooUnNu5daG2WYEPSClqs+J1nn1ZeYqh/faq9OPwufJJvL3iefFXPKxGg+Fy6lGYnv/JjGGsD7PPrRqBSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:11.120066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:227c66dd11c31ea59a153ef6c719b233c7486175291536c8ad91cac57649789e","sha256:5ed05ab898f4719fe9871ec8daf87f5e8dc0925aa8a0f9e2edc3bc8450dafa40"],"state_sha256":"6f0b085abcf4c8cf24dd96eae362197f85ffb899284693f80d6ca01044fec8e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XmVPsKGrTvnkag7NnTYkL1FRseIUjQsZM+Unj5OhW9TyCvPMwNY0vN/IcidnO/DZb1PN3hna4yiStk6mO3EDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:00:47.293749Z","bundle_sha256":"8aa51a5b878c3e25fee736e0d6df1c6e7e5794917eed420fc920edee406f39ba"}}