{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7K2A44KN4J4DFZYPTTVAD7DD5A","short_pith_number":"pith:7K2A44KN","canonical_record":{"source":{"id":"1808.10312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"675687ed3e79cc266c06f664dcd7a14e5d7380e148bfd447556238640baf3cee","abstract_canon_sha256":"df0d9eee19b4d9ef9f3035dc93e79c94994f53fabf18984cae26ec011788825d"},"schema_version":"1.0"},"canonical_sha256":"fab40e714de27832e70f9cea01fc63e82de12034ce054d85dc98ae95aa87221a","source":{"kind":"arxiv","id":"1808.10312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10312","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10312v1","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10312","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"7K2A44KN4J4D","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7K2A44KN4J4DFZYP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7K2A44KN","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7K2A44KN4J4DFZYPTTVAD7DD5A","target":"record","payload":{"canonical_record":{"source":{"id":"1808.10312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"675687ed3e79cc266c06f664dcd7a14e5d7380e148bfd447556238640baf3cee","abstract_canon_sha256":"df0d9eee19b4d9ef9f3035dc93e79c94994f53fabf18984cae26ec011788825d"},"schema_version":"1.0"},"canonical_sha256":"fab40e714de27832e70f9cea01fc63e82de12034ce054d85dc98ae95aa87221a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:49.183382Z","signature_b64":"jvmH79i4skAMJtQJdhISdo97zp4Ou3+DItH+Osjj+MQvxkWlNrEnhwucluC107NKskLbTQ+DP9L9f2mQZI1bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab40e714de27832e70f9cea01fc63e82de12034ce054d85dc98ae95aa87221a","last_reissued_at":"2026-05-18T00:06:49.182865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:49.182865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.10312","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":"2026-05-18T00:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhmCVvSnj7WwtT5N0DHXnWsKghsADmbee5+DlFRLeYj8qBUnLd17jSKOIO8RUDdFT5Lad7B+83lyoBKcBprrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:35:21.251405Z"},"content_sha256":"397cba2c2df0e3df49291f248be01a446a4bff124a2cdc0a3ec6ef1099ec4257","schema_version":"1.0","event_id":"sha256:397cba2c2df0e3df49291f248be01a446a4bff124a2cdc0a3ec6ef1099ec4257"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7K2A44KN4J4DFZYPTTVAD7DD5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logic for approximate entailment in ordered universes of discourse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Francesc Esteva, Llu\\'is Godo, Thomas Vetterlein","submitted_at":"2018-08-30T14:30:05Z","abstract_excerpt":"The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10312","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":"2026-05-18T00:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UOjTMX3OA0BEo6qMtaeMD/Ke+0lSIUIsR0wHBKauBL1MOI/aPzF79qHJsNNz+UlXStt8BYiVGRt2zw5zNDtICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:35:21.251748Z"},"content_sha256":"762fa705f16e5dd95079579f89abf76c143d2528eb039a70e3625252b8087555","schema_version":"1.0","event_id":"sha256:762fa705f16e5dd95079579f89abf76c143d2528eb039a70e3625252b8087555"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/bundle.json","state_url":"https://pith.science/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/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":"2026-06-01T07:35:21Z","links":{"resolver":"https://pith.science/pith/7K2A44KN4J4DFZYPTTVAD7DD5A","bundle":"https://pith.science/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/bundle.json","state":"https://pith.science/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K2A44KN4J4DFZYPTTVAD7DD5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7K2A44KN4J4DFZYPTTVAD7DD5A","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":"df0d9eee19b4d9ef9f3035dc93e79c94994f53fabf18984cae26ec011788825d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:30:05Z","title_canon_sha256":"675687ed3e79cc266c06f664dcd7a14e5d7380e148bfd447556238640baf3cee"},"schema_version":"1.0","source":{"id":"1808.10312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10312","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10312v1","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10312","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"7K2A44KN4J4D","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7K2A44KN4J4DFZYP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7K2A44KN","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:762fa705f16e5dd95079579f89abf76c143d2528eb039a70e3625252b8087555","target":"graph","created_at":"2026-05-18T00:06:49Z","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":"The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an ord","authors_text":"Francesc Esteva, Llu\\'is Godo, Thomas Vetterlein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:30:05Z","title":"Logic for approximate entailment in ordered universes of discourse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10312","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":"sha256:397cba2c2df0e3df49291f248be01a446a4bff124a2cdc0a3ec6ef1099ec4257","target":"record","created_at":"2026-05-18T00:06:49Z","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":"df0d9eee19b4d9ef9f3035dc93e79c94994f53fabf18984cae26ec011788825d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:30:05Z","title_canon_sha256":"675687ed3e79cc266c06f664dcd7a14e5d7380e148bfd447556238640baf3cee"},"schema_version":"1.0","source":{"id":"1808.10312","kind":"arxiv","version":1}},"canonical_sha256":"fab40e714de27832e70f9cea01fc63e82de12034ce054d85dc98ae95aa87221a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab40e714de27832e70f9cea01fc63e82de12034ce054d85dc98ae95aa87221a","first_computed_at":"2026-05-18T00:06:49.182865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:49.182865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jvmH79i4skAMJtQJdhISdo97zp4Ou3+DItH+Osjj+MQvxkWlNrEnhwucluC107NKskLbTQ+DP9L9f2mQZI1bCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:49.183382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:397cba2c2df0e3df49291f248be01a446a4bff124a2cdc0a3ec6ef1099ec4257","sha256:762fa705f16e5dd95079579f89abf76c143d2528eb039a70e3625252b8087555"],"state_sha256":"75f4a700d3ddba57b4d122b812f3e1985194ca4bd611d99f5413e86e45390fbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"71XcXanUDJdIYduXIFV8IG1ZO/wGQkCFobTEduJL++2RMfFabLf6c2a9MYBFf6r5LI5SKQRhKio/OgaxeFMVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:35:21.253830Z","bundle_sha256":"423df6f1757f18abfa435c4997b8d30890cb56754fca26124bdc3383907544b9"}}