{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2JLULW7VO4DZYV5NUVKOYC7GCX","short_pith_number":"pith:2JLULW7V","canonical_record":{"source":{"id":"1304.1537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-04T15:08:57Z","cross_cats_sorted":[],"title_canon_sha256":"00e9fa2b125189eaa2eb8bcdb7ae0202fa80f1f29f8289b29b9a41e798617c83","abstract_canon_sha256":"aab2123c388c8aa6f86e22dab617eb5869f15fa9e5b1f1a4c3ca73c570fc1a6e"},"schema_version":"1.0"},"canonical_sha256":"d25745dbf577079c57ada554ec0be615fc64a6b24813988a4f8cb015f45f8f8f","source":{"kind":"arxiv","id":"1304.1537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1537","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1537v1","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1537","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"2JLULW7VO4DZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JLULW7VO4DZYV5N","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JLULW7V","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2JLULW7VO4DZYV5NUVKOYC7GCX","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-04T15:08:57Z","cross_cats_sorted":[],"title_canon_sha256":"00e9fa2b125189eaa2eb8bcdb7ae0202fa80f1f29f8289b29b9a41e798617c83","abstract_canon_sha256":"aab2123c388c8aa6f86e22dab617eb5869f15fa9e5b1f1a4c3ca73c570fc1a6e"},"schema_version":"1.0"},"canonical_sha256":"d25745dbf577079c57ada554ec0be615fc64a6b24813988a4f8cb015f45f8f8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:55.438833Z","signature_b64":"q5uMJhEOIBzJ+gZxu8l0jLecOWX60lOEQes98rPY0zjS2Z6ZuRR/WPUnQ0wKjI81QEclAcUpoimjNgCdmgN5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d25745dbf577079c57ada554ec0be615fc64a6b24813988a4f8cb015f45f8f8f","last_reissued_at":"2026-05-18T03:28:55.438305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:55.438305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1537","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":"2026-05-18T03:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TM7Mwmb+RpsYQ57qhxElSXnZBRNYix5Y/cOniUvOMzrw5XdKH6lBUmBgwS3n3bt/FD2pFq+s/MY818iNAx9UDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:07:18.282440Z"},"content_sha256":"d0129a600d1c1212f6beb290610e2c3d1086d44b91ad09c0c2fa5c5152f38f59","schema_version":"1.0","event_id":"sha256:d0129a600d1c1212f6beb290610e2c3d1086d44b91ad09c0c2fa5c5152f38f59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2JLULW7VO4DZYV5NUVKOYC7GCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Amalgmation in Boolean algebras with operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-04T15:08:57Z","abstract_excerpt":"We study various forms of amalgamation for Boolean algebras with operations. We will also have the occasion to weaken the Boolean structure dealing with MV and BL algebras with operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1537","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":"2026-05-18T03:28:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28jB24j6blCjPaKuFyhWaaKO4PEeSkmnlk5ea6cPT8fZ6iFtCXpWMPEv0ZPI0Wt7ruVzz8ljMoTSX+po8PHBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:07:18.282786Z"},"content_sha256":"241cbc1cebf21d5f4e429333f369ebaa1d1d316e9590ca6a67edee8055214ef1","schema_version":"1.0","event_id":"sha256:241cbc1cebf21d5f4e429333f369ebaa1d1d316e9590ca6a67edee8055214ef1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/bundle.json","state_url":"https://pith.science/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/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":"2026-06-26T10:07:18Z","links":{"resolver":"https://pith.science/pith/2JLULW7VO4DZYV5NUVKOYC7GCX","bundle":"https://pith.science/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/bundle.json","state":"https://pith.science/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JLULW7VO4DZYV5NUVKOYC7GCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2JLULW7VO4DZYV5NUVKOYC7GCX","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":"aab2123c388c8aa6f86e22dab617eb5869f15fa9e5b1f1a4c3ca73c570fc1a6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-04T15:08:57Z","title_canon_sha256":"00e9fa2b125189eaa2eb8bcdb7ae0202fa80f1f29f8289b29b9a41e798617c83"},"schema_version":"1.0","source":{"id":"1304.1537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1537","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1537v1","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1537","created_at":"2026-05-18T03:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"2JLULW7VO4DZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JLULW7VO4DZYV5N","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JLULW7V","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:241cbc1cebf21d5f4e429333f369ebaa1d1d316e9590ca6a67edee8055214ef1","target":"graph","created_at":"2026-05-18T03:28:55Z","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 study various forms of amalgamation for Boolean algebras with operations. We will also have the occasion to weaken the Boolean structure dealing with MV and BL algebras with operators.","authors_text":"Tarek Sayed Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-04T15:08:57Z","title":"Amalgmation in Boolean algebras with operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1537","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:d0129a600d1c1212f6beb290610e2c3d1086d44b91ad09c0c2fa5c5152f38f59","target":"record","created_at":"2026-05-18T03:28:55Z","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":"aab2123c388c8aa6f86e22dab617eb5869f15fa9e5b1f1a4c3ca73c570fc1a6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-04T15:08:57Z","title_canon_sha256":"00e9fa2b125189eaa2eb8bcdb7ae0202fa80f1f29f8289b29b9a41e798617c83"},"schema_version":"1.0","source":{"id":"1304.1537","kind":"arxiv","version":1}},"canonical_sha256":"d25745dbf577079c57ada554ec0be615fc64a6b24813988a4f8cb015f45f8f8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d25745dbf577079c57ada554ec0be615fc64a6b24813988a4f8cb015f45f8f8f","first_computed_at":"2026-05-18T03:28:55.438305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:55.438305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5uMJhEOIBzJ+gZxu8l0jLecOWX60lOEQes98rPY0zjS2Z6ZuRR/WPUnQ0wKjI81QEclAcUpoimjNgCdmgN5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:55.438833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0129a600d1c1212f6beb290610e2c3d1086d44b91ad09c0c2fa5c5152f38f59","sha256:241cbc1cebf21d5f4e429333f369ebaa1d1d316e9590ca6a67edee8055214ef1"],"state_sha256":"dd76bfccd5690859fc4d791c0cadbfc61fca38af1a9b09a674cdb1fb1d529d56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqznkqiOsSqZwRfXJT98s/j10L/mKCzk174BYkD3FCGJ+0hZn3aQDOa8b+lasrrZP/ih750Yk4Ciimj65tk+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:07:18.284798Z","bundle_sha256":"202c827310264ba35ab61045c601251dbebaf848d90707d770765c3e20a5461f"}}