{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EFG5BI6G54PECBR6ZV3D5NBNAD","short_pith_number":"pith:EFG5BI6G","canonical_record":{"source":{"id":"1304.5152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-17T13:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"4ebd27c915df2aa3cbc200d87e6e1e2a93e5035e0396a96e226e2b8a781da97b","abstract_canon_sha256":"bd86fe3c8d691e3f37c01dc1aa2bc0abac3d1d0c65588d75ff97b5283832c605"},"schema_version":"1.0"},"canonical_sha256":"214dd0a3c6ef1e41063ecd763eb42d00c7956d3161feedfa65066427a3e1c1de","source":{"kind":"arxiv","id":"1304.5152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5152","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5152v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5152","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"EFG5BI6G54PE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EFG5BI6G54PECBR6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EFG5BI6G","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EFG5BI6G54PECBR6ZV3D5NBNAD","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-17T13:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"4ebd27c915df2aa3cbc200d87e6e1e2a93e5035e0396a96e226e2b8a781da97b","abstract_canon_sha256":"bd86fe3c8d691e3f37c01dc1aa2bc0abac3d1d0c65588d75ff97b5283832c605"},"schema_version":"1.0"},"canonical_sha256":"214dd0a3c6ef1e41063ecd763eb42d00c7956d3161feedfa65066427a3e1c1de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:41.629215Z","signature_b64":"ifaWa4ohdJyPVAKkqBtPBJE15OoU/2BlNBeVkf1uTtUVt82kXlgEwl/z6RBctLCNn0tK9HGdk/+bB3up2iJHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"214dd0a3c6ef1e41063ecd763eb42d00c7956d3161feedfa65066427a3e1c1de","last_reissued_at":"2026-05-18T03:27:41.628596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:41.628596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5152","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KBB0CkLl9zqT6R0yK3k/jN/AtmJ91ofPWZla95SKwgRNVAd2pWGgh6+kB9MLnzFujEbo4v0S6xG5CVgUuga9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:50:40.985026Z"},"content_sha256":"735ff2c0c5cc4e77d1d197d4af73b525ec667f4488fee60ec5ece3e88301ad38","schema_version":"1.0","event_id":"sha256:735ff2c0c5cc4e77d1d197d4af73b525ec667f4488fee60ec5ece3e88301ad38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EFG5BI6G54PECBR6ZV3D5NBNAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow up and Blur constructions in Algebraic Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-17T13:50:04Z","abstract_excerpt":"The idea in the title is to blow up a finite structure, replacing each 'colour or atom' by infinitely many, using blurs to represent the resulting term algebra, but the blurs are not enough to blur the structure of the finite structure in the complex algebra. Then, the latter cannot be representable due to a {finite- infinite} contradiction. This structure can be a finite clique in a graph or a finite relation algebra or a finite cylindric algebra. This theme gives examples of weakly representable atom structures that are not strongly representable. Many constructions existing in the literatur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5152","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYfAo6TonueVeaWKq5lsR/usSwCRzkjFTTISOqq4aH0yTCAR1fPPc4nPgdRo1SiuXEXXY+2z7Q/p6Y3GW2xiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:50:40.985383Z"},"content_sha256":"b604c67f989784ef4a200f18022694771a1ce3dd0295badf64d11f52d32a9d52","schema_version":"1.0","event_id":"sha256:b604c67f989784ef4a200f18022694771a1ce3dd0295badf64d11f52d32a9d52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/bundle.json","state_url":"https://pith.science/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/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":"2026-06-26T16:50:40Z","links":{"resolver":"https://pith.science/pith/EFG5BI6G54PECBR6ZV3D5NBNAD","bundle":"https://pith.science/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/bundle.json","state":"https://pith.science/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFG5BI6G54PECBR6ZV3D5NBNAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EFG5BI6G54PECBR6ZV3D5NBNAD","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":"bd86fe3c8d691e3f37c01dc1aa2bc0abac3d1d0c65588d75ff97b5283832c605","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-17T13:50:04Z","title_canon_sha256":"4ebd27c915df2aa3cbc200d87e6e1e2a93e5035e0396a96e226e2b8a781da97b"},"schema_version":"1.0","source":{"id":"1304.5152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5152","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5152v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5152","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"EFG5BI6G54PE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EFG5BI6G54PECBR6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EFG5BI6G","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b604c67f989784ef4a200f18022694771a1ce3dd0295badf64d11f52d32a9d52","target":"graph","created_at":"2026-05-18T03:27:41Z","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 idea in the title is to blow up a finite structure, replacing each 'colour or atom' by infinitely many, using blurs to represent the resulting term algebra, but the blurs are not enough to blur the structure of the finite structure in the complex algebra. Then, the latter cannot be representable due to a {finite- infinite} contradiction. This structure can be a finite clique in a graph or a finite relation algebra or a finite cylindric algebra. This theme gives examples of weakly representable atom structures that are not strongly representable. Many constructions existing in the literatur","authors_text":"Tarek Sayed Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-17T13:50:04Z","title":"Blow up and Blur constructions in Algebraic Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5152","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":"sha256:735ff2c0c5cc4e77d1d197d4af73b525ec667f4488fee60ec5ece3e88301ad38","target":"record","created_at":"2026-05-18T03:27:41Z","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":"bd86fe3c8d691e3f37c01dc1aa2bc0abac3d1d0c65588d75ff97b5283832c605","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-17T13:50:04Z","title_canon_sha256":"4ebd27c915df2aa3cbc200d87e6e1e2a93e5035e0396a96e226e2b8a781da97b"},"schema_version":"1.0","source":{"id":"1304.5152","kind":"arxiv","version":1}},"canonical_sha256":"214dd0a3c6ef1e41063ecd763eb42d00c7956d3161feedfa65066427a3e1c1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"214dd0a3c6ef1e41063ecd763eb42d00c7956d3161feedfa65066427a3e1c1de","first_computed_at":"2026-05-18T03:27:41.628596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.628596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifaWa4ohdJyPVAKkqBtPBJE15OoU/2BlNBeVkf1uTtUVt82kXlgEwl/z6RBctLCNn0tK9HGdk/+bB3up2iJHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.629215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:735ff2c0c5cc4e77d1d197d4af73b525ec667f4488fee60ec5ece3e88301ad38","sha256:b604c67f989784ef4a200f18022694771a1ce3dd0295badf64d11f52d32a9d52"],"state_sha256":"64a0d110243a649f9da90a8d72fdc9098b0626f49cff84934cac97979d09b428"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fy40FSsWUny0s1AoYTkJyM0l2BRVIXSO2kbFlu8BeMiA0AWxjBKLRjadGPBmTX6k4c8ZCBGBMzLeGu1NeUAqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:50:40.987244Z","bundle_sha256":"934eb9de15f045c734a60631bff42a302ab1069ac1eb2132fbb2ab0bcae647fd"}}