{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EPLYGJEWVB6V3QMJKC7AH7VGOH","short_pith_number":"pith:EPLYGJEW","canonical_record":{"source":{"id":"1503.02651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-09T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"e6170844fe479c9b37d7a27dbc0fd41aee05ca79c465a5d0aa902769bb8a0a26","abstract_canon_sha256":"e20dd5aac6ce04d32fda501b3cf37b59ed7d1e480e80c5a2d4c4214026782b15"},"schema_version":"1.0"},"canonical_sha256":"23d7832496a87d5dc18950be03fea671e0f028a39899e1b7708c6f5738d6fb86","source":{"kind":"arxiv","id":"1503.02651","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02651","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02651v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02651","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"EPLYGJEWVB6V","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EPLYGJEWVB6V3QMJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EPLYGJEW","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EPLYGJEWVB6V3QMJKC7AH7VGOH","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-09T19:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"e6170844fe479c9b37d7a27dbc0fd41aee05ca79c465a5d0aa902769bb8a0a26","abstract_canon_sha256":"e20dd5aac6ce04d32fda501b3cf37b59ed7d1e480e80c5a2d4c4214026782b15"},"schema_version":"1.0"},"canonical_sha256":"23d7832496a87d5dc18950be03fea671e0f028a39899e1b7708c6f5738d6fb86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.281968Z","signature_b64":"iyDTqIzT56GcBYzSfTkm5YwTCXdWSlSGpqLvS8rjXfVfUgVXwueM2qKrJv84T32prCaziNoOBjJ1eb7kHTmyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23d7832496a87d5dc18950be03fea671e0f028a39899e1b7708c6f5738d6fb86","last_reissued_at":"2026-05-18T02:25:19.281625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.281625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02651","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJ4HFtrmM55+qW6MZpFuJQLkFAdwxZ2OevJrC1mD2JhQxU9N4u8lS2gV/O5fpEqdRJ9KdHjblcancdrE8qwwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:45:22.525862Z"},"content_sha256":"5e4dfa62a99f4b5961abaad90772d519331d68e0a4dc6457b6964e854661b223","schema_version":"1.0","event_id":"sha256:5e4dfa62a99f4b5961abaad90772d519331d68e0a4dc6457b6964e854661b223"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EPLYGJEWVB6V3QMJKC7AH7VGOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite Abelian algebras are dualizable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Pierre Gillibert","submitted_at":"2015-03-09T19:53:28Z","abstract_excerpt":"A finite algebra $\\bA=\\alg{A;\\cF}$ is \\emph{dualizable} if there exists a discrete topological relational structure $\\BA=\\alg{A;\\cG;\\cT}$, compatible with $\\cF$, such that the canonical evaluation map $e\\_{\\bB}\\colon \\bB\\to \\Hom( \\Hom(\\bB,\\bA),\\BA)$ is an isomorphism for every $\\bB$ in the quasivariety generated by $\\bA$. Here, $e\\_{\\bB}$ is defined by $e\\_{\\bB}(x)(f)=f(x)$ for all $x\\in B$ and all $f\\in \\Hom(\\bB,\\bA)$.\n\nWe prove that, given a finite congruence-modular Abelian algebra $\\bA$, the set of all relations compatible with $\\bA$, up to a certain arity, \\emph{entails} the whole set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02651","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zDxVzbB39sTUCJ+0h8EGqloLr1vNKUgRSejyKK3tIg+qm09PQIkdcYNPXN8HN/HdDD9UCNtPCPPndkL5M4cKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:45:22.526205Z"},"content_sha256":"961b42c0ac1c6976e5d59b9e2ae95f2b98ce5eb7a9695963b33d2948d432ddf4","schema_version":"1.0","event_id":"sha256:961b42c0ac1c6976e5d59b9e2ae95f2b98ce5eb7a9695963b33d2948d432ddf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/bundle.json","state_url":"https://pith.science/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/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":"2026-06-21T20:45:22Z","links":{"resolver":"https://pith.science/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH","bundle":"https://pith.science/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/bundle.json","state":"https://pith.science/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPLYGJEWVB6V3QMJKC7AH7VGOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EPLYGJEWVB6V3QMJKC7AH7VGOH","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":"e20dd5aac6ce04d32fda501b3cf37b59ed7d1e480e80c5a2d4c4214026782b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-09T19:53:28Z","title_canon_sha256":"e6170844fe479c9b37d7a27dbc0fd41aee05ca79c465a5d0aa902769bb8a0a26"},"schema_version":"1.0","source":{"id":"1503.02651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02651","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02651v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02651","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"EPLYGJEWVB6V","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EPLYGJEWVB6V3QMJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EPLYGJEW","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:961b42c0ac1c6976e5d59b9e2ae95f2b98ce5eb7a9695963b33d2948d432ddf4","target":"graph","created_at":"2026-05-18T02:25:19Z","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":"A finite algebra $\\bA=\\alg{A;\\cF}$ is \\emph{dualizable} if there exists a discrete topological relational structure $\\BA=\\alg{A;\\cG;\\cT}$, compatible with $\\cF$, such that the canonical evaluation map $e\\_{\\bB}\\colon \\bB\\to \\Hom( \\Hom(\\bB,\\bA),\\BA)$ is an isomorphism for every $\\bB$ in the quasivariety generated by $\\bA$. Here, $e\\_{\\bB}$ is defined by $e\\_{\\bB}(x)(f)=f(x)$ for all $x\\in B$ and all $f\\in \\Hom(\\bB,\\bA)$.\n\nWe prove that, given a finite congruence-modular Abelian algebra $\\bA$, the set of all relations compatible with $\\bA$, up to a certain arity, \\emph{entails} the whole set of ","authors_text":"Pierre Gillibert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-09T19:53:28Z","title":"Finite Abelian algebras are dualizable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02651","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":"sha256:5e4dfa62a99f4b5961abaad90772d519331d68e0a4dc6457b6964e854661b223","target":"record","created_at":"2026-05-18T02:25:19Z","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":"e20dd5aac6ce04d32fda501b3cf37b59ed7d1e480e80c5a2d4c4214026782b15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-09T19:53:28Z","title_canon_sha256":"e6170844fe479c9b37d7a27dbc0fd41aee05ca79c465a5d0aa902769bb8a0a26"},"schema_version":"1.0","source":{"id":"1503.02651","kind":"arxiv","version":1}},"canonical_sha256":"23d7832496a87d5dc18950be03fea671e0f028a39899e1b7708c6f5738d6fb86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23d7832496a87d5dc18950be03fea671e0f028a39899e1b7708c6f5738d6fb86","first_computed_at":"2026-05-18T02:25:19.281625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.281625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iyDTqIzT56GcBYzSfTkm5YwTCXdWSlSGpqLvS8rjXfVfUgVXwueM2qKrJv84T32prCaziNoOBjJ1eb7kHTmyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.281968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e4dfa62a99f4b5961abaad90772d519331d68e0a4dc6457b6964e854661b223","sha256:961b42c0ac1c6976e5d59b9e2ae95f2b98ce5eb7a9695963b33d2948d432ddf4"],"state_sha256":"7553d0afe915b2523a61d4f3653671cecb9b1b102384b54cdac00200fcf02431"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3G+4Fl9DUGUwYeOL6fVDHonSs+cASkiIjcc1vj8SsUYZdBd6pIzFddal0nSRbJ+J4zGX8CfB+2VtQW98RYaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:45:22.528183Z","bundle_sha256":"3db0ed272b2f76a47ba741b078b5f230cd2e73f22ffedb46f3dba6dc67d89a89"}}