{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EKEYBBEADPXKPK7XM5PCMA6YT6","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":"efcdbb97010d6489ab433e90eb29b663a9c08fb22f02cf5f9bea61ae4875edc5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-18T08:31:53Z","title_canon_sha256":"38c0643db453c969b0231b1d85c5b74a4ea97f1ff1248390190726f624cba0d5"},"schema_version":"1.0","source":{"id":"1212.4265","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4265","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4265v3","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4265","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"EKEYBBEADPXK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EKEYBBEADPXKPK7X","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EKEYBBEA","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:14f4742b752438a8fd5074bd4d3d315587975464055d9e198076c2f1258fae1e","target":"graph","created_at":"2026-05-18T02:55:19Z","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":"It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a non-extension theorem.","authors_text":"Andreea Nicoara, Fabrizio Broglia, Francesca Acquistapace, Michail Bronshtein, Nahum Zobin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-18T08:31:53Z","title":"Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4265","kind":"arxiv","version":3},"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":"sha256:7a0c83256851a53ecdd291cbf4aca6b59cf492b0f6bf96f4c2200ab32db7c05f","target":"record","created_at":"2026-05-18T02:55:19Z","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":"efcdbb97010d6489ab433e90eb29b663a9c08fb22f02cf5f9bea61ae4875edc5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-18T08:31:53Z","title_canon_sha256":"38c0643db453c969b0231b1d85c5b74a4ea97f1ff1248390190726f624cba0d5"},"schema_version":"1.0","source":{"id":"1212.4265","kind":"arxiv","version":3}},"canonical_sha256":"22898084801beea7abf7675e2603d89f85f656f8c22fca4d9315e87bfcf8ece7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22898084801beea7abf7675e2603d89f85f656f8c22fca4d9315e87bfcf8ece7","first_computed_at":"2026-05-18T02:55:19.429075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:19.429075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOi88lM9Q+5UtUnweLo0B+Pqk15LIss6YjaFYRCAVphs6f5eNi4FrOQ/D7Gop3L8utRr+TwzYAjzFtfLCP4BBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:19.429501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4265","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a0c83256851a53ecdd291cbf4aca6b59cf492b0f6bf96f4c2200ab32db7c05f","sha256:14f4742b752438a8fd5074bd4d3d315587975464055d9e198076c2f1258fae1e"],"state_sha256":"a94ad57ab7ff54858cfd91934769f0be4269a5aba6efee36ddd935cff263e821"}