{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YUPB3WNSCHGT4IG5UM7ISNQ2O2","short_pith_number":"pith:YUPB3WNS","canonical_record":{"source":{"id":"1312.2191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-08T10:58:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1bd284ecbf6ce13914f9a212787db1eb043bc82849b77d9e43ab8391b8c8a5f2","abstract_canon_sha256":"4d73a4d7444a2ddcd583d6b2e2984c12a318580c01b573e9d2d1deb9d86e0976"},"schema_version":"1.0"},"canonical_sha256":"c51e1dd9b211cd3e20dda33e89361a76acdd8dc490214b77ebb0cedc33ffd1b1","source":{"kind":"arxiv","id":"1312.2191","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2191","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2191v2","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2191","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"YUPB3WNSCHGT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUPB3WNSCHGT4IG5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUPB3WNS","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YUPB3WNSCHGT4IG5UM7ISNQ2O2","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-08T10:58:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1bd284ecbf6ce13914f9a212787db1eb043bc82849b77d9e43ab8391b8c8a5f2","abstract_canon_sha256":"4d73a4d7444a2ddcd583d6b2e2984c12a318580c01b573e9d2d1deb9d86e0976"},"schema_version":"1.0"},"canonical_sha256":"c51e1dd9b211cd3e20dda33e89361a76acdd8dc490214b77ebb0cedc33ffd1b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:00.664284Z","signature_b64":"IwRlC0psql2LxM0Wd81kV0TY5m/F8ZnVhVb0VdozCqESov4MwEt8C2zx9YxR7mEc8zm3NiKRTjMbUo8/+fyNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51e1dd9b211cd3e20dda33e89361a76acdd8dc490214b77ebb0cedc33ffd1b1","last_reissued_at":"2026-05-18T02:50:00.663624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:00.663624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2191","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z16KQtQz8MMO0hsH+iwRRSblIWA39234xS3VAFhLitVbqEZOBL2hNlyFJp1jYqBII/FJKpJbI+T2ChPX2QLwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:07:00.528572Z"},"content_sha256":"0e8e1b0911360ffe639eb236546a78e8a1877836a4ad98c308ab9661549edcac","schema_version":"1.0","event_id":"sha256:0e8e1b0911360ffe639eb236546a78e8a1877836a4ad98c308ab9661549edcac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YUPB3WNSCHGT4IG5UM7ISNQ2O2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A structure theorem for 2-stretched Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Gianfranco Casnati, Roberto Notari","submitted_at":"2013-12-08T10:58:25Z","abstract_excerpt":"In this paper we study the isomorphism classes of local, Artinian, Gorenstein k-algebras A whose maximal ideal M satisfies dim_k(M^3/M^4)=1 by means of Macaulay's inverse system generalizing a recent result by J. Elias and M.E. Rossi. Then we use such results in order to complete the description of the singular locus of the Gorenstein locus of the punctual Hilbert scheme of degree 11."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2191","kind":"arxiv","version":2},"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":"2026-05-18T02:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d345r8GeUEkUtHBp7B1fsQfaR7GgQ/4GyF4H93RFlKdbFfIilvWIeZtdkEWe2yE11fS0UllA9Ogqi+jkreiCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:07:00.528942Z"},"content_sha256":"24b5836ff135edebc3c201d25c5a025d9588600048338295a5588ffdc4b29f12","schema_version":"1.0","event_id":"sha256:24b5836ff135edebc3c201d25c5a025d9588600048338295a5588ffdc4b29f12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/bundle.json","state_url":"https://pith.science/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/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":"2026-05-27T20:07:00Z","links":{"resolver":"https://pith.science/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2","bundle":"https://pith.science/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/bundle.json","state":"https://pith.science/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUPB3WNSCHGT4IG5UM7ISNQ2O2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YUPB3WNSCHGT4IG5UM7ISNQ2O2","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":"4d73a4d7444a2ddcd583d6b2e2984c12a318580c01b573e9d2d1deb9d86e0976","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-08T10:58:25Z","title_canon_sha256":"1bd284ecbf6ce13914f9a212787db1eb043bc82849b77d9e43ab8391b8c8a5f2"},"schema_version":"1.0","source":{"id":"1312.2191","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2191","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2191v2","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2191","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"YUPB3WNSCHGT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YUPB3WNSCHGT4IG5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YUPB3WNS","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:24b5836ff135edebc3c201d25c5a025d9588600048338295a5588ffdc4b29f12","target":"graph","created_at":"2026-05-18T02:50:00Z","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":"In this paper we study the isomorphism classes of local, Artinian, Gorenstein k-algebras A whose maximal ideal M satisfies dim_k(M^3/M^4)=1 by means of Macaulay's inverse system generalizing a recent result by J. Elias and M.E. Rossi. Then we use such results in order to complete the description of the singular locus of the Gorenstein locus of the punctual Hilbert scheme of degree 11.","authors_text":"Gianfranco Casnati, Roberto Notari","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-08T10:58:25Z","title":"A structure theorem for 2-stretched Gorenstein algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2191","kind":"arxiv","version":2},"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":"sha256:0e8e1b0911360ffe639eb236546a78e8a1877836a4ad98c308ab9661549edcac","target":"record","created_at":"2026-05-18T02:50:00Z","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":"4d73a4d7444a2ddcd583d6b2e2984c12a318580c01b573e9d2d1deb9d86e0976","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-08T10:58:25Z","title_canon_sha256":"1bd284ecbf6ce13914f9a212787db1eb043bc82849b77d9e43ab8391b8c8a5f2"},"schema_version":"1.0","source":{"id":"1312.2191","kind":"arxiv","version":2}},"canonical_sha256":"c51e1dd9b211cd3e20dda33e89361a76acdd8dc490214b77ebb0cedc33ffd1b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c51e1dd9b211cd3e20dda33e89361a76acdd8dc490214b77ebb0cedc33ffd1b1","first_computed_at":"2026-05-18T02:50:00.663624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:00.663624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IwRlC0psql2LxM0Wd81kV0TY5m/F8ZnVhVb0VdozCqESov4MwEt8C2zx9YxR7mEc8zm3NiKRTjMbUo8/+fyNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:00.664284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2191","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e8e1b0911360ffe639eb236546a78e8a1877836a4ad98c308ab9661549edcac","sha256:24b5836ff135edebc3c201d25c5a025d9588600048338295a5588ffdc4b29f12"],"state_sha256":"7f72cb8b440a7c88f29ba72f41a06909659da4f7c999f1c093dbe54e1687588f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4eUe2VjkoGzI9LQpDBO6EZGdVJ1XXeb+wE4PC4zkjEksI7Npk+Z17nRCmy58Sja9bo8h3AtgXx6GX1Cnu4RBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:07:00.532138Z","bundle_sha256":"ea07535df1265a951e983ac43f5bdbe701fc80834556865b6a8498645dc3688f"}}