{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QDCTU7A6EZDBLU6JF6A3UJYVUP","short_pith_number":"pith:QDCTU7A6","canonical_record":{"source":{"id":"1112.1498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-07T08:41:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f886385480c8d00736b3ad9bf58e5b165159f919a06ad3d771493c180cc26924","abstract_canon_sha256":"4da36c9f3289a15dd4ab127acab8ec340ff11c925dbc35fa8b6500019ecf1c0e"},"schema_version":"1.0"},"canonical_sha256":"80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5","source":{"kind":"arxiv","id":"1112.1498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1498","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1498v1","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1498","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"QDCTU7A6EZDB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDCTU7A6EZDBLU6J","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDCTU7A6","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QDCTU7A6EZDBLU6JF6A3UJYVUP","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-07T08:41:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f886385480c8d00736b3ad9bf58e5b165159f919a06ad3d771493c180cc26924","abstract_canon_sha256":"4da36c9f3289a15dd4ab127acab8ec340ff11c925dbc35fa8b6500019ecf1c0e"},"schema_version":"1.0"},"canonical_sha256":"80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:54.459537Z","signature_b64":"f1XkQKulSvRRXnDdaK3JzawfEpqyK3VYsRZniaj8XZPyZxPqhoTFzX6VP/2deommcqCfQwwKJ6INoT/yH+GQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5","last_reissued_at":"2026-05-18T04:06:54.459069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:54.459069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1498","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":"2026-05-18T04:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHEBVp6mxO4NIfT3FF3WfE/qnI3L1vbklYTcAScRd2t0N00kX4p/gnVDbSueHWTkKMkGTrRpmkdGuzuLFYqVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:40:16.223930Z"},"content_sha256":"cebf6e5c2a6d06dee05a5de1b2c6075b2f03d195a54b7ced32e3a3a6d70439f8","schema_version":"1.0","event_id":"sha256:cebf6e5c2a6d06dee05a5de1b2c6075b2f03d195a54b7ced32e3a3a6d70439f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QDCTU7A6EZDBLU6JF6A3UJYVUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Weak-Lefschetz property for Artinian Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Alfio Ragusa, Giuseppe Zappala","submitted_at":"2011-12-07T08:41:41Z","abstract_excerpt":"We deal with the Weak Lefschetz property (WLP) for Artinian standard graded Gorenstein algebras of codimension $3.$ We prove that many Gorenstein sequences force the WLP for such algebras. Moreover for every Gorenstein sequence $H$ of codimension 3 we found several Gorenstein Betti sequences compatible with $H$ which again force the WLP. Finally we show that for every Gorenstein Betti sequence the general Artinian standard graded Gorenstein algebra with such Betti sequence has the WLP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1498","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":"2026-05-18T04:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pu6Lg2lSYkz4ZaQZ1cb8k2x3idcXfbavHCzEVDF4OCjUPa+uHJV7BiC5N/0fOdHzLfJLsqZh278I7TYQ68R6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:40:16.224276Z"},"content_sha256":"da3c681d8118ab31bdd79b1f9bf873d3bb51dc259917690bdb7ce895d1a38ef5","schema_version":"1.0","event_id":"sha256:da3c681d8118ab31bdd79b1f9bf873d3bb51dc259917690bdb7ce895d1a38ef5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/bundle.json","state_url":"https://pith.science/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/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":"2026-06-24T22:40:16Z","links":{"resolver":"https://pith.science/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP","bundle":"https://pith.science/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/bundle.json","state":"https://pith.science/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDCTU7A6EZDBLU6JF6A3UJYVUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QDCTU7A6EZDBLU6JF6A3UJYVUP","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":"4da36c9f3289a15dd4ab127acab8ec340ff11c925dbc35fa8b6500019ecf1c0e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-07T08:41:41Z","title_canon_sha256":"f886385480c8d00736b3ad9bf58e5b165159f919a06ad3d771493c180cc26924"},"schema_version":"1.0","source":{"id":"1112.1498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1498","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1498v1","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1498","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"QDCTU7A6EZDB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDCTU7A6EZDBLU6J","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDCTU7A6","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:da3c681d8118ab31bdd79b1f9bf873d3bb51dc259917690bdb7ce895d1a38ef5","target":"graph","created_at":"2026-05-18T04:06:54Z","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 deal with the Weak Lefschetz property (WLP) for Artinian standard graded Gorenstein algebras of codimension $3.$ We prove that many Gorenstein sequences force the WLP for such algebras. Moreover for every Gorenstein sequence $H$ of codimension 3 we found several Gorenstein Betti sequences compatible with $H$ which again force the WLP. Finally we show that for every Gorenstein Betti sequence the general Artinian standard graded Gorenstein algebra with such Betti sequence has the WLP.","authors_text":"Alfio Ragusa, Giuseppe Zappala","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-07T08:41:41Z","title":"On the Weak-Lefschetz property for Artinian Gorenstein algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1498","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:cebf6e5c2a6d06dee05a5de1b2c6075b2f03d195a54b7ced32e3a3a6d70439f8","target":"record","created_at":"2026-05-18T04:06:54Z","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":"4da36c9f3289a15dd4ab127acab8ec340ff11c925dbc35fa8b6500019ecf1c0e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-07T08:41:41Z","title_canon_sha256":"f886385480c8d00736b3ad9bf58e5b165159f919a06ad3d771493c180cc26924"},"schema_version":"1.0","source":{"id":"1112.1498","kind":"arxiv","version":1}},"canonical_sha256":"80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5","first_computed_at":"2026-05-18T04:06:54.459069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:54.459069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1XkQKulSvRRXnDdaK3JzawfEpqyK3VYsRZniaj8XZPyZxPqhoTFzX6VP/2deommcqCfQwwKJ6INoT/yH+GQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:54.459537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebf6e5c2a6d06dee05a5de1b2c6075b2f03d195a54b7ced32e3a3a6d70439f8","sha256:da3c681d8118ab31bdd79b1f9bf873d3bb51dc259917690bdb7ce895d1a38ef5"],"state_sha256":"ae65a845065609ca48307939342320a2dd8ef061444d1e8d3804e33b4e0a66b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ty8kSZdixLa9U6hTHL7o6zOUF8fOzTpvf5GMCX7Gp//JRDuMl4RvAajmEOQK5klc9wCCcUyi8qf/Ild+vahMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:40:16.226271Z","bundle_sha256":"cc842de2261c5a3fc799b2f9584ef82933d114113dbeb6073c6154b3a9bdbbf5"}}