{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ABRELWO2LN6PMAEFIFRAP7CMIF","short_pith_number":"pith:ABRELWO2","canonical_record":{"source":{"id":"1505.05210","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T23:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"aaf4f64ae15e8ff5800b1afcc094fe8e4f078a93fc207fc8f1b75370a598a588","abstract_canon_sha256":"1c1b1acd92374f051b2a1823b3600c4152c7e4afa3c88a4f4582035328912819"},"schema_version":"1.0"},"canonical_sha256":"006245d9da5b7cf60085416207fc4c41607d06800dce18cfb6e79ad23665f936","source":{"kind":"arxiv","id":"1505.05210","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05210","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05210v2","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05210","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"ABRELWO2LN6P","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABRELWO2LN6PMAEF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABRELWO2","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ABRELWO2LN6PMAEFIFRAP7CMIF","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05210","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T23:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"aaf4f64ae15e8ff5800b1afcc094fe8e4f078a93fc207fc8f1b75370a598a588","abstract_canon_sha256":"1c1b1acd92374f051b2a1823b3600c4152c7e4afa3c88a4f4582035328912819"},"schema_version":"1.0"},"canonical_sha256":"006245d9da5b7cf60085416207fc4c41607d06800dce18cfb6e79ad23665f936","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:00.477311Z","signature_b64":"U1xsg+pohi2iFEFhxjQ5jGqoHmhGw5ItDXIPIR5PgCzABFM58QCYSPXlO1eBvlMtAom7ZAn80EJfthGxJ06wAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"006245d9da5b7cf60085416207fc4c41607d06800dce18cfb6e79ad23665f936","last_reissued_at":"2026-05-18T00:21:00.476843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:00.476843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05210","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":"2026-05-18T00:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J41h3a18ext2C8+TZObDxhfAqy+AQFL6DCGaMSE6oWCfBOZP5Y9z3D65rx3OSVrsuzZX1ybqvZlvt9+IG0pPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:04:09.037584Z"},"content_sha256":"7a6a6f16924d35639d47621829ed83a87c30eed3b8d114677cdd00a70059a531","schema_version":"1.0","event_id":"sha256:7a6a6f16924d35639d47621829ed83a87c30eed3b8d114677cdd00a70059a531"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ABRELWO2LN6PMAEFIFRAP7CMIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The equations defining blowup algebras of height three Gorenstein ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin, Bernd Ulrich, Claudia Polini","submitted_at":"2015-05-19T23:33:46Z","abstract_excerpt":"We find the defining equations of Rees rings of linearly presented height three Gorenstein ideals. To prove our main theorem we use local cohomology techniques to bound the maximum generator degree of the torsion submodule of symmetric powers in order to conclude that the defining equations of the Rees algebra and the special fiber ring have the same image in the symmetric algebra. We show that this image is the unmixed part of the ideal generated by the maximal minors of a matrix of linear forms which is annihilated by a vector of indeterminates, and otherwise has maximal possible grade. An i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05210","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":"2026-05-18T00:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+5S+JTfWtfxMn9WClQbXBUwEBTN3XW+9iV04PoVtRs+tPfUifFufjE4idj41WwBHV/arjF8/hPP7xYf0bJhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:04:09.037951Z"},"content_sha256":"af6a36fafc1a778a967000f64eb8275479f7c5374cdd053245d3d9ad8d56b3ec","schema_version":"1.0","event_id":"sha256:af6a36fafc1a778a967000f64eb8275479f7c5374cdd053245d3d9ad8d56b3ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/bundle.json","state_url":"https://pith.science/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/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":"2026-06-21T20:04:09Z","links":{"resolver":"https://pith.science/pith/ABRELWO2LN6PMAEFIFRAP7CMIF","bundle":"https://pith.science/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/bundle.json","state":"https://pith.science/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABRELWO2LN6PMAEFIFRAP7CMIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ABRELWO2LN6PMAEFIFRAP7CMIF","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":"1c1b1acd92374f051b2a1823b3600c4152c7e4afa3c88a4f4582035328912819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T23:33:46Z","title_canon_sha256":"aaf4f64ae15e8ff5800b1afcc094fe8e4f078a93fc207fc8f1b75370a598a588"},"schema_version":"1.0","source":{"id":"1505.05210","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05210","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05210v2","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05210","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"ABRELWO2LN6P","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABRELWO2LN6PMAEF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABRELWO2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:af6a36fafc1a778a967000f64eb8275479f7c5374cdd053245d3d9ad8d56b3ec","target":"graph","created_at":"2026-05-18T00:21:00Z","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":"We find the defining equations of Rees rings of linearly presented height three Gorenstein ideals. To prove our main theorem we use local cohomology techniques to bound the maximum generator degree of the torsion submodule of symmetric powers in order to conclude that the defining equations of the Rees algebra and the special fiber ring have the same image in the symmetric algebra. We show that this image is the unmixed part of the ideal generated by the maximal minors of a matrix of linear forms which is annihilated by a vector of indeterminates, and otherwise has maximal possible grade. An i","authors_text":"Andrew R. Kustin, Bernd Ulrich, Claudia Polini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T23:33:46Z","title":"The equations defining blowup algebras of height three Gorenstein ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05210","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":"sha256:7a6a6f16924d35639d47621829ed83a87c30eed3b8d114677cdd00a70059a531","target":"record","created_at":"2026-05-18T00:21:00Z","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":"1c1b1acd92374f051b2a1823b3600c4152c7e4afa3c88a4f4582035328912819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-19T23:33:46Z","title_canon_sha256":"aaf4f64ae15e8ff5800b1afcc094fe8e4f078a93fc207fc8f1b75370a598a588"},"schema_version":"1.0","source":{"id":"1505.05210","kind":"arxiv","version":2}},"canonical_sha256":"006245d9da5b7cf60085416207fc4c41607d06800dce18cfb6e79ad23665f936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"006245d9da5b7cf60085416207fc4c41607d06800dce18cfb6e79ad23665f936","first_computed_at":"2026-05-18T00:21:00.476843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.476843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U1xsg+pohi2iFEFhxjQ5jGqoHmhGw5ItDXIPIR5PgCzABFM58QCYSPXlO1eBvlMtAom7ZAn80EJfthGxJ06wAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.477311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05210","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a6a6f16924d35639d47621829ed83a87c30eed3b8d114677cdd00a70059a531","sha256:af6a36fafc1a778a967000f64eb8275479f7c5374cdd053245d3d9ad8d56b3ec"],"state_sha256":"bb976a9e11238e06329f84a56cd16be5bad1d93aa5824326cf8b75433cc9e6be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYMI6g4q3M21U7aVKmXbmnjxnmxmIR7IM93bTp6T0EXsC/tkqbZiyiW/+d0zNJY6XST02h4JqUmCtqEyLpowCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:04:09.039928Z","bundle_sha256":"8e33ac1f38241ac7bdf3dc97aa55f496bd74095af0251d39615ec9eeacf5eba5"}}