{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:F3GTY27VNPP23ZJSQJADOGLPHM","short_pith_number":"pith:F3GTY27V","canonical_record":{"source":{"id":"1207.1790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-07T12:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"2ff2ab4af74e1642866af6e395ed52cde15136908cecb3de59a986e42c9402f6","abstract_canon_sha256":"8533f95f93a9cb10f310da686ae4e5f1593e6114b78351fe67f0315400167de3"},"schema_version":"1.0"},"canonical_sha256":"2ecd3c6bf56bdfade532824037196f3b0d3cdd9f54544c30fc36e5f2d5dc1df8","source":{"kind":"arxiv","id":"1207.1790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1790","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1790v1","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1790","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"F3GTY27VNPP2","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F3GTY27VNPP23ZJS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F3GTY27V","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:F3GTY27VNPP23ZJSQJADOGLPHM","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-07T12:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"2ff2ab4af74e1642866af6e395ed52cde15136908cecb3de59a986e42c9402f6","abstract_canon_sha256":"8533f95f93a9cb10f310da686ae4e5f1593e6114b78351fe67f0315400167de3"},"schema_version":"1.0"},"canonical_sha256":"2ecd3c6bf56bdfade532824037196f3b0d3cdd9f54544c30fc36e5f2d5dc1df8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.073483Z","signature_b64":"mIogCQ2JgnKzYGNNFjfmQooKKSDIGbr0M3tDGeBpA0zWgatVjKKu2Sl7JlF6kKPaRZPb2J7OjW1MezWmo6M5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ecd3c6bf56bdfade532824037196f3b0d3cdd9f54544c30fc36e5f2d5dc1df8","last_reissued_at":"2026-05-18T01:11:52.073119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.073119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1790","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":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckPQWTCF8gGm6h1raLal9yBhNsQjYT6NwL4/MrifK+3e8fn83R5UoUVlYYVH69vv8y7o4XTXkw3fiWHHMJXzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:26:26.369972Z"},"content_sha256":"98ed98dd4a426c6924cf7fc47d6836d5606966cd3efe877a751099f01d1622dd","schema_version":"1.0","event_id":"sha256:98ed98dd4a426c6924cf7fc47d6836d5606966cd3efe877a751099f01d1622dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:F3GTY27VNPP23ZJSQJADOGLPHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity and Free Resolution of Ideals which are Minimal to $d$-linearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Akbar Yazdan Pour, Marcel Morales, Rashid Zaare-Nahandi","submitted_at":"2012-07-07T12:06:43Z","abstract_excerpt":"Toward a partial classification of monomial ideals with $d$-linear resolution, in this paper, some classes of $d$-uniform clutters which do not have linear resolution, but every proper subclutter of them has a $d$-linear resolution, are introduced and the regularity and Betti numbers of circuit ideals of such clutters are computed. Also, it is proved that for given two $d$-uniform clutters $\\mathcal{C}_1, \\mathcal{C}_2$, the Castelnuovo-Mumford regularity of the ideal $I(\\bar{\\mathcal{C}_1 \\cup \\mathcal{C}_2})$ is equal to the maximum of regularities of $I(\\bar{\\C}_1)$ and $I(\\bar{\\C}_2)$, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1790","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":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+/0Yn1m6rWmkGnpMn7BI5WrdS613I3q5HluJlTsjUnX7ss3Ve9jCx+5NwFmiTWaLqsqv+8f5O9A2lJNGG0HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:26:26.370673Z"},"content_sha256":"91cbb8b5530fade066f6d0a7a99abb33bcd1a90d4f34fb0b87ab3979863c4c00","schema_version":"1.0","event_id":"sha256:91cbb8b5530fade066f6d0a7a99abb33bcd1a90d4f34fb0b87ab3979863c4c00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3GTY27VNPP23ZJSQJADOGLPHM/bundle.json","state_url":"https://pith.science/pith/F3GTY27VNPP23ZJSQJADOGLPHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3GTY27VNPP23ZJSQJADOGLPHM/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":"2026-06-07T14:26:26Z","links":{"resolver":"https://pith.science/pith/F3GTY27VNPP23ZJSQJADOGLPHM","bundle":"https://pith.science/pith/F3GTY27VNPP23ZJSQJADOGLPHM/bundle.json","state":"https://pith.science/pith/F3GTY27VNPP23ZJSQJADOGLPHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3GTY27VNPP23ZJSQJADOGLPHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F3GTY27VNPP23ZJSQJADOGLPHM","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":"8533f95f93a9cb10f310da686ae4e5f1593e6114b78351fe67f0315400167de3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-07T12:06:43Z","title_canon_sha256":"2ff2ab4af74e1642866af6e395ed52cde15136908cecb3de59a986e42c9402f6"},"schema_version":"1.0","source":{"id":"1207.1790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1790","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1790v1","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1790","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"F3GTY27VNPP2","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F3GTY27VNPP23ZJS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F3GTY27V","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:91cbb8b5530fade066f6d0a7a99abb33bcd1a90d4f34fb0b87ab3979863c4c00","target":"graph","created_at":"2026-05-18T01:11:52Z","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":"Toward a partial classification of monomial ideals with $d$-linear resolution, in this paper, some classes of $d$-uniform clutters which do not have linear resolution, but every proper subclutter of them has a $d$-linear resolution, are introduced and the regularity and Betti numbers of circuit ideals of such clutters are computed. Also, it is proved that for given two $d$-uniform clutters $\\mathcal{C}_1, \\mathcal{C}_2$, the Castelnuovo-Mumford regularity of the ideal $I(\\bar{\\mathcal{C}_1 \\cup \\mathcal{C}_2})$ is equal to the maximum of regularities of $I(\\bar{\\C}_1)$ and $I(\\bar{\\C}_2)$, whe","authors_text":"Ali Akbar Yazdan Pour, Marcel Morales, Rashid Zaare-Nahandi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-07T12:06:43Z","title":"Regularity and Free Resolution of Ideals which are Minimal to $d$-linearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1790","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":"sha256:98ed98dd4a426c6924cf7fc47d6836d5606966cd3efe877a751099f01d1622dd","target":"record","created_at":"2026-05-18T01:11:52Z","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":"8533f95f93a9cb10f310da686ae4e5f1593e6114b78351fe67f0315400167de3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-07T12:06:43Z","title_canon_sha256":"2ff2ab4af74e1642866af6e395ed52cde15136908cecb3de59a986e42c9402f6"},"schema_version":"1.0","source":{"id":"1207.1790","kind":"arxiv","version":1}},"canonical_sha256":"2ecd3c6bf56bdfade532824037196f3b0d3cdd9f54544c30fc36e5f2d5dc1df8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ecd3c6bf56bdfade532824037196f3b0d3cdd9f54544c30fc36e5f2d5dc1df8","first_computed_at":"2026-05-18T01:11:52.073119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:52.073119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mIogCQ2JgnKzYGNNFjfmQooKKSDIGbr0M3tDGeBpA0zWgatVjKKu2Sl7JlF6kKPaRZPb2J7OjW1MezWmo6M5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:52.073483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98ed98dd4a426c6924cf7fc47d6836d5606966cd3efe877a751099f01d1622dd","sha256:91cbb8b5530fade066f6d0a7a99abb33bcd1a90d4f34fb0b87ab3979863c4c00"],"state_sha256":"fd211d035a32438d97203f0d7f49ac910048ceadfbec02bafc749978977e39a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l767R6B7AO6N4uY/zyrmsmr5CI+8UdYoi1YTncUywP+QIQRRqCFWLAFndhZlYNXo3ZaBSd9GbVsgq6EcKigfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:26:26.375332Z","bundle_sha256":"e60d8da1154088e65bec495f6764d586f597cfdf157a42527e7e1dddafa7e933"}}