{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6KDKVELIRSHFW3HHBFN6AQS5L7","short_pith_number":"pith:6KDKVELI","canonical_record":{"source":{"id":"2412.01060","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T02:42:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4aa4e2b988c267fa55bb7421252769d71bb1c4482eef89af43138e73fbb41c67","abstract_canon_sha256":"1f297d8fd528433d1a1a31c4c3cd20d069b70db754daf9c00d25dd59d6557771"},"schema_version":"1.0"},"canonical_sha256":"f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe","source":{"kind":"arxiv","id":"2412.01060","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01060","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01060v2","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01060","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"6KDKVELIRSHF","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_16","alias_value":"6KDKVELIRSHFW3HH","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_8","alias_value":"6KDKVELI","created_at":"2026-07-05T11:54:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6KDKVELIRSHFW3HHBFN6AQS5L7","target":"record","payload":{"canonical_record":{"source":{"id":"2412.01060","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T02:42:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4aa4e2b988c267fa55bb7421252769d71bb1c4482eef89af43138e73fbb41c67","abstract_canon_sha256":"1f297d8fd528433d1a1a31c4c3cd20d069b70db754daf9c00d25dd59d6557771"},"schema_version":"1.0"},"canonical_sha256":"f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:42.758646Z","signature_b64":"uqlDdZxOnDSRydjZRF7XlA/KyYL8fQTU17EqUXcXwGM4MLb0oBex7iEYu6hF/rDme3dliV4y/Va3gCfuRKkQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe","last_reissued_at":"2026-07-05T11:54:42.758201Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:42.758201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.01060","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":"2026-07-05T11:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aV4fjpn8QkwaSjQO1Thrz6CZKSg0ji68v4tPWSmzKmmgDDUosUdPVYYXHQY0iTTjhB7PvaJOHozjgcu1VY8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:56:10.624338Z"},"content_sha256":"cf07189760215b378ababd152efdf4c3f590bd0b7e294b3525ff7a1ee9ca0d2c","schema_version":"1.0","event_id":"sha256:cf07189760215b378ababd152efdf4c3f590bd0b7e294b3525ff7a1ee9ca0d2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6KDKVELIRSHFW3HHBFN6AQS5L7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ranks of matrix factorizations and sheaf cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Mark E. Walker, Michael K. Brown","submitted_at":"2024-12-02T02:42:49Z","abstract_excerpt":"Buchweitz-Greuel-Schreyer conjectured in 1987 a lower bound on the ranks of matrix factorizations over certain local hypersurface rings. We study a graded version of this conjecture, and we show that it implies a novel conjecture concerning the cohomology of sheaves over non-Fano projective hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01060","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.01060/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NezPbA/6fJYwBJpdezRgX6CMVfS8Pm7clLR6xcMxolUvE0By1sN0JmLh0eNYPva6357UwF4+kFh+Co/xrLUNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:56:10.624881Z"},"content_sha256":"6d57cfebe2c46217c0a82361d3cbc2654e6bd1c29e9cdf9becb719a88b228ca5","schema_version":"1.0","event_id":"sha256:6d57cfebe2c46217c0a82361d3cbc2654e6bd1c29e9cdf9becb719a88b228ca5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/bundle.json","state_url":"https://pith.science/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/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":"2026-08-13T11:56:10Z","links":{"resolver":"https://pith.science/pith/6KDKVELIRSHFW3HHBFN6AQS5L7","bundle":"https://pith.science/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/bundle.json","state":"https://pith.science/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KDKVELIRSHFW3HHBFN6AQS5L7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6KDKVELIRSHFW3HHBFN6AQS5L7","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":"1f297d8fd528433d1a1a31c4c3cd20d069b70db754daf9c00d25dd59d6557771","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T02:42:49Z","title_canon_sha256":"4aa4e2b988c267fa55bb7421252769d71bb1c4482eef89af43138e73fbb41c67"},"schema_version":"1.0","source":{"id":"2412.01060","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01060","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01060v2","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01060","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"6KDKVELIRSHF","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_16","alias_value":"6KDKVELIRSHFW3HH","created_at":"2026-07-05T11:54:42Z"},{"alias_kind":"pith_short_8","alias_value":"6KDKVELI","created_at":"2026-07-05T11:54:42Z"}],"graph_snapshots":[{"event_id":"sha256:6d57cfebe2c46217c0a82361d3cbc2654e6bd1c29e9cdf9becb719a88b228ca5","target":"graph","created_at":"2026-07-05T11:54:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.01060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Buchweitz-Greuel-Schreyer conjectured in 1987 a lower bound on the ranks of matrix factorizations over certain local hypersurface rings. We study a graded version of this conjecture, and we show that it implies a novel conjecture concerning the cohomology of sheaves over non-Fano projective hypersurfaces.","authors_text":"Mark E. Walker, Michael K. Brown","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T02:42:49Z","title":"Ranks of matrix factorizations and sheaf cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01060","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:cf07189760215b378ababd152efdf4c3f590bd0b7e294b3525ff7a1ee9ca0d2c","target":"record","created_at":"2026-07-05T11:54:42Z","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":"1f297d8fd528433d1a1a31c4c3cd20d069b70db754daf9c00d25dd59d6557771","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T02:42:49Z","title_canon_sha256":"4aa4e2b988c267fa55bb7421252769d71bb1c4482eef89af43138e73fbb41c67"},"schema_version":"1.0","source":{"id":"2412.01060","kind":"arxiv","version":2}},"canonical_sha256":"f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe","first_computed_at":"2026-07-05T11:54:42.758201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:54:42.758201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uqlDdZxOnDSRydjZRF7XlA/KyYL8fQTU17EqUXcXwGM4MLb0oBex7iEYu6hF/rDme3dliV4y/Va3gCfuRKkQAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:54:42.758646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.01060","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf07189760215b378ababd152efdf4c3f590bd0b7e294b3525ff7a1ee9ca0d2c","sha256:6d57cfebe2c46217c0a82361d3cbc2654e6bd1c29e9cdf9becb719a88b228ca5"],"state_sha256":"e0085ddd6fe6c2c2567824a3e6474025894b5bda2f96abd715e485c5bb9082c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8olWt7eV795k8TtUzqW223LXoPCSP1Z47YKgAw2qNMxbU6JmM98o+crFH2l7WXimZCp7/2eIvPafojxpe97CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T11:56:10.631447Z","bundle_sha256":"eefa13f3d4e51ace03287fa7fdc2a2893bdf005e9ff8316c999fd80218728f2e"}}