{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MTADQKIOWX2LJBJIBVOI3R4ZUU","short_pith_number":"pith:MTADQKIO","canonical_record":{"source":{"id":"2507.00771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-01T14:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"4660246fd125176744826fe2d5d125ad9fd706a664b445bb8af1396d50cc20bf","abstract_canon_sha256":"4c17e83e54d88806545ff1f73f6951570b29e547e9a3d9b09e458f0171d4c55f"},"schema_version":"1.0"},"canonical_sha256":"64c038290eb5f4b485280d5c8dc799a52d68286afb17d8dd1ba38f373cd7e0db","source":{"kind":"arxiv","id":"2507.00771","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00771","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00771v2","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00771","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"MTADQKIOWX2L","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"MTADQKIOWX2LJBJI","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"MTADQKIO","created_at":"2026-06-19T16:11:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MTADQKIOWX2LJBJIBVOI3R4ZUU","target":"record","payload":{"canonical_record":{"source":{"id":"2507.00771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-01T14:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"4660246fd125176744826fe2d5d125ad9fd706a664b445bb8af1396d50cc20bf","abstract_canon_sha256":"4c17e83e54d88806545ff1f73f6951570b29e547e9a3d9b09e458f0171d4c55f"},"schema_version":"1.0"},"canonical_sha256":"64c038290eb5f4b485280d5c8dc799a52d68286afb17d8dd1ba38f373cd7e0db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:11.595450Z","signature_b64":"SX3f70Dfw2N67/ayYGOMzk+8sMIxSxpHDGhjCvQem7Kvh6Ql2nR49Wi/wT0gASBH+I22/6wrdHIdpfkDUbA4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64c038290eb5f4b485280d5c8dc799a52d68286afb17d8dd1ba38f373cd7e0db","last_reissued_at":"2026-06-19T16:11:11.595018Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:11.595018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.00771","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":"2026-06-19T16:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6ASEgEmR5mvgFcJWky2DfPoNRpWSJjXIut4C/FnylYbCtyUzDDJOH5UAfx7zKE5kCwRrH65TwxY0XS/S4qYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:31:28.243837Z"},"content_sha256":"bf4c873a3f556799886cb1bf061f858fd66989d443a9183536c816d1f2faaa72","schema_version":"1.0","event_id":"sha256:bf4c873a3f556799886cb1bf061f858fd66989d443a9183536c816d1f2faaa72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MTADQKIOWX2LJBJIBVOI3R4ZUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic vanishing theory in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jefferson Baudin","submitted_at":"2025-07-01T14:11:42Z","abstract_excerpt":"We simplify and improve the main fundamental theorems of positive characteristic generic vanishing theory. As a quick corollary of the theory, we prove that a normal variety $X$ of maximal Albanese dimension satisfies $H^0(X, \\omega_X) \\neq 0$ and that if $\\mathrm{Alb}(X)$ is ordinary, then $S^0(X, \\omega_X) \\neq 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00771","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/2507.00771/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":"2026-06-19T16:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XXrmTcM15UKEjcU53gyqmmBcpzkICj2CwnGnTnPP4Lg8Bp36StiV0xQp3u4v5vCAd93NKM4VCU3D9vnU1mjcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:31:28.244329Z"},"content_sha256":"f7aa5e216ea371e7909d0dfd90f494823a64203795f8025bbd0b99694241d1b7","schema_version":"1.0","event_id":"sha256:f7aa5e216ea371e7909d0dfd90f494823a64203795f8025bbd0b99694241d1b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/bundle.json","state_url":"https://pith.science/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/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":"2026-08-10T19:31:28Z","links":{"resolver":"https://pith.science/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU","bundle":"https://pith.science/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/bundle.json","state":"https://pith.science/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTADQKIOWX2LJBJIBVOI3R4ZUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MTADQKIOWX2LJBJIBVOI3R4ZUU","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":"4c17e83e54d88806545ff1f73f6951570b29e547e9a3d9b09e458f0171d4c55f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-01T14:11:42Z","title_canon_sha256":"4660246fd125176744826fe2d5d125ad9fd706a664b445bb8af1396d50cc20bf"},"schema_version":"1.0","source":{"id":"2507.00771","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00771","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00771v2","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00771","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"MTADQKIOWX2L","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"MTADQKIOWX2LJBJI","created_at":"2026-06-19T16:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"MTADQKIO","created_at":"2026-06-19T16:11:11Z"}],"graph_snapshots":[{"event_id":"sha256:f7aa5e216ea371e7909d0dfd90f494823a64203795f8025bbd0b99694241d1b7","target":"graph","created_at":"2026-06-19T16:11:11Z","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/2507.00771/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We simplify and improve the main fundamental theorems of positive characteristic generic vanishing theory. As a quick corollary of the theory, we prove that a normal variety $X$ of maximal Albanese dimension satisfies $H^0(X, \\omega_X) \\neq 0$ and that if $\\mathrm{Alb}(X)$ is ordinary, then $S^0(X, \\omega_X) \\neq 0$.","authors_text":"Jefferson Baudin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00771","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:bf4c873a3f556799886cb1bf061f858fd66989d443a9183536c816d1f2faaa72","target":"record","created_at":"2026-06-19T16:11:11Z","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":"4c17e83e54d88806545ff1f73f6951570b29e547e9a3d9b09e458f0171d4c55f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-01T14:11:42Z","title_canon_sha256":"4660246fd125176744826fe2d5d125ad9fd706a664b445bb8af1396d50cc20bf"},"schema_version":"1.0","source":{"id":"2507.00771","kind":"arxiv","version":2}},"canonical_sha256":"64c038290eb5f4b485280d5c8dc799a52d68286afb17d8dd1ba38f373cd7e0db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64c038290eb5f4b485280d5c8dc799a52d68286afb17d8dd1ba38f373cd7e0db","first_computed_at":"2026-06-19T16:11:11.595018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:11.595018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SX3f70Dfw2N67/ayYGOMzk+8sMIxSxpHDGhjCvQem7Kvh6Ql2nR49Wi/wT0gASBH+I22/6wrdHIdpfkDUbA4Cw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:11.595450Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.00771","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf4c873a3f556799886cb1bf061f858fd66989d443a9183536c816d1f2faaa72","sha256:f7aa5e216ea371e7909d0dfd90f494823a64203795f8025bbd0b99694241d1b7"],"state_sha256":"cc5135ac9a754fa981b467c8b91c230152ce1515a48e786706a2d8922ccf4eda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fy/g/Dh7lZo6LBezl6kNeDoNrnNxHSg1O+L0zeNIi/gIuVJTOxdvhkt71UIYD65oI0WiFj7jhrsEdu4EG3trAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:31:28.248108Z","bundle_sha256":"e29738a461eb52e20201831569de981e03a21781aece9bfd32161bf3b83cf695"}}