{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YZ77HI3XFHNHVCXL6HCN36GYAS","short_pith_number":"pith:YZ77HI3X","canonical_record":{"source":{"id":"1706.02843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-09T06:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"fa8263eae258848462ab5c54f39fcf4e7d120d4536fb7569269584d5ddc22695","abstract_canon_sha256":"bd9e7231761922c18b671fe20f1ca8fa9c45e626e0cf007e32b063848aaf6b30"},"schema_version":"1.0"},"canonical_sha256":"c67ff3a37729da7a8aebf1c4ddf8d804a9526e6be6081d20b81ab55689b40961","source":{"kind":"arxiv","id":"1706.02843","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02843","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02843v2","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02843","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"pith_short_12","alias_value":"YZ77HI3XFHNH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZ77HI3XFHNHVCXL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZ77HI3X","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YZ77HI3XFHNHVCXL6HCN36GYAS","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-09T06:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"fa8263eae258848462ab5c54f39fcf4e7d120d4536fb7569269584d5ddc22695","abstract_canon_sha256":"bd9e7231761922c18b671fe20f1ca8fa9c45e626e0cf007e32b063848aaf6b30"},"schema_version":"1.0"},"canonical_sha256":"c67ff3a37729da7a8aebf1c4ddf8d804a9526e6be6081d20b81ab55689b40961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:39.120888Z","signature_b64":"CcmLfzr4CkIAlu3a/162IpEcOZY/QsTKwKa5m6BRteO5eXyaIcerHDcCYsygmauQjnacxybrcGK7IIq7H7M0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c67ff3a37729da7a8aebf1c4ddf8d804a9526e6be6081d20b81ab55689b40961","last_reissued_at":"2026-05-18T00:01:39.120482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:39.120482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02843","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":"2026-05-18T00:01:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DA89ZzKIk3r9qgr2aSint4t9ycsDELdbub9HVtpbrCV5qlmWQy0ITXXcqgQgr0wpUsx/10iHO+XMbdFwyZnQCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:57:45.515985Z"},"content_sha256":"f93774815049d5e5285315d4449299d3900d41548478ab55356d21ae4a75b3b0","schema_version":"1.0","event_id":"sha256:f93774815049d5e5285315d4449299d3900d41548478ab55356d21ae4a75b3b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YZ77HI3XFHNHVCXL6HCN36GYAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Length of local cohomology in positive characteristic and ordinarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Bitoun","submitted_at":"2017-06-09T06:16:25Z","abstract_excerpt":"Let $D$ be the ring of Grothendieck differential operators of the ring $R$ of polynomials in $d\\geq3$ variables with coefficients in a perfect field of positive characteristic $p.$ We compute the $D$-module length of the first local cohomology module $H^1_f(R)$ of $R$ with respect to an irreducible polynomial $f$ with an isolated singularity, for $p$ large enough. The expression we give is in terms of the Frobenius action on the top coherent cohomology of the structure sheaf of the exceptional divisor of a resolution of the singularity. Our proof rests on a tight closure computation due to Har"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02843","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":"2026-05-18T00:01:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvVoi1O6FhGrKS5KN3m8ZWh67F8ytzLaLoVjVCt3Co0Cij4QciFoUx6FtdnI7tp3R2JOVMFTzfihHNmezO4GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:57:45.516604Z"},"content_sha256":"2993d8ab8f8fe560e63b2af8c4c816cd6c2f7b2dfbbdba0782171d205628182f","schema_version":"1.0","event_id":"sha256:2993d8ab8f8fe560e63b2af8c4c816cd6c2f7b2dfbbdba0782171d205628182f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/bundle.json","state_url":"https://pith.science/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/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":"2026-06-04T22:57:45Z","links":{"resolver":"https://pith.science/pith/YZ77HI3XFHNHVCXL6HCN36GYAS","bundle":"https://pith.science/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/bundle.json","state":"https://pith.science/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZ77HI3XFHNHVCXL6HCN36GYAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YZ77HI3XFHNHVCXL6HCN36GYAS","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":"bd9e7231761922c18b671fe20f1ca8fa9c45e626e0cf007e32b063848aaf6b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-09T06:16:25Z","title_canon_sha256":"fa8263eae258848462ab5c54f39fcf4e7d120d4536fb7569269584d5ddc22695"},"schema_version":"1.0","source":{"id":"1706.02843","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02843","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02843v2","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02843","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"pith_short_12","alias_value":"YZ77HI3XFHNH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZ77HI3XFHNHVCXL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZ77HI3X","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:2993d8ab8f8fe560e63b2af8c4c816cd6c2f7b2dfbbdba0782171d205628182f","target":"graph","created_at":"2026-05-18T00:01:39Z","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":"Let $D$ be the ring of Grothendieck differential operators of the ring $R$ of polynomials in $d\\geq3$ variables with coefficients in a perfect field of positive characteristic $p.$ We compute the $D$-module length of the first local cohomology module $H^1_f(R)$ of $R$ with respect to an irreducible polynomial $f$ with an isolated singularity, for $p$ large enough. The expression we give is in terms of the Frobenius action on the top coherent cohomology of the structure sheaf of the exceptional divisor of a resolution of the singularity. Our proof rests on a tight closure computation due to Har","authors_text":"Thomas Bitoun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-09T06:16:25Z","title":"Length of local cohomology in positive characteristic and ordinarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02843","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:f93774815049d5e5285315d4449299d3900d41548478ab55356d21ae4a75b3b0","target":"record","created_at":"2026-05-18T00:01:39Z","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":"bd9e7231761922c18b671fe20f1ca8fa9c45e626e0cf007e32b063848aaf6b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-09T06:16:25Z","title_canon_sha256":"fa8263eae258848462ab5c54f39fcf4e7d120d4536fb7569269584d5ddc22695"},"schema_version":"1.0","source":{"id":"1706.02843","kind":"arxiv","version":2}},"canonical_sha256":"c67ff3a37729da7a8aebf1c4ddf8d804a9526e6be6081d20b81ab55689b40961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c67ff3a37729da7a8aebf1c4ddf8d804a9526e6be6081d20b81ab55689b40961","first_computed_at":"2026-05-18T00:01:39.120482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:39.120482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CcmLfzr4CkIAlu3a/162IpEcOZY/QsTKwKa5m6BRteO5eXyaIcerHDcCYsygmauQjnacxybrcGK7IIq7H7M0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:39.120888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02843","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f93774815049d5e5285315d4449299d3900d41548478ab55356d21ae4a75b3b0","sha256:2993d8ab8f8fe560e63b2af8c4c816cd6c2f7b2dfbbdba0782171d205628182f"],"state_sha256":"08f36263e4f912d7de4fc9e682a8e24d2dd07cb65574a7d4154837df291b63ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TT542DkHTwFDonDBlFMxc1i7+FBU5/83lLxmWwH+WW8EozUNou5MLWZ+3OYjD84opEbJIm+H/hbvFK/gPouxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:57:45.520109Z","bundle_sha256":"f0a0bb640f37a1a9e03f6f8d63887a75a3981f93ac07073b4fb7b73e8575a1be"}}