{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DTFOHOUBJPRYFTBYBJZLXVNTBT","short_pith_number":"pith:DTFOHOUB","canonical_record":{"source":{"id":"1212.0245","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2012-12-02T21:04:26Z","cross_cats_sorted":[],"title_canon_sha256":"edea7d7f21bad5cdebd9696fec36ed89872b91a8fc85b61697cee9d94e89b690","abstract_canon_sha256":"16c8f618f4c028b5c5dde20a239daa571da5c31295d59890397ee26498f207ef"},"schema_version":"1.0"},"canonical_sha256":"1ccae3ba814be382cc380a72bbd5b30cfcd99e24cbbf058b8738fa00868fc988","source":{"kind":"arxiv","id":"1212.0245","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0245","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0245v2","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0245","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"DTFOHOUBJPRY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DTFOHOUBJPRYFTBY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DTFOHOUB","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DTFOHOUBJPRYFTBYBJZLXVNTBT","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0245","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2012-12-02T21:04:26Z","cross_cats_sorted":[],"title_canon_sha256":"edea7d7f21bad5cdebd9696fec36ed89872b91a8fc85b61697cee9d94e89b690","abstract_canon_sha256":"16c8f618f4c028b5c5dde20a239daa571da5c31295d59890397ee26498f207ef"},"schema_version":"1.0"},"canonical_sha256":"1ccae3ba814be382cc380a72bbd5b30cfcd99e24cbbf058b8738fa00868fc988","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:48.765943Z","signature_b64":"+zAef+KSyGA12DHVN8BmPuCp5EaclJPRnfaYkBB1AML7KaQAoUXENh1OV6WlPdIRkCdnzvIiI7H8T9l+RK/JCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ccae3ba814be382cc380a72bbd5b30cfcd99e24cbbf058b8738fa00868fc988","last_reissued_at":"2026-05-18T00:06:48.765489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:48.765489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0245","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/R2I9NsAFGom46+r0MJJSTe0ErrSIB/ljaX24rCoTHT+Q353RyH/PZdPHy0tV7mJHwT8aD5DHfhuXut3XyjBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:30:40.265489Z"},"content_sha256":"9cd3278db795a1e0a5d7cbccba0f733c942f1cdee8b6e9bba3fdb258425b92a6","schema_version":"1.0","event_id":"sha256:9cd3278db795a1e0a5d7cbccba0f733c942f1cdee8b6e9bba3fdb258425b92a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DTFOHOUBJPRYFTBYBJZLXVNTBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on some top local cohomology modules","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Majid Eghbali","submitted_at":"2012-12-02T21:04:26Z","abstract_excerpt":"Let $\\fa$ be an ideal of a $d$-dimensional commutative Noetherian ring $R$. In this paper we give some information on some last non-zero local cohomology modules known as top local cohomology modules in particular, $H^{d-1}_{\\fa}(R)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0245","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ufBnp0bbhn5DYvZ4deyGWTW7lL37PuNjlG27edqc3BFMMfrcdwI6LNwp8D8ZHrc1o1mCemx2KWmV0JyXQYsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:30:40.265819Z"},"content_sha256":"d024c4fe3d7e51765b65812050dddcce268f606cb28e4522b5f055f83d990f41","schema_version":"1.0","event_id":"sha256:d024c4fe3d7e51765b65812050dddcce268f606cb28e4522b5f055f83d990f41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/bundle.json","state_url":"https://pith.science/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/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":"2026-06-03T01:30:40Z","links":{"resolver":"https://pith.science/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT","bundle":"https://pith.science/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/bundle.json","state":"https://pith.science/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTFOHOUBJPRYFTBYBJZLXVNTBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DTFOHOUBJPRYFTBYBJZLXVNTBT","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":"16c8f618f4c028b5c5dde20a239daa571da5c31295d59890397ee26498f207ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2012-12-02T21:04:26Z","title_canon_sha256":"edea7d7f21bad5cdebd9696fec36ed89872b91a8fc85b61697cee9d94e89b690"},"schema_version":"1.0","source":{"id":"1212.0245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0245","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0245v2","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0245","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"DTFOHOUBJPRY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DTFOHOUBJPRYFTBY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DTFOHOUB","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:d024c4fe3d7e51765b65812050dddcce268f606cb28e4522b5f055f83d990f41","target":"graph","created_at":"2026-05-18T00:06:48Z","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 $\\fa$ be an ideal of a $d$-dimensional commutative Noetherian ring $R$. In this paper we give some information on some last non-zero local cohomology modules known as top local cohomology modules in particular, $H^{d-1}_{\\fa}(R)$.","authors_text":"Majid Eghbali","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2012-12-02T21:04:26Z","title":"A note on some top local cohomology modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0245","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":"sha256:9cd3278db795a1e0a5d7cbccba0f733c942f1cdee8b6e9bba3fdb258425b92a6","target":"record","created_at":"2026-05-18T00:06:48Z","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":"16c8f618f4c028b5c5dde20a239daa571da5c31295d59890397ee26498f207ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2012-12-02T21:04:26Z","title_canon_sha256":"edea7d7f21bad5cdebd9696fec36ed89872b91a8fc85b61697cee9d94e89b690"},"schema_version":"1.0","source":{"id":"1212.0245","kind":"arxiv","version":2}},"canonical_sha256":"1ccae3ba814be382cc380a72bbd5b30cfcd99e24cbbf058b8738fa00868fc988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ccae3ba814be382cc380a72bbd5b30cfcd99e24cbbf058b8738fa00868fc988","first_computed_at":"2026-05-18T00:06:48.765489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:48.765489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+zAef+KSyGA12DHVN8BmPuCp5EaclJPRnfaYkBB1AML7KaQAoUXENh1OV6WlPdIRkCdnzvIiI7H8T9l+RK/JCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:48.765943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd3278db795a1e0a5d7cbccba0f733c942f1cdee8b6e9bba3fdb258425b92a6","sha256:d024c4fe3d7e51765b65812050dddcce268f606cb28e4522b5f055f83d990f41"],"state_sha256":"1c6867adc6956fb0bb6cabd0bf5d41198177d015d7985ec990c9576c448563f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfKPsnaOxPYUOmX675CWb6k8sRy0jcUlVkQoqsrjDnOnUFdku33ydF3W/zvKG6wtq1BeMc+rY5+gnZcbzAzRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:30:40.267709Z","bundle_sha256":"7ca4f44588dd99f4cdcebd8ede5a60f544e2976bcca1dd779b9f23a6e30a4c4b"}}