{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CCEQOTVWCXL53D27QWXP25NW2V","short_pith_number":"pith:CCEQOTVW","canonical_record":{"source":{"id":"0904.1408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-04-08T19:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"6c13fef56e3e1eb622ba103d291af8c47e8ca67ac767f8aff8695eb0443260cd","abstract_canon_sha256":"f135041aa529d4573203cc3b49728fa5fa993049652338574275ce4d8b07b3b8"},"schema_version":"1.0"},"canonical_sha256":"1089074eb615d7dd8f5f85aefd75b6d540b41486bd68d422ea47909581045c46","source":{"kind":"arxiv","id":"0904.1408","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1408","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1408v3","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1408","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"CCEQOTVWCXL5","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CCEQOTVWCXL53D27","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CCEQOTVW","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CCEQOTVWCXL53D27QWXP25NW2V","target":"record","payload":{"canonical_record":{"source":{"id":"0904.1408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-04-08T19:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"6c13fef56e3e1eb622ba103d291af8c47e8ca67ac767f8aff8695eb0443260cd","abstract_canon_sha256":"f135041aa529d4573203cc3b49728fa5fa993049652338574275ce4d8b07b3b8"},"schema_version":"1.0"},"canonical_sha256":"1089074eb615d7dd8f5f85aefd75b6d540b41486bd68d422ea47909581045c46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:29.005295Z","signature_b64":"DNTEuLPE53xFpfhZBAzON4Fs6hJJqeN3mzxfwALffhVQVjHVOcUbi+e/6FyE7jl3s7FxhT6PRbt7B8mDyOvGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1089074eb615d7dd8f5f85aefd75b6d540b41486bd68d422ea47909581045c46","last_reissued_at":"2026-05-18T00:55:29.004833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:29.004833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.1408","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"abCLXffVvybF3ZtZQzsnmCjqLnhgsGhoiUwrkhc2rX13r5bTUIKJl9stnvaT5ssshVqqlN/dRMVoeO5zIelxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:56:08.838059Z"},"content_sha256":"13aa10f02477a4dd926f287013057908e0ce6278351fb971183acf772bf855e7","schema_version":"1.0","event_id":"sha256:13aa10f02477a4dd926f287013057908e0ce6278351fb971183acf772bf855e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CCEQOTVWCXL53D27QWXP25NW2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vanishing of Tor Over Complete Intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Olgur Celikbas","submitted_at":"2009-04-08T19:16:02Z","abstract_excerpt":"In this paper we are concerned with the vanishing of $\\textnormal{Tor}$ over complete intersection rings. Building on results of C. Huneke, D. Jorgensen and R. Wiegand, and, more recently, H. Dao, we obtain new results showing that good depth properties on the $R$-modules $M$, $N$ and $M\\otimes_RN$ force the vanishing of $\\textnormal{Tor}^{R}_{i}(M,N)$ for all $i\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1408","kind":"arxiv","version":3},"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":"2026-05-18T00:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2g6OTpAh3n1QwfQdx6aOGA9J4LDkqcKaa/nwKD/TR7QRtFgFQdWrfBdVsnDPaogvUCJtt7WHM0iK8AUrjyQaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:56:08.838785Z"},"content_sha256":"e38bc199c96fcdc663982320eeec2f8b5cf810e9c91a1c8d992919d744824973","schema_version":"1.0","event_id":"sha256:e38bc199c96fcdc663982320eeec2f8b5cf810e9c91a1c8d992919d744824973"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCEQOTVWCXL53D27QWXP25NW2V/bundle.json","state_url":"https://pith.science/pith/CCEQOTVWCXL53D27QWXP25NW2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCEQOTVWCXL53D27QWXP25NW2V/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":"2026-06-08T04:56:08Z","links":{"resolver":"https://pith.science/pith/CCEQOTVWCXL53D27QWXP25NW2V","bundle":"https://pith.science/pith/CCEQOTVWCXL53D27QWXP25NW2V/bundle.json","state":"https://pith.science/pith/CCEQOTVWCXL53D27QWXP25NW2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCEQOTVWCXL53D27QWXP25NW2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CCEQOTVWCXL53D27QWXP25NW2V","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":"f135041aa529d4573203cc3b49728fa5fa993049652338574275ce4d8b07b3b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-04-08T19:16:02Z","title_canon_sha256":"6c13fef56e3e1eb622ba103d291af8c47e8ca67ac767f8aff8695eb0443260cd"},"schema_version":"1.0","source":{"id":"0904.1408","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.1408","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"0904.1408v3","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1408","created_at":"2026-05-18T00:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"CCEQOTVWCXL5","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CCEQOTVWCXL53D27","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CCEQOTVW","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:e38bc199c96fcdc663982320eeec2f8b5cf810e9c91a1c8d992919d744824973","target":"graph","created_at":"2026-05-18T00:55:29Z","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":"In this paper we are concerned with the vanishing of $\\textnormal{Tor}$ over complete intersection rings. Building on results of C. Huneke, D. Jorgensen and R. Wiegand, and, more recently, H. Dao, we obtain new results showing that good depth properties on the $R$-modules $M$, $N$ and $M\\otimes_RN$ force the vanishing of $\\textnormal{Tor}^{R}_{i}(M,N)$ for all $i\\geq 1$.","authors_text":"Olgur Celikbas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-04-08T19:16:02Z","title":"Vanishing of Tor Over Complete Intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1408","kind":"arxiv","version":3},"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":"sha256:13aa10f02477a4dd926f287013057908e0ce6278351fb971183acf772bf855e7","target":"record","created_at":"2026-05-18T00:55:29Z","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":"f135041aa529d4573203cc3b49728fa5fa993049652338574275ce4d8b07b3b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-04-08T19:16:02Z","title_canon_sha256":"6c13fef56e3e1eb622ba103d291af8c47e8ca67ac767f8aff8695eb0443260cd"},"schema_version":"1.0","source":{"id":"0904.1408","kind":"arxiv","version":3}},"canonical_sha256":"1089074eb615d7dd8f5f85aefd75b6d540b41486bd68d422ea47909581045c46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1089074eb615d7dd8f5f85aefd75b6d540b41486bd68d422ea47909581045c46","first_computed_at":"2026-05-18T00:55:29.004833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:29.004833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNTEuLPE53xFpfhZBAzON4Fs6hJJqeN3mzxfwALffhVQVjHVOcUbi+e/6FyE7jl3s7FxhT6PRbt7B8mDyOvGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:29.005295Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.1408","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13aa10f02477a4dd926f287013057908e0ce6278351fb971183acf772bf855e7","sha256:e38bc199c96fcdc663982320eeec2f8b5cf810e9c91a1c8d992919d744824973"],"state_sha256":"0414ab182bd55f651e455bbc46b0555fb0ca3092bdc4b2459c24b4c4ac4831c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"quXvDexGBrOnZE2tL9awQHih9KiH9E3EtEwGjg6+/2yBPBubJjMbOuafHw6sB2te1YFCXE47JKnLNZzz//mXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:56:08.842613Z","bundle_sha256":"6f246ab25d526428d0e222b423058c9dc71643a20c64c608d1a0f415956e1dad"}}