{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NP4VWKFRSFCSKKRVXRR4MR67AO","short_pith_number":"pith:NP4VWKFR","canonical_record":{"source":{"id":"1412.6456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-19T17:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"1f0ad937afbcc50bb5bd65634a18f646aa7730ae7224e2902ffebac19f2d88be","abstract_canon_sha256":"83ef1c255e216447bdf05ca1690f4a08e8bdff3e490a379d8531fe140cb5b9ff"},"schema_version":"1.0"},"canonical_sha256":"6bf95b28b19145252a35bc63c647df039954b9feff9e7bc8f5a2fd377e410d54","source":{"kind":"arxiv","id":"1412.6456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6456","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6456v1","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6456","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"NP4VWKFRSFCS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NP4VWKFRSFCSKKRV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NP4VWKFR","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NP4VWKFRSFCSKKRVXRR4MR67AO","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-19T17:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"1f0ad937afbcc50bb5bd65634a18f646aa7730ae7224e2902ffebac19f2d88be","abstract_canon_sha256":"83ef1c255e216447bdf05ca1690f4a08e8bdff3e490a379d8531fe140cb5b9ff"},"schema_version":"1.0"},"canonical_sha256":"6bf95b28b19145252a35bc63c647df039954b9feff9e7bc8f5a2fd377e410d54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:53.449362Z","signature_b64":"1LFDuLNjPSazT+1ZQgrARvdhsHj3MqreX7Z1WbiDGpytcWZRY/ZgUSQ571TXOIGnV7TGnUlTMKaplxUBIwL+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf95b28b19145252a35bc63c647df039954b9feff9e7bc8f5a2fd377e410d54","last_reissued_at":"2026-05-18T02:30:53.448898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:53.448898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6456","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0OWiehPNtrqgWOep6eAIRWd1nR9uLNgY2XLvBLypS0gdn2lP0ZBkjMVj1UZS8r3bjc1G0mVdGVvHrBecUBb7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:20:17.689382Z"},"content_sha256":"239692f591adc32d2a0e4ce2b61eda0ed16ae02421002cba9d664aa9afc0bfb9","schema_version":"1.0","event_id":"sha256:239692f591adc32d2a0e4ce2b61eda0ed16ae02421002cba9d664aa9afc0bfb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NP4VWKFRSFCSKKRVXRR4MR67AO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Criteria for vanishing of Tor over Complete Intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Greg Piepmeyer, Olgur Celikbas, Roger Wiegand, Srikanth B. Iyengar","submitted_at":"2014-12-19T17:50:46Z","abstract_excerpt":"In this paper we exploit properties of Dao's eta-pairing as well as techniques of Huneke, Jorgensen, and Wiegand to study the vanishing of Tor_i(M,N) of finitely generated modules M, N over complete intersections. We prove vanishing of Tor_i(M, N) for all positive integers i under depth conditions on M, N, and their tensor product. Our arguments improve a result of Dao and establish a new connection between the vanishing of Tor and the depth of tensor products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6456","kind":"arxiv","version":1},"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":"2026-05-18T02:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A53JkCingO2+ejiH2PlSy/CKrf8UT/TJV/LXlw8KPkhvBvCtckIlTe5GEy4k4o1NHUoqIDj1AJs7YMukm7/kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:20:17.689728Z"},"content_sha256":"0f43df645cda30bdaf7388a9d2a70e602039b942018d9be48153dbd26274414c","schema_version":"1.0","event_id":"sha256:0f43df645cda30bdaf7388a9d2a70e602039b942018d9be48153dbd26274414c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/bundle.json","state_url":"https://pith.science/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/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":"2026-06-03T01:20:17Z","links":{"resolver":"https://pith.science/pith/NP4VWKFRSFCSKKRVXRR4MR67AO","bundle":"https://pith.science/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/bundle.json","state":"https://pith.science/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NP4VWKFRSFCSKKRVXRR4MR67AO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NP4VWKFRSFCSKKRVXRR4MR67AO","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":"83ef1c255e216447bdf05ca1690f4a08e8bdff3e490a379d8531fe140cb5b9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-19T17:50:46Z","title_canon_sha256":"1f0ad937afbcc50bb5bd65634a18f646aa7730ae7224e2902ffebac19f2d88be"},"schema_version":"1.0","source":{"id":"1412.6456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6456","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6456v1","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6456","created_at":"2026-05-18T02:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"NP4VWKFRSFCS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NP4VWKFRSFCSKKRV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NP4VWKFR","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:0f43df645cda30bdaf7388a9d2a70e602039b942018d9be48153dbd26274414c","target":"graph","created_at":"2026-05-18T02:30:53Z","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 exploit properties of Dao's eta-pairing as well as techniques of Huneke, Jorgensen, and Wiegand to study the vanishing of Tor_i(M,N) of finitely generated modules M, N over complete intersections. We prove vanishing of Tor_i(M, N) for all positive integers i under depth conditions on M, N, and their tensor product. Our arguments improve a result of Dao and establish a new connection between the vanishing of Tor and the depth of tensor products.","authors_text":"Greg Piepmeyer, Olgur Celikbas, Roger Wiegand, Srikanth B. Iyengar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-19T17:50:46Z","title":"Criteria for vanishing of Tor over Complete Intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6456","kind":"arxiv","version":1},"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":"sha256:239692f591adc32d2a0e4ce2b61eda0ed16ae02421002cba9d664aa9afc0bfb9","target":"record","created_at":"2026-05-18T02:30:53Z","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":"83ef1c255e216447bdf05ca1690f4a08e8bdff3e490a379d8531fe140cb5b9ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-12-19T17:50:46Z","title_canon_sha256":"1f0ad937afbcc50bb5bd65634a18f646aa7730ae7224e2902ffebac19f2d88be"},"schema_version":"1.0","source":{"id":"1412.6456","kind":"arxiv","version":1}},"canonical_sha256":"6bf95b28b19145252a35bc63c647df039954b9feff9e7bc8f5a2fd377e410d54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf95b28b19145252a35bc63c647df039954b9feff9e7bc8f5a2fd377e410d54","first_computed_at":"2026-05-18T02:30:53.448898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:53.448898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LFDuLNjPSazT+1ZQgrARvdhsHj3MqreX7Z1WbiDGpytcWZRY/ZgUSQ571TXOIGnV7TGnUlTMKaplxUBIwL+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:53.449362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:239692f591adc32d2a0e4ce2b61eda0ed16ae02421002cba9d664aa9afc0bfb9","sha256:0f43df645cda30bdaf7388a9d2a70e602039b942018d9be48153dbd26274414c"],"state_sha256":"60d67c6431d1b3c73131e605a841adf8e0be086973b3cf6bdb656e0ebf61cafd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbF2vwhqdKbo+cy10gpuOWzp1HIH6W351euVm0ymYjkowC8y3El+/SQE8jG9GdQDh66Ln1a+viBAIYUw2rJVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:20:17.691735Z","bundle_sha256":"84970d82dce81edef90f42ae0b73355f402ee84f7ea2f0b8b34d0e646bf69d86"}}