{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4JCAH25VQ6IUJLT7KCDVWRQTUP","short_pith_number":"pith:4JCAH25V","canonical_record":{"source":{"id":"1701.08087","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-27T15:47:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"16a9997553c979dfc040d0095102be9c6486d8e588289bbefa0cb195260beb68","abstract_canon_sha256":"2429dfa6043f51dff3b449673e029bb42c76c1957f58fd1e9ad19868f8fc86be"},"schema_version":"1.0"},"canonical_sha256":"e24403ebb5879144ae7f50875b4613a3f045ae5803eb0935f90219d6d83c67f2","source":{"kind":"arxiv","id":"1701.08087","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08087","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08087v4","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08087","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"4JCAH25VQ6IU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JCAH25VQ6IUJLT7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JCAH25V","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4JCAH25VQ6IUJLT7KCDVWRQTUP","target":"record","payload":{"canonical_record":{"source":{"id":"1701.08087","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-27T15:47:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"16a9997553c979dfc040d0095102be9c6486d8e588289bbefa0cb195260beb68","abstract_canon_sha256":"2429dfa6043f51dff3b449673e029bb42c76c1957f58fd1e9ad19868f8fc86be"},"schema_version":"1.0"},"canonical_sha256":"e24403ebb5879144ae7f50875b4613a3f045ae5803eb0935f90219d6d83c67f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:27.914616Z","signature_b64":"A2h4Rnn02lIECDfU6rF8k6ZVnHv4fiAF2lcPhsOoeKtqqmufe2fBCfH/Aam4IBtll99uAS+FxfGFHTm4x6tMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e24403ebb5879144ae7f50875b4613a3f045ae5803eb0935f90219d6d83c67f2","last_reissued_at":"2026-05-17T23:39:27.913905Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:27.913905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.08087","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ieEoPOku0/3MFQvrFszhLKfkPNwUeOBCxdzEykcB3x1PXN9tb17U88+5BKVosQBKDaMdP8d0hOMrMZ1JBKn9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:59:52.702473Z"},"content_sha256":"47df3323b85c1a20ef6074b28425302dedd1575b6e4493dd17c4233478d40b02","schema_version":"1.0","event_id":"sha256:47df3323b85c1a20ef6074b28425302dedd1575b6e4493dd17c4233478d40b02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4JCAH25VQ6IUJLT7KCDVWRQTUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohen-Macaulayness and canonical module of residual intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Jos\\'e Na\\'eliton, Marc Chardin, Quang Hoa Tran","submitted_at":"2017-01-27T15:47:23Z","abstract_excerpt":"We show the Cohen-Macaulayness and describe the canonical module of residual intersections $J=\\mathfrak{a}\\colon_R I$ in a Cohen-Macaulay local ring $R$, under sliding depth type hypotheses. For this purpose, we construct and study, using a recent article of Hassanzadeh and the second named author, a family of complexes that contains important informations on a residual intersection and its canonical module. We also determine several invariants of residual intersections as the graded canonical module, the Hilbert series, the Castelnuovo-Mumford regularity and the type. Finally, whenever $I$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08087","kind":"arxiv","version":4},"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":"2026-05-17T23:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESbHNbGJFrewMlvZdiNHeq34ihw4GQrr+tCcg5ZQf6OSOjWCcl1HXCO6ImTvFz06MA3wLHxu7JiTssiRCZIrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:59:52.702824Z"},"content_sha256":"14e5dbd62f3e315ed663803958619e8affcb76c7782ee9355b4ce77e16aec3bb","schema_version":"1.0","event_id":"sha256:14e5dbd62f3e315ed663803958619e8affcb76c7782ee9355b4ce77e16aec3bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/bundle.json","state_url":"https://pith.science/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/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":"2026-06-02T22:59:52Z","links":{"resolver":"https://pith.science/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP","bundle":"https://pith.science/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/bundle.json","state":"https://pith.science/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JCAH25VQ6IUJLT7KCDVWRQTUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4JCAH25VQ6IUJLT7KCDVWRQTUP","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":"2429dfa6043f51dff3b449673e029bb42c76c1957f58fd1e9ad19868f8fc86be","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-27T15:47:23Z","title_canon_sha256":"16a9997553c979dfc040d0095102be9c6486d8e588289bbefa0cb195260beb68"},"schema_version":"1.0","source":{"id":"1701.08087","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08087","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08087v4","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08087","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"4JCAH25VQ6IU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JCAH25VQ6IUJLT7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JCAH25V","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:14e5dbd62f3e315ed663803958619e8affcb76c7782ee9355b4ce77e16aec3bb","target":"graph","created_at":"2026-05-17T23:39:27Z","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":"We show the Cohen-Macaulayness and describe the canonical module of residual intersections $J=\\mathfrak{a}\\colon_R I$ in a Cohen-Macaulay local ring $R$, under sliding depth type hypotheses. For this purpose, we construct and study, using a recent article of Hassanzadeh and the second named author, a family of complexes that contains important informations on a residual intersection and its canonical module. We also determine several invariants of residual intersections as the graded canonical module, the Hilbert series, the Castelnuovo-Mumford regularity and the type. Finally, whenever $I$ is","authors_text":"Jos\\'e Na\\'eliton, Marc Chardin, Quang Hoa Tran","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-27T15:47:23Z","title":"Cohen-Macaulayness and canonical module of residual intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08087","kind":"arxiv","version":4},"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":"sha256:47df3323b85c1a20ef6074b28425302dedd1575b6e4493dd17c4233478d40b02","target":"record","created_at":"2026-05-17T23:39:27Z","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":"2429dfa6043f51dff3b449673e029bb42c76c1957f58fd1e9ad19868f8fc86be","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-27T15:47:23Z","title_canon_sha256":"16a9997553c979dfc040d0095102be9c6486d8e588289bbefa0cb195260beb68"},"schema_version":"1.0","source":{"id":"1701.08087","kind":"arxiv","version":4}},"canonical_sha256":"e24403ebb5879144ae7f50875b4613a3f045ae5803eb0935f90219d6d83c67f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e24403ebb5879144ae7f50875b4613a3f045ae5803eb0935f90219d6d83c67f2","first_computed_at":"2026-05-17T23:39:27.913905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:27.913905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2h4Rnn02lIECDfU6rF8k6ZVnHv4fiAF2lcPhsOoeKtqqmufe2fBCfH/Aam4IBtll99uAS+FxfGFHTm4x6tMDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:27.914616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08087","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47df3323b85c1a20ef6074b28425302dedd1575b6e4493dd17c4233478d40b02","sha256:14e5dbd62f3e315ed663803958619e8affcb76c7782ee9355b4ce77e16aec3bb"],"state_sha256":"5b334f10784f0623db36e9b94225976fbc2a57acae26d40de9d35bbf83ef44be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HLzgrJRNK0hZkxX3d8h+OVt11AAC8GPdMEyNYV3yRvNEkeugr91/N8TWGLiE12SRWEO4OzxUsOccgTz8gX8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:59:52.705171Z","bundle_sha256":"18f769d7a20de40d6c5a4d200cd6df7d4dcbf69afc2e303f8beed8812d5d6edf"}}