{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PAWELHFCQ6WSTH7XTNIGHLPI37","short_pith_number":"pith:PAWELHFC","canonical_record":{"source":{"id":"1502.06653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-23T23:39:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bb926ca9eee7af87aa2eb32f2818ea6d61874422d5274daab71994c72e24c217","abstract_canon_sha256":"acb8f75255e0faac605410234eb9c42b4973bdae4d99d7cf2148664d6890c116"},"schema_version":"1.0"},"canonical_sha256":"782c459ca287ad299ff79b5063ade8dfd820b8766aad0e269b75fe77da6739a8","source":{"kind":"arxiv","id":"1502.06653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06653","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06653v1","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06653","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"pith_short_12","alias_value":"PAWELHFCQ6WS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"PAWELHFCQ6WSTH7X","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"PAWELHFC","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PAWELHFCQ6WSTH7XTNIGHLPI37","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-23T23:39:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"bb926ca9eee7af87aa2eb32f2818ea6d61874422d5274daab71994c72e24c217","abstract_canon_sha256":"acb8f75255e0faac605410234eb9c42b4973bdae4d99d7cf2148664d6890c116"},"schema_version":"1.0"},"canonical_sha256":"782c459ca287ad299ff79b5063ade8dfd820b8766aad0e269b75fe77da6739a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:29.526926Z","signature_b64":"3nFq2awdkZeG36DYi1nMCfc8Icm40vFydPOTmvkET6fnwOBbXPfCqwGklEZx9j/jBSsyab6UAwNCK/TpbvOtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"782c459ca287ad299ff79b5063ade8dfd820b8766aad0e269b75fe77da6739a8","last_reissued_at":"2026-05-18T02:26:29.526409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:29.526409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06653","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":"2026-05-18T02:26:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c0Gl+jx06WkL1cMm9x5BR/2k8Fmg1niK4Ppll0yqoL5naz+mK1jpettX6LnEkuOmyUEVtKz2EnaPacccJsddBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:59:09.132921Z"},"content_sha256":"4f253e083e996b8692f2659b9ca8f040b3d3a9a80fa63d6d50ae046798fbe006","schema_version":"1.0","event_id":"sha256:4f253e083e996b8692f2659b9ca8f040b3d3a9a80fa63d6d50ae046798fbe006"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PAWELHFCQ6WSTH7XTNIGHLPI37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension closedness of syzygies and local Gorensteinness of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Ryo Takahashi, Shiro Goto","submitted_at":"2015-02-23T23:39:47Z","abstract_excerpt":"We refine a well-known theorem of Auslander and Reiten about the extension closedness of n-th syzygies over noether algebras. Applying it, we obtain the converse of a celebrated theorem of Evans and Griffith on Serre's condition (S_n) and the local Gorensteiness of a commutative ring in height less than n. This especially extends a recent result of Araya and Iima concerning a Cohen-Macaulay local ring with canonical module to an arbitrary local ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06653","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":"2026-05-18T02:26:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/BIzB5ENzNrdGR41X1vb7Kp/cxGadEX1CsqnjVqGWlPK5K1rX4q2mIBC3qigD+ECZ+ilzXyQOzgy2diKrcdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:59:09.133265Z"},"content_sha256":"547aafcdeee7192aef7cd4e58173fc8041493e4c49c3485f4465c0f69fe51b89","schema_version":"1.0","event_id":"sha256:547aafcdeee7192aef7cd4e58173fc8041493e4c49c3485f4465c0f69fe51b89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/bundle.json","state_url":"https://pith.science/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/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":"2026-06-21T06:59:09Z","links":{"resolver":"https://pith.science/pith/PAWELHFCQ6WSTH7XTNIGHLPI37","bundle":"https://pith.science/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/bundle.json","state":"https://pith.science/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAWELHFCQ6WSTH7XTNIGHLPI37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PAWELHFCQ6WSTH7XTNIGHLPI37","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":"acb8f75255e0faac605410234eb9c42b4973bdae4d99d7cf2148664d6890c116","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-23T23:39:47Z","title_canon_sha256":"bb926ca9eee7af87aa2eb32f2818ea6d61874422d5274daab71994c72e24c217"},"schema_version":"1.0","source":{"id":"1502.06653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06653","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06653v1","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06653","created_at":"2026-05-18T02:26:29Z"},{"alias_kind":"pith_short_12","alias_value":"PAWELHFCQ6WS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"PAWELHFCQ6WSTH7X","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"PAWELHFC","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:547aafcdeee7192aef7cd4e58173fc8041493e4c49c3485f4465c0f69fe51b89","target":"graph","created_at":"2026-05-18T02:26:29Z","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":"We refine a well-known theorem of Auslander and Reiten about the extension closedness of n-th syzygies over noether algebras. Applying it, we obtain the converse of a celebrated theorem of Evans and Griffith on Serre's condition (S_n) and the local Gorensteiness of a commutative ring in height less than n. This especially extends a recent result of Araya and Iima concerning a Cohen-Macaulay local ring with canonical module to an arbitrary local ring.","authors_text":"Ryo Takahashi, Shiro Goto","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-23T23:39:47Z","title":"Extension closedness of syzygies and local Gorensteinness of commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06653","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":"sha256:4f253e083e996b8692f2659b9ca8f040b3d3a9a80fa63d6d50ae046798fbe006","target":"record","created_at":"2026-05-18T02:26:29Z","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":"acb8f75255e0faac605410234eb9c42b4973bdae4d99d7cf2148664d6890c116","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-23T23:39:47Z","title_canon_sha256":"bb926ca9eee7af87aa2eb32f2818ea6d61874422d5274daab71994c72e24c217"},"schema_version":"1.0","source":{"id":"1502.06653","kind":"arxiv","version":1}},"canonical_sha256":"782c459ca287ad299ff79b5063ade8dfd820b8766aad0e269b75fe77da6739a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"782c459ca287ad299ff79b5063ade8dfd820b8766aad0e269b75fe77da6739a8","first_computed_at":"2026-05-18T02:26:29.526409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:29.526409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3nFq2awdkZeG36DYi1nMCfc8Icm40vFydPOTmvkET6fnwOBbXPfCqwGklEZx9j/jBSsyab6UAwNCK/TpbvOtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:29.526926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f253e083e996b8692f2659b9ca8f040b3d3a9a80fa63d6d50ae046798fbe006","sha256:547aafcdeee7192aef7cd4e58173fc8041493e4c49c3485f4465c0f69fe51b89"],"state_sha256":"eb62f2527c27bb780515c6a334d3f9b800bcba4723295b2fbe99b7c836bf6d30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RrS104rySIwsAdaWUEP63yH/i/pfvFNxhUxWtMukCfk566HO3iKi7rOfQ122tOMQ5Szz1qipJ70CWb1AlA5ICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:59:09.135198Z","bundle_sha256":"ac788d9d62ddfe5f139c22ea9f5a2a0e5b21928821266819907193fb7ade783c"}}