{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C4UIL3BFLDKFROIN5DDN7V3SYB","short_pith_number":"pith:C4UIL3BF","canonical_record":{"source":{"id":"1403.7240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-27T22:52:51Z","cross_cats_sorted":[],"title_canon_sha256":"816214c102330946994bb4e016772c8ddca19c929f225d7435c1810f8ee7bde8","abstract_canon_sha256":"c4ecfb2e40f630e17e0fc3aef0bf22c5b6746c124506d2a78824955b99ae4793"},"schema_version":"1.0"},"canonical_sha256":"172885ec2558d458b90de8c6dfd772c05f116d361e2a2ec595b143613ea838a1","source":{"kind":"arxiv","id":"1403.7240","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7240","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7240v2","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7240","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"C4UIL3BFLDKF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C4UIL3BFLDKFROIN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C4UIL3BF","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C4UIL3BFLDKFROIN5DDN7V3SYB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-27T22:52:51Z","cross_cats_sorted":[],"title_canon_sha256":"816214c102330946994bb4e016772c8ddca19c929f225d7435c1810f8ee7bde8","abstract_canon_sha256":"c4ecfb2e40f630e17e0fc3aef0bf22c5b6746c124506d2a78824955b99ae4793"},"schema_version":"1.0"},"canonical_sha256":"172885ec2558d458b90de8c6dfd772c05f116d361e2a2ec595b143613ea838a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:58.845390Z","signature_b64":"hp3SAK/z+BfP2A7srv9FZcamvivukbOmXLUV+X2H09cesrDH4TXWcNNrnc7ljjQj1q3HHmmRJ0MJvlflL66sAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"172885ec2558d458b90de8c6dfd772c05f116d361e2a2ec595b143613ea838a1","last_reissued_at":"2026-05-18T01:12:58.845021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:58.845021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7240","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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76CdlJ7Qn5CvP3HbxH39rbP0aJ8F0OYpYC7GpnuFeDLjLaT9IvWkLnUnfA/X/G4MLPYRZFCZB6qr+ojg9DVtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:24:18.551018Z"},"content_sha256":"97d7ef1f5753548de369d2a36007da019f72d38df79cd3d276b0e9234e237cf4","schema_version":"1.0","event_id":"sha256:97d7ef1f5753548de369d2a36007da019f72d38df79cd3d276b0e9234e237cf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C4UIL3BFLDKFROIN5DDN7V3SYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditions for the Yoneda algebra of a local ring to be generated in low degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Justin Hoffmeier, Liana M. \\c{S}ega","submitted_at":"2014-03-27T22:52:51Z","abstract_excerpt":"The powers ${\\mathfrak m}^n$ of the maximal ideal $\\mathfrak m$ of a local Noetherian ring $R$ are known to satisfy certain homological properties for large values of $n$. For example, the homomorphism $R\\to R/{\\mathfrak m}^n$ is Golod for $n\\gg 0$. We study when such properties hold for small values of $n$, and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of $R$ is generated in degrees $1$ and $2$. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7240","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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GNoI3CaEdto5AoqQ/rFB43vOORB6kEP7xO94NF7NKE1FX8qCtnqUd/pNn2G/8fwNgIwpHYdjGbg0Ew05L18fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:24:18.551372Z"},"content_sha256":"13bb1f4823f1a747e61e57e6d465932fa1edd6ec011eb893fbd2a481ca7b4855","schema_version":"1.0","event_id":"sha256:13bb1f4823f1a747e61e57e6d465932fa1edd6ec011eb893fbd2a481ca7b4855"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/bundle.json","state_url":"https://pith.science/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/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":"2026-06-21T19:24:18Z","links":{"resolver":"https://pith.science/pith/C4UIL3BFLDKFROIN5DDN7V3SYB","bundle":"https://pith.science/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/bundle.json","state":"https://pith.science/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4UIL3BFLDKFROIN5DDN7V3SYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C4UIL3BFLDKFROIN5DDN7V3SYB","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":"c4ecfb2e40f630e17e0fc3aef0bf22c5b6746c124506d2a78824955b99ae4793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-27T22:52:51Z","title_canon_sha256":"816214c102330946994bb4e016772c8ddca19c929f225d7435c1810f8ee7bde8"},"schema_version":"1.0","source":{"id":"1403.7240","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7240","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7240v2","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7240","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"C4UIL3BFLDKF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C4UIL3BFLDKFROIN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C4UIL3BF","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:13bb1f4823f1a747e61e57e6d465932fa1edd6ec011eb893fbd2a481ca7b4855","target":"graph","created_at":"2026-05-18T01:12:58Z","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":"The powers ${\\mathfrak m}^n$ of the maximal ideal $\\mathfrak m$ of a local Noetherian ring $R$ are known to satisfy certain homological properties for large values of $n$. For example, the homomorphism $R\\to R/{\\mathfrak m}^n$ is Golod for $n\\gg 0$. We study when such properties hold for small values of $n$, and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of $R$ is generated in degrees $1$ and $2$. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings.","authors_text":"Justin Hoffmeier, Liana M. \\c{S}ega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-27T22:52:51Z","title":"Conditions for the Yoneda algebra of a local ring to be generated in low degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7240","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":"sha256:97d7ef1f5753548de369d2a36007da019f72d38df79cd3d276b0e9234e237cf4","target":"record","created_at":"2026-05-18T01:12:58Z","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":"c4ecfb2e40f630e17e0fc3aef0bf22c5b6746c124506d2a78824955b99ae4793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-27T22:52:51Z","title_canon_sha256":"816214c102330946994bb4e016772c8ddca19c929f225d7435c1810f8ee7bde8"},"schema_version":"1.0","source":{"id":"1403.7240","kind":"arxiv","version":2}},"canonical_sha256":"172885ec2558d458b90de8c6dfd772c05f116d361e2a2ec595b143613ea838a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"172885ec2558d458b90de8c6dfd772c05f116d361e2a2ec595b143613ea838a1","first_computed_at":"2026-05-18T01:12:58.845021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.845021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hp3SAK/z+BfP2A7srv9FZcamvivukbOmXLUV+X2H09cesrDH4TXWcNNrnc7ljjQj1q3HHmmRJ0MJvlflL66sAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.845390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7240","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97d7ef1f5753548de369d2a36007da019f72d38df79cd3d276b0e9234e237cf4","sha256:13bb1f4823f1a747e61e57e6d465932fa1edd6ec011eb893fbd2a481ca7b4855"],"state_sha256":"b33e7cc604b1a797dde4a9fdb4ba7a387881e8283406f738555a699ad41b65a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRi07YbLY+aQ44eNFby8CQhlrtg/cePFYh1a0W/xekvBFF+70D51fWR8vexGMc2i1MfDP8HYzIlEhWzE/mlsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:24:18.553268Z","bundle_sha256":"ada34529aacd056d3651dbef6cd2bf53883c6c1801516bae2464f26bf469164e"}}