{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J54X4JTFAXUXVN6DP2GZEE3VTS","short_pith_number":"pith:J54X4JTF","canonical_record":{"source":{"id":"1507.04556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-16T13:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"dcfea1d888ad151bf0d7b0c3c9dbd29b31eba58e165af640c25b0b04f0694454","abstract_canon_sha256":"26d3ffb7ed8e131d07041942dc94e25d21b5df7a80c6a34c23d4006e4a288265"},"schema_version":"1.0"},"canonical_sha256":"4f797e266505e97ab7c37e8d9213759caed734e6042038dcee44f5705f47527d","source":{"kind":"arxiv","id":"1507.04556","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04556","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04556v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04556","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"J54X4JTFAXUX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J54X4JTFAXUXVN6D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J54X4JTF","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J54X4JTFAXUXVN6DP2GZEE3VTS","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-16T13:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"dcfea1d888ad151bf0d7b0c3c9dbd29b31eba58e165af640c25b0b04f0694454","abstract_canon_sha256":"26d3ffb7ed8e131d07041942dc94e25d21b5df7a80c6a34c23d4006e4a288265"},"schema_version":"1.0"},"canonical_sha256":"4f797e266505e97ab7c37e8d9213759caed734e6042038dcee44f5705f47527d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:53.073541Z","signature_b64":"MZBP9aVk+RRqJZ3/23DRIh8EZ5h0lEE3P2kJXrg3vTxoDWW9h4JDbU9Qp9bZo46dgGGma47Ku10lp/ffNaEFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f797e266505e97ab7c37e8d9213759caed734e6042038dcee44f5705f47527d","last_reissued_at":"2026-05-18T01:14:53.072910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:53.072910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04556","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OrMiDF5QZ5SOC73kpR/35fVNTQd0oSJMDgCbzcjKfkTbSKE8OV+Q97JaEfZK6dzWFegow9CLBj4ARW80YJnhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:03:47.000083Z"},"content_sha256":"889d6f8be9b87e3ca2b82725537942f0dc39f2bf5ae74feeec2328a4a26e692c","schema_version":"1.0","event_id":"sha256:889d6f8be9b87e3ca2b82725537942f0dc39f2bf5ae74feeec2328a4a26e692c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J54X4JTFAXUXVN6DP2GZEE3VTS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ulrich ideals and almost Gorenstein rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Naoki Taniguchi, Ryo Takahashi, Shiro Goto","submitted_at":"2015-07-16T13:05:38Z","abstract_excerpt":"The structure of the complex $\\operatorname{\\mathbf{R}Hom}_R(R/I,R)$ is explored for an Ulrich ideal $I$ in a Cohen-Macaulay local ring $R$. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04556","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYCLeaBPxRfPcLVR4eykOFPEuTfR4g6SrT0gUNvul4fLqDLQPwEgBMKn/eXUe/O19EbMMr8Oxjqlp+S8QqhFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:03:47.000479Z"},"content_sha256":"b3dfe29684357cc9c1754db98c1721a69bc8ef3f20e185119470b96f59b899cc","schema_version":"1.0","event_id":"sha256:b3dfe29684357cc9c1754db98c1721a69bc8ef3f20e185119470b96f59b899cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/bundle.json","state_url":"https://pith.science/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/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":"2026-06-21T07:03:47Z","links":{"resolver":"https://pith.science/pith/J54X4JTFAXUXVN6DP2GZEE3VTS","bundle":"https://pith.science/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/bundle.json","state":"https://pith.science/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J54X4JTFAXUXVN6DP2GZEE3VTS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J54X4JTFAXUXVN6DP2GZEE3VTS","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":"26d3ffb7ed8e131d07041942dc94e25d21b5df7a80c6a34c23d4006e4a288265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-16T13:05:38Z","title_canon_sha256":"dcfea1d888ad151bf0d7b0c3c9dbd29b31eba58e165af640c25b0b04f0694454"},"schema_version":"1.0","source":{"id":"1507.04556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04556","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04556v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04556","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"J54X4JTFAXUX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J54X4JTFAXUXVN6D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J54X4JTF","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:b3dfe29684357cc9c1754db98c1721a69bc8ef3f20e185119470b96f59b899cc","target":"graph","created_at":"2026-05-18T01:14:53Z","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":"The structure of the complex $\\operatorname{\\mathbf{R}Hom}_R(R/I,R)$ is explored for an Ulrich ideal $I$ in a Cohen-Macaulay local ring $R$. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.","authors_text":"Naoki Taniguchi, Ryo Takahashi, Shiro Goto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-16T13:05:38Z","title":"Ulrich ideals and almost Gorenstein rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04556","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":"sha256:889d6f8be9b87e3ca2b82725537942f0dc39f2bf5ae74feeec2328a4a26e692c","target":"record","created_at":"2026-05-18T01:14:53Z","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":"26d3ffb7ed8e131d07041942dc94e25d21b5df7a80c6a34c23d4006e4a288265","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-07-16T13:05:38Z","title_canon_sha256":"dcfea1d888ad151bf0d7b0c3c9dbd29b31eba58e165af640c25b0b04f0694454"},"schema_version":"1.0","source":{"id":"1507.04556","kind":"arxiv","version":2}},"canonical_sha256":"4f797e266505e97ab7c37e8d9213759caed734e6042038dcee44f5705f47527d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f797e266505e97ab7c37e8d9213759caed734e6042038dcee44f5705f47527d","first_computed_at":"2026-05-18T01:14:53.072910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:53.072910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MZBP9aVk+RRqJZ3/23DRIh8EZ5h0lEE3P2kJXrg3vTxoDWW9h4JDbU9Qp9bZo46dgGGma47Ku10lp/ffNaEFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:53.073541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:889d6f8be9b87e3ca2b82725537942f0dc39f2bf5ae74feeec2328a4a26e692c","sha256:b3dfe29684357cc9c1754db98c1721a69bc8ef3f20e185119470b96f59b899cc"],"state_sha256":"349df580356ea43700cb7d74bb6ab1b86ded2daaf4dc53e9c059dc80a33cd273"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"od6nYgcSknM1yoESVEzY/cf2TOX55g9XER39V2eVDl6VQLeIKCyXyu2rZZGigKaqNu1OLPe4Oqc4d31OzMuiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T07:03:47.002488Z","bundle_sha256":"44d80e190bfe1a7e811b6d8cf93b0476b538ad2121ea70823b365f0994683ccb"}}