{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RB5QOYGUHXQGD7LSY7VUXSQLZG","short_pith_number":"pith:RB5QOYGU","canonical_record":{"source":{"id":"1005.1304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-07T22:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"cc1c8cce4ae0c287dcea22d2f6edb2fe7422a2faa12115c4a6d400a461426821","abstract_canon_sha256":"97d3e864fc9408467f4c80640cea66f6eacbd1e6cb4747f4d71f51b03aa932fa"},"schema_version":"1.0"},"canonical_sha256":"887b0760d43de061fd72c7eb4bca0bc9be0e3395cde53e0c560752e0e724de1c","source":{"kind":"arxiv","id":"1005.1304","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1304","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1304v2","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1304","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"RB5QOYGUHXQG","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RB5QOYGUHXQGD7LS","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RB5QOYGU","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RB5QOYGUHXQGD7LSY7VUXSQLZG","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-07T22:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"cc1c8cce4ae0c287dcea22d2f6edb2fe7422a2faa12115c4a6d400a461426821","abstract_canon_sha256":"97d3e864fc9408467f4c80640cea66f6eacbd1e6cb4747f4d71f51b03aa932fa"},"schema_version":"1.0"},"canonical_sha256":"887b0760d43de061fd72c7eb4bca0bc9be0e3395cde53e0c560752e0e724de1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:34.989591Z","signature_b64":"YS+B66PhpeGeKyhKD+idz4mcnv0BN2n6U1iIjqMeD7l0WVySjpXPiCrmFjNyMaiBp40zvCDJ/Dhw/GoFT9dVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"887b0760d43de061fd72c7eb4bca0bc9be0e3395cde53e0c560752e0e724de1c","last_reissued_at":"2026-05-18T04:29:34.989205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:34.989205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1304","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":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a83GSukekiCaJj925pLzEkaSqUYkXxnqyIKxfEgLyBI7ajnI3TguSu6FwYMNOwH0u5mNIyh/yQcJAU16dz+GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:45:24.469401Z"},"content_sha256":"f3715ad410bd7314066e111c62d91905f4afa698a556ba5c5c7e7cff283263a2","schema_version":"1.0","event_id":"sha256:f3715ad410bd7314066e111c62d91905f4afa698a556ba5c5c7e7cff283263a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RB5QOYGUHXQGD7LSY7VUXSQLZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connected sums of Gorenstein local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"H. Ananthnarayan, Luchezar L. Avramov, W. Frank Moore","submitted_at":"2010-05-07T22:28:10Z","abstract_excerpt":"A new construction of rings is introduced, studied, and applied. Given surjective homomorphisms $R\\to T\\gets S$ of local rings, and ideals in $R$ and $S$ that are isomorphic to some $T$-module $V$, the \\emph{connected sum} $R#_TS$ is defined to be the local ring obtained by factoring out the diagonal image of $V$ in the fiber product $R\\times_TS$. When $T$ is Cohen-Macaulay of dimension $d$ and $V$ is a canonical module of $T$, it is proved that if $R$ and $S$ are Gorenstein of dimension $d$, then so is $R#_TS$. This result is used to study how closely an artinian ring can be approximated by G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1304","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":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9MYcZ4DSogVZS3AHUvChyELmo7qO+yV3AtEoe89yYrJcwiZCdRRCYhirbr1qZ2QXNx8oPDN59+ROsNjptfMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:45:24.469753Z"},"content_sha256":"001dd58b9de6a37a8984af1b10f7e8bdb059b7c9262d20414a22d8e345adade3","schema_version":"1.0","event_id":"sha256:001dd58b9de6a37a8984af1b10f7e8bdb059b7c9262d20414a22d8e345adade3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/bundle.json","state_url":"https://pith.science/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/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":"2026-06-21T19:45:24Z","links":{"resolver":"https://pith.science/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG","bundle":"https://pith.science/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/bundle.json","state":"https://pith.science/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RB5QOYGUHXQGD7LSY7VUXSQLZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RB5QOYGUHXQGD7LSY7VUXSQLZG","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":"97d3e864fc9408467f4c80640cea66f6eacbd1e6cb4747f4d71f51b03aa932fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-07T22:28:10Z","title_canon_sha256":"cc1c8cce4ae0c287dcea22d2f6edb2fe7422a2faa12115c4a6d400a461426821"},"schema_version":"1.0","source":{"id":"1005.1304","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1304","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1304v2","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1304","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"RB5QOYGUHXQG","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RB5QOYGUHXQGD7LS","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RB5QOYGU","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:001dd58b9de6a37a8984af1b10f7e8bdb059b7c9262d20414a22d8e345adade3","target":"graph","created_at":"2026-05-18T04:29:34Z","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":"A new construction of rings is introduced, studied, and applied. Given surjective homomorphisms $R\\to T\\gets S$ of local rings, and ideals in $R$ and $S$ that are isomorphic to some $T$-module $V$, the \\emph{connected sum} $R#_TS$ is defined to be the local ring obtained by factoring out the diagonal image of $V$ in the fiber product $R\\times_TS$. When $T$ is Cohen-Macaulay of dimension $d$ and $V$ is a canonical module of $T$, it is proved that if $R$ and $S$ are Gorenstein of dimension $d$, then so is $R#_TS$. This result is used to study how closely an artinian ring can be approximated by G","authors_text":"H. Ananthnarayan, Luchezar L. Avramov, W. Frank Moore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-07T22:28:10Z","title":"Connected sums of Gorenstein local rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1304","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:f3715ad410bd7314066e111c62d91905f4afa698a556ba5c5c7e7cff283263a2","target":"record","created_at":"2026-05-18T04:29:34Z","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":"97d3e864fc9408467f4c80640cea66f6eacbd1e6cb4747f4d71f51b03aa932fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-07T22:28:10Z","title_canon_sha256":"cc1c8cce4ae0c287dcea22d2f6edb2fe7422a2faa12115c4a6d400a461426821"},"schema_version":"1.0","source":{"id":"1005.1304","kind":"arxiv","version":2}},"canonical_sha256":"887b0760d43de061fd72c7eb4bca0bc9be0e3395cde53e0c560752e0e724de1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"887b0760d43de061fd72c7eb4bca0bc9be0e3395cde53e0c560752e0e724de1c","first_computed_at":"2026-05-18T04:29:34.989205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:34.989205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YS+B66PhpeGeKyhKD+idz4mcnv0BN2n6U1iIjqMeD7l0WVySjpXPiCrmFjNyMaiBp40zvCDJ/Dhw/GoFT9dVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:34.989591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1304","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3715ad410bd7314066e111c62d91905f4afa698a556ba5c5c7e7cff283263a2","sha256:001dd58b9de6a37a8984af1b10f7e8bdb059b7c9262d20414a22d8e345adade3"],"state_sha256":"935cdad756cdf3ab562139d920ef7b90039afa1622c9eedff6e8b4965165420f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X5g7CZ0YWWbU5+R/3kQwlMCbTEudFPIR2KbETCtSN+ffUCL0/N9Phs7ZuTrh66CBT3bf0PX8oM4O1sGxei6RBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:45:24.471728Z","bundle_sha256":"619063ede2775b05f3cc35b18a395b267f7e60279f4defd84273163721558a3b"}}