{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A7KYRNMOL54NRAFQQ2IIXPGJGT","short_pith_number":"pith:A7KYRNMO","canonical_record":{"source":{"id":"1611.05790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-17T17:23:42Z","cross_cats_sorted":[],"title_canon_sha256":"07421183c20b051476260b493051d0db5a08e8f97d3fec9085a507fc3ea8369f","abstract_canon_sha256":"fc82dbf5d92c3a6480153797a2893cb37adbcade1f159b94fbc474cd4030ce7a"},"schema_version":"1.0"},"canonical_sha256":"07d588b58e5f78d880b086908bbcc934d8728849a4f50a6a5708e313b0b78397","source":{"kind":"arxiv","id":"1611.05790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05790","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05790v1","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05790","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"A7KYRNMOL54N","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7KYRNMOL54NRAFQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7KYRNMO","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A7KYRNMOL54NRAFQQ2IIXPGJGT","target":"record","payload":{"canonical_record":{"source":{"id":"1611.05790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-17T17:23:42Z","cross_cats_sorted":[],"title_canon_sha256":"07421183c20b051476260b493051d0db5a08e8f97d3fec9085a507fc3ea8369f","abstract_canon_sha256":"fc82dbf5d92c3a6480153797a2893cb37adbcade1f159b94fbc474cd4030ce7a"},"schema_version":"1.0"},"canonical_sha256":"07d588b58e5f78d880b086908bbcc934d8728849a4f50a6a5708e313b0b78397","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:02.568919Z","signature_b64":"rgLBJ+u/fDBVEiSu4d1jSkyuBnvYqj0AlHppDkLAjlOQNuh/K8Js2rVuGwL1ZA80lkPGr7KDncfj+lqDZdVAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07d588b58e5f78d880b086908bbcc934d8728849a4f50a6a5708e313b0b78397","last_reissued_at":"2026-05-18T00:58:02.568475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:02.568475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.05790","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":"2026-05-18T00:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JI96sCI++3ZXrh0+s7sziOIcdEHVuz6ai0uTF9cVZvjAPX7RbZG37BafCMu93kgOl2j2d6qmKgeySycdJQcCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:44:19.783915Z"},"content_sha256":"e005f73fb7931858ccf17b56ea61feb34df2ab3bd0821d97e744623175edd290","schema_version":"1.0","event_id":"sha256:e005f73fb7931858ccf17b56ea61feb34df2ab3bd0821d97e744623175edd290"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A7KYRNMOL54NRAFQQ2IIXPGJGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chains of semidualizing modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ensiyeh Amanzadeh","submitted_at":"2016-11-17T17:23:42Z","abstract_excerpt":"Let $(R, \\mathfrak{m}, k)$ be a commutative Noetherian local ring. We study the suitable chains of semidualizing $R$-modules. We prove that when $R$ is Artinian, the existence of a suitable chain of semidualizing modules of length $n=\\mathrm{max}\\,\\{\\,i\\geqslant 0\\ |\\ \\mathfrak{m}^{i}\\neq 0\\,\\}$ implies that the the Poincar$\\acute{\\mathrm{e}}$ series of $k$ and the Bass series of $R$ have very specific forms. Also, in this case we show that the Bass numbers of $R$ are strictly increasing. This gives an insight into the question of Huneke about the Bass numbers of $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05790","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":"2026-05-18T00:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sj1TlSDp/Fqi8pnCqDi8eo/q4+N5OYS/OT4JDvKoV+pV/I5uk2/nWS1//fhCmWIAMHKrZhv2TEyFmPtOd7y4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:44:19.784283Z"},"content_sha256":"5288c7e1a4038a20df2f60e8f92dec34105df3ba6512e596d12f2f26922bea2e","schema_version":"1.0","event_id":"sha256:5288c7e1a4038a20df2f60e8f92dec34105df3ba6512e596d12f2f26922bea2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/bundle.json","state_url":"https://pith.science/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/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":"2026-06-01T00:44:19Z","links":{"resolver":"https://pith.science/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT","bundle":"https://pith.science/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/bundle.json","state":"https://pith.science/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7KYRNMOL54NRAFQQ2IIXPGJGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A7KYRNMOL54NRAFQQ2IIXPGJGT","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":"fc82dbf5d92c3a6480153797a2893cb37adbcade1f159b94fbc474cd4030ce7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-17T17:23:42Z","title_canon_sha256":"07421183c20b051476260b493051d0db5a08e8f97d3fec9085a507fc3ea8369f"},"schema_version":"1.0","source":{"id":"1611.05790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05790","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05790v1","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05790","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"A7KYRNMOL54N","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7KYRNMOL54NRAFQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7KYRNMO","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:5288c7e1a4038a20df2f60e8f92dec34105df3ba6512e596d12f2f26922bea2e","target":"graph","created_at":"2026-05-18T00:58:02Z","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":"Let $(R, \\mathfrak{m}, k)$ be a commutative Noetherian local ring. We study the suitable chains of semidualizing $R$-modules. We prove that when $R$ is Artinian, the existence of a suitable chain of semidualizing modules of length $n=\\mathrm{max}\\,\\{\\,i\\geqslant 0\\ |\\ \\mathfrak{m}^{i}\\neq 0\\,\\}$ implies that the the Poincar$\\acute{\\mathrm{e}}$ series of $k$ and the Bass series of $R$ have very specific forms. Also, in this case we show that the Bass numbers of $R$ are strictly increasing. This gives an insight into the question of Huneke about the Bass numbers of $R$.","authors_text":"Ensiyeh Amanzadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-17T17:23:42Z","title":"Chains of semidualizing modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05790","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:e005f73fb7931858ccf17b56ea61feb34df2ab3bd0821d97e744623175edd290","target":"record","created_at":"2026-05-18T00:58:02Z","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":"fc82dbf5d92c3a6480153797a2893cb37adbcade1f159b94fbc474cd4030ce7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-11-17T17:23:42Z","title_canon_sha256":"07421183c20b051476260b493051d0db5a08e8f97d3fec9085a507fc3ea8369f"},"schema_version":"1.0","source":{"id":"1611.05790","kind":"arxiv","version":1}},"canonical_sha256":"07d588b58e5f78d880b086908bbcc934d8728849a4f50a6a5708e313b0b78397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07d588b58e5f78d880b086908bbcc934d8728849a4f50a6a5708e313b0b78397","first_computed_at":"2026-05-18T00:58:02.568475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:02.568475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgLBJ+u/fDBVEiSu4d1jSkyuBnvYqj0AlHppDkLAjlOQNuh/K8Js2rVuGwL1ZA80lkPGr7KDncfj+lqDZdVAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:02.568919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e005f73fb7931858ccf17b56ea61feb34df2ab3bd0821d97e744623175edd290","sha256:5288c7e1a4038a20df2f60e8f92dec34105df3ba6512e596d12f2f26922bea2e"],"state_sha256":"5d630b02480ea80f5423bf055a8f3ab135bd6091678bd6843eadd0ed2ce50f2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h3oX1VPCZkQ1cB67w7mwtsWcIzGGfpXhaNtxi/IgdwDAPwfnzU/JC90Jysb3nggrG7eN0AbN+K5t45FC9o4WAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:44:19.786768Z","bundle_sha256":"2e4b99bef8ce331f9d92518937d2d7a26a2b6be904eaa7f39e2e5120d25223b0"}}