{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SW7IUF6NW5X67NX3KDQIUJNQKG","short_pith_number":"pith:SW7IUF6N","canonical_record":{"source":{"id":"1405.5299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-21T05:07:03Z","cross_cats_sorted":["math.AC","math.CT","math.RA"],"title_canon_sha256":"c06eba5691dae551d7cdcf73b3544fca0672d9645e6455910d4c81d4994ca14d","abstract_canon_sha256":"e3fb01933fdac3047252d31033e78f65f66350720c8e4bfdc8b9b5c958391eab"},"schema_version":"1.0"},"canonical_sha256":"95be8a17cdb76fefb6fb50e08a25b051ab33ac138bdb93c66dc6c378cd9ec55e","source":{"kind":"arxiv","id":"1405.5299","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5299","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5299v2","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5299","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"SW7IUF6NW5X6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SW7IUF6NW5X67NX3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SW7IUF6N","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SW7IUF6NW5X67NX3KDQIUJNQKG","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-21T05:07:03Z","cross_cats_sorted":["math.AC","math.CT","math.RA"],"title_canon_sha256":"c06eba5691dae551d7cdcf73b3544fca0672d9645e6455910d4c81d4994ca14d","abstract_canon_sha256":"e3fb01933fdac3047252d31033e78f65f66350720c8e4bfdc8b9b5c958391eab"},"schema_version":"1.0"},"canonical_sha256":"95be8a17cdb76fefb6fb50e08a25b051ab33ac138bdb93c66dc6c378cd9ec55e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:42.055531Z","signature_b64":"Tv/CMklWo+JowWNTy+s1D58K0CLnvB0wvbnJZJAwhpBN4pZ5HfP0JkU/Zvyp7URGhkcRp8YYhyISYkL0w4Z7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95be8a17cdb76fefb6fb50e08a25b051ab33ac138bdb93c66dc6c378cd9ec55e","last_reissued_at":"2026-05-18T02:44:42.055039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:42.055039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5299","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":"2026-05-18T02:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mFqfJXMa2DqoU6CFRuwJ8Ke5zoq8HTR65ron8KFOr/qI2l2baVTeIERo/sEwByl7bDfCH7VKleEPgnTSjRD7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:30:49.511408Z"},"content_sha256":"4c09de2fc9f18b2ccae6546808e9f81bca62a01fd44f4677ba03b3018d728090","schema_version":"1.0","event_id":"sha256:4c09de2fc9f18b2ccae6546808e9f81bca62a01fd44f4677ba03b3018d728090"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SW7IUF6NW5X67NX3KDQIUJNQKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Annihilation of cohomology and decompositions of derived categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Ryo Takahashi, Srikanth B. Iyengar","submitted_at":"2014-05-21T05:07:03Z","abstract_excerpt":"It is proved that an element $r$ in the center of a coherent ring $\\Lambda$ annihilates $\\mathrm{Ext}^{n}_{\\Lambda}(M,N)$, for some positive integer $n$ and all finitely presented $\\Lambda$-modules $M$ and $N$, if and only if the bounded derived category of $\\Lambda$ is an extension of the subcategory consisting of complexes annihilated by $r$ and those obtained as $n$-fold extensions of $\\Lambda$. This has applications to finiteness of dimension of derived categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5299","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":"2026-05-18T02:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rALc9s2hZZDLGvZsiiDhFKIH42NQv7dkAurT7no7FbYzabQWehfpXX3hLW/FewC6gpVCgz3A6IaSoMgj5+FAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:30:49.511750Z"},"content_sha256":"896310b7b439709398d0d052dfd005ffc1d7b523ffd27fed8955465f77bae1a2","schema_version":"1.0","event_id":"sha256:896310b7b439709398d0d052dfd005ffc1d7b523ffd27fed8955465f77bae1a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/bundle.json","state_url":"https://pith.science/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/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":"2026-06-22T01:30:49Z","links":{"resolver":"https://pith.science/pith/SW7IUF6NW5X67NX3KDQIUJNQKG","bundle":"https://pith.science/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/bundle.json","state":"https://pith.science/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW7IUF6NW5X67NX3KDQIUJNQKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SW7IUF6NW5X67NX3KDQIUJNQKG","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":"e3fb01933fdac3047252d31033e78f65f66350720c8e4bfdc8b9b5c958391eab","cross_cats_sorted":["math.AC","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-21T05:07:03Z","title_canon_sha256":"c06eba5691dae551d7cdcf73b3544fca0672d9645e6455910d4c81d4994ca14d"},"schema_version":"1.0","source":{"id":"1405.5299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5299","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5299v2","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5299","created_at":"2026-05-18T02:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"SW7IUF6NW5X6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SW7IUF6NW5X67NX3","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SW7IUF6N","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:896310b7b439709398d0d052dfd005ffc1d7b523ffd27fed8955465f77bae1a2","target":"graph","created_at":"2026-05-18T02:44:42Z","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":"It is proved that an element $r$ in the center of a coherent ring $\\Lambda$ annihilates $\\mathrm{Ext}^{n}_{\\Lambda}(M,N)$, for some positive integer $n$ and all finitely presented $\\Lambda$-modules $M$ and $N$, if and only if the bounded derived category of $\\Lambda$ is an extension of the subcategory consisting of complexes annihilated by $r$ and those obtained as $n$-fold extensions of $\\Lambda$. This has applications to finiteness of dimension of derived categories.","authors_text":"Ryo Takahashi, Srikanth B. Iyengar","cross_cats":["math.AC","math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-21T05:07:03Z","title":"Annihilation of cohomology and decompositions of derived categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5299","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":"sha256:4c09de2fc9f18b2ccae6546808e9f81bca62a01fd44f4677ba03b3018d728090","target":"record","created_at":"2026-05-18T02:44:42Z","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":"e3fb01933fdac3047252d31033e78f65f66350720c8e4bfdc8b9b5c958391eab","cross_cats_sorted":["math.AC","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-05-21T05:07:03Z","title_canon_sha256":"c06eba5691dae551d7cdcf73b3544fca0672d9645e6455910d4c81d4994ca14d"},"schema_version":"1.0","source":{"id":"1405.5299","kind":"arxiv","version":2}},"canonical_sha256":"95be8a17cdb76fefb6fb50e08a25b051ab33ac138bdb93c66dc6c378cd9ec55e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95be8a17cdb76fefb6fb50e08a25b051ab33ac138bdb93c66dc6c378cd9ec55e","first_computed_at":"2026-05-18T02:44:42.055039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:42.055039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tv/CMklWo+JowWNTy+s1D58K0CLnvB0wvbnJZJAwhpBN4pZ5HfP0JkU/Zvyp7URGhkcRp8YYhyISYkL0w4Z7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:42.055531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c09de2fc9f18b2ccae6546808e9f81bca62a01fd44f4677ba03b3018d728090","sha256:896310b7b439709398d0d052dfd005ffc1d7b523ffd27fed8955465f77bae1a2"],"state_sha256":"faaef0f8a879a7e61f5da1d2f416bf0bbc2b3eaa552a86a39c151f25973bd76b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8eZM2VM95hvknDVT+6CDansHPlCHgcCraP/+s7+ZY188kRgUp6ww0X5G4AIS+VhGram3WM8Qq77E9scC3kdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:30:49.513657Z","bundle_sha256":"55e03653036639ba75816d3ad087e4a6cb09aaf5ccdcfd3fa5c39b98901c7d7c"}}