{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z4RVIJ4LQ4IHEEYNG477AJJSMP","short_pith_number":"pith:Z4RVIJ4L","canonical_record":{"source":{"id":"1302.1274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"023f915d4f20a197ba919ba023551020ec4875f8c4fedaa1fc01915289411697","abstract_canon_sha256":"2f079e91c6d4e0e1736f28aa14aa9fa1ca01f8c4dc10c82343a659230ba8b7fc"},"schema_version":"1.0"},"canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","source":{"kind":"arxiv","id":"1302.1274","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1274","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1274v2","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1274","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"Z4RVIJ4LQ4IH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z4RVIJ4LQ4IHEEYN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z4RVIJ4L","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z4RVIJ4LQ4IHEEYNG477AJJSMP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"023f915d4f20a197ba919ba023551020ec4875f8c4fedaa1fc01915289411697","abstract_canon_sha256":"2f079e91c6d4e0e1736f28aa14aa9fa1ca01f8c4dc10c82343a659230ba8b7fc"},"schema_version":"1.0"},"canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.581875Z","signature_b64":"9xta7+Y9Jm3mAmLwTem/9Hh1OuYwOTpJsddEWvOAhE/a6kFxr6JDkpUDeMFHoVVLJ9TDwBeZhc8IatpIWLTaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","last_reissued_at":"2026-05-18T00:08:05.581497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.581497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1274","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":"2026-05-18T00:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BugoUdvUN0Lbw7H1SsjQtuZnRwQ5x8oIKoLfuH8pdy90vzf+dLanYLT5dLAT3+CF4BqHkTWNmOoZ4lasbxesCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:33:45.853152Z"},"content_sha256":"eba8368d8e7ffece4dd518b1e5e904678d4b3b6fd7dbb05d81ed9a9e22ce0b3f","schema_version":"1.0","event_id":"sha256:eba8368d8e7ffece4dd518b1e5e904678d4b3b6fd7dbb05d81ed9a9e22ce0b3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z4RVIJ4LQ4IHEEYNG477AJJSMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On top local cohomology modules, Matlis duality and tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"KH. Ahmadi-amoli, M. Eghbali, M.Y. Sadeghi","submitted_at":"2013-02-06T06:27:56Z","abstract_excerpt":"Let $\\mathfrak{a}$ be an ideal of a local ring $(R, \\mathfrak{m})$ with $c = \\mathrm{cd}(\\mathfrak{a},R)$ the cohomological dimension of $\\mathfrak{a}$ in $R$. In the case that $c=\\dim R$, we first give a bound for depth~$D(H^c_\\mathfrak{a}(R))$, where $c>2$ and $(R,\\mathfrak{m})$ is complete. Later, $H^c_\\mathfrak{a}(R) \\otimes_R H^c_\\mathfrak{a}(R)$, $D(H^c_\\mathfrak{a}(R)) \\otimes_R D(H^c_\\mathfrak{a}(R))$ and $H^c_\\mathfrak{a}(R) \\otimes_R D(H^c_\\mathfrak{a}(R))$ are examined. In the case $c=\\dim R-1$, the set Att$_R H^c_\\mathfrak{a}(R)$ is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1274","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":"2026-05-18T00:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGFJw9Q1Hl9bAL+2QUckz42yKvVtl7LmgSZ5wwPAxan92dja/vri+CLdhhh0DJrioz6gL95U2xajyuPnq6w9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:33:45.853725Z"},"content_sha256":"e2ed29205b7c9fde1661217cc702732d4b4a89eebb8b259def284414ad2288df","schema_version":"1.0","event_id":"sha256:e2ed29205b7c9fde1661217cc702732d4b4a89eebb8b259def284414ad2288df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/bundle.json","state_url":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/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":"2026-06-27T05:33:45Z","links":{"resolver":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP","bundle":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/bundle.json","state":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z4RVIJ4LQ4IHEEYNG477AJJSMP","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":"2f079e91c6d4e0e1736f28aa14aa9fa1ca01f8c4dc10c82343a659230ba8b7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","title_canon_sha256":"023f915d4f20a197ba919ba023551020ec4875f8c4fedaa1fc01915289411697"},"schema_version":"1.0","source":{"id":"1302.1274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1274","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1274v2","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1274","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"Z4RVIJ4LQ4IH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z4RVIJ4LQ4IHEEYN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z4RVIJ4L","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:e2ed29205b7c9fde1661217cc702732d4b4a89eebb8b259def284414ad2288df","target":"graph","created_at":"2026-05-18T00:08:05Z","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 $\\mathfrak{a}$ be an ideal of a local ring $(R, \\mathfrak{m})$ with $c = \\mathrm{cd}(\\mathfrak{a},R)$ the cohomological dimension of $\\mathfrak{a}$ in $R$. In the case that $c=\\dim R$, we first give a bound for depth~$D(H^c_\\mathfrak{a}(R))$, where $c>2$ and $(R,\\mathfrak{m})$ is complete. Later, $H^c_\\mathfrak{a}(R) \\otimes_R H^c_\\mathfrak{a}(R)$, $D(H^c_\\mathfrak{a}(R)) \\otimes_R D(H^c_\\mathfrak{a}(R))$ and $H^c_\\mathfrak{a}(R) \\otimes_R D(H^c_\\mathfrak{a}(R))$ are examined. In the case $c=\\dim R-1$, the set Att$_R H^c_\\mathfrak{a}(R)$ is considered.","authors_text":"KH. Ahmadi-amoli, M. Eghbali, M.Y. Sadeghi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","title":"On top local cohomology modules, Matlis duality and tensor products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1274","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:eba8368d8e7ffece4dd518b1e5e904678d4b3b6fd7dbb05d81ed9a9e22ce0b3f","target":"record","created_at":"2026-05-18T00:08:05Z","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":"2f079e91c6d4e0e1736f28aa14aa9fa1ca01f8c4dc10c82343a659230ba8b7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","title_canon_sha256":"023f915d4f20a197ba919ba023551020ec4875f8c4fedaa1fc01915289411697"},"schema_version":"1.0","source":{"id":"1302.1274","kind":"arxiv","version":2}},"canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","first_computed_at":"2026-05-18T00:08:05.581497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:05.581497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xta7+Y9Jm3mAmLwTem/9Hh1OuYwOTpJsddEWvOAhE/a6kFxr6JDkpUDeMFHoVVLJ9TDwBeZhc8IatpIWLTaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:05.581875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eba8368d8e7ffece4dd518b1e5e904678d4b3b6fd7dbb05d81ed9a9e22ce0b3f","sha256:e2ed29205b7c9fde1661217cc702732d4b4a89eebb8b259def284414ad2288df"],"state_sha256":"c8063e43c3bf402b34b9b363b5a18d4e2fc2131417a128b4731e89b35b464280"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nQOLsqk5Kdv4egTVJyvzN5Wy9oOyIcqgV4w2nWl1LpfSnA9Qmh1L4zPyVu0LezrJ/80Z7TmeOdBVszcC/NUxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:33:45.857559Z","bundle_sha256":"554d2b50357c70851dcf35696774877a5e49b5aa50033ee67535f0c2804887b4"}}