{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JTVVX64AA6NQRCSA5UHAGG5YRN","short_pith_number":"pith:JTVVX64A","canonical_record":{"source":{"id":"1406.7461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-06-29T04:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"9a0be762d40f1ac682432e6df746ce57392c81041cf43cb01236d7d8131cb550","abstract_canon_sha256":"00b0ded544ba590f4b9454f747b6e4f22f44c58d3d193051a8b71e8b642f77b0"},"schema_version":"1.0"},"canonical_sha256":"4ceb5bfb80079b088a40ed0e031bb88b7938766357f3dbb64da4f2d394738752","source":{"kind":"arxiv","id":"1406.7461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7461","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7461v1","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7461","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"JTVVX64AA6NQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JTVVX64AA6NQRCSA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JTVVX64A","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JTVVX64AA6NQRCSA5UHAGG5YRN","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-06-29T04:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"9a0be762d40f1ac682432e6df746ce57392c81041cf43cb01236d7d8131cb550","abstract_canon_sha256":"00b0ded544ba590f4b9454f747b6e4f22f44c58d3d193051a8b71e8b642f77b0"},"schema_version":"1.0"},"canonical_sha256":"4ceb5bfb80079b088a40ed0e031bb88b7938766357f3dbb64da4f2d394738752","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:45.243596Z","signature_b64":"xjXzmSOUj0kp3UmSoXcn00PpjVbY4ou1oSDMF+tmc0Qg0vekPBKomvHKtX9cE38S416pttzeS9lI+bDaQ/npCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ceb5bfb80079b088a40ed0e031bb88b7938766357f3dbb64da4f2d394738752","last_reissued_at":"2026-05-18T02:48:45.242973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:45.242973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7461","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":"2026-05-18T02:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NId03siM/lCzp/OH0w9ukn9cQjCL8KOEM+jsLIUbCWbeDkd/sD8LGM0SC7kJUpEyP7C6P7sZnukpBvS/FI6EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:40:11.344242Z"},"content_sha256":"c22dac301b38390e3dbc544a4a0381860fcddcfb5c5b05f3b755efa249344f5f","schema_version":"1.0","event_id":"sha256:c22dac301b38390e3dbc544a4a0381860fcddcfb5c5b05f3b755efa249344f5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JTVVX64AA6NQRCSA5UHAGG5YRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On natural homomorphisms of local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Waqas Mahmood","submitted_at":"2014-06-29T04:58:51Z","abstract_excerpt":"Let $M$ be a non-zero finitely generated module over a finite dimensional commutative Noetherian local ring $(R,\\mathfrak{m})$ with dim$_R(M)=t$. Let $I$ be an ideal of $R$ with grade$(I,M)=c$. In this article we will investigate several natural homomorphisms of local cohomology modules. The main purpose of this article is to investigate that the natural homomorphisms Tor$^R_c(k,H^c_I(M))\\to k\\otimes_R M$ and Ext$^{d}_R(k,H^c_I(M))\\to {\\rm Ext}^t_R(k, M)$ are non-zero where $d:=t-c$. In fact for a Cohen-Macaulay module $M$ we will show that the homomorphism Ext$^d_R(k,H^c_I(M))\\to {\\rm Ext}^t_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7461","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":"2026-05-18T02:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zn8Yv3HPODxxy71j6IyU66TfQgOHXnE/A+8Y/1sqazNXlrNyVazUQ0K72+iYjZk3MFHuoQa9NO6aOOsk0jrtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:40:11.344601Z"},"content_sha256":"55f787f733b1d64c7297e44464e28bda0bbf471949c3be9a6794fbbc2924578b","schema_version":"1.0","event_id":"sha256:55f787f733b1d64c7297e44464e28bda0bbf471949c3be9a6794fbbc2924578b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/bundle.json","state_url":"https://pith.science/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/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":"2026-06-03T22:40:11Z","links":{"resolver":"https://pith.science/pith/JTVVX64AA6NQRCSA5UHAGG5YRN","bundle":"https://pith.science/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/bundle.json","state":"https://pith.science/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTVVX64AA6NQRCSA5UHAGG5YRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JTVVX64AA6NQRCSA5UHAGG5YRN","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":"00b0ded544ba590f4b9454f747b6e4f22f44c58d3d193051a8b71e8b642f77b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-06-29T04:58:51Z","title_canon_sha256":"9a0be762d40f1ac682432e6df746ce57392c81041cf43cb01236d7d8131cb550"},"schema_version":"1.0","source":{"id":"1406.7461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7461","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7461v1","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7461","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"JTVVX64AA6NQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JTVVX64AA6NQRCSA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JTVVX64A","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:55f787f733b1d64c7297e44464e28bda0bbf471949c3be9a6794fbbc2924578b","target":"graph","created_at":"2026-05-18T02:48:45Z","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 $M$ be a non-zero finitely generated module over a finite dimensional commutative Noetherian local ring $(R,\\mathfrak{m})$ with dim$_R(M)=t$. Let $I$ be an ideal of $R$ with grade$(I,M)=c$. In this article we will investigate several natural homomorphisms of local cohomology modules. The main purpose of this article is to investigate that the natural homomorphisms Tor$^R_c(k,H^c_I(M))\\to k\\otimes_R M$ and Ext$^{d}_R(k,H^c_I(M))\\to {\\rm Ext}^t_R(k, M)$ are non-zero where $d:=t-c$. In fact for a Cohen-Macaulay module $M$ we will show that the homomorphism Ext$^d_R(k,H^c_I(M))\\to {\\rm Ext}^t_","authors_text":"Waqas Mahmood","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-06-29T04:58:51Z","title":"On natural homomorphisms of local cohomology modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7461","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:c22dac301b38390e3dbc544a4a0381860fcddcfb5c5b05f3b755efa249344f5f","target":"record","created_at":"2026-05-18T02:48:45Z","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":"00b0ded544ba590f4b9454f747b6e4f22f44c58d3d193051a8b71e8b642f77b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-06-29T04:58:51Z","title_canon_sha256":"9a0be762d40f1ac682432e6df746ce57392c81041cf43cb01236d7d8131cb550"},"schema_version":"1.0","source":{"id":"1406.7461","kind":"arxiv","version":1}},"canonical_sha256":"4ceb5bfb80079b088a40ed0e031bb88b7938766357f3dbb64da4f2d394738752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ceb5bfb80079b088a40ed0e031bb88b7938766357f3dbb64da4f2d394738752","first_computed_at":"2026-05-18T02:48:45.242973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:45.242973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjXzmSOUj0kp3UmSoXcn00PpjVbY4ou1oSDMF+tmc0Qg0vekPBKomvHKtX9cE38S416pttzeS9lI+bDaQ/npCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:45.243596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c22dac301b38390e3dbc544a4a0381860fcddcfb5c5b05f3b755efa249344f5f","sha256:55f787f733b1d64c7297e44464e28bda0bbf471949c3be9a6794fbbc2924578b"],"state_sha256":"f4d616d24be2c5ab514b1483cd4418fc4d5e8baa5612818fc03f31da9b1e549c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l19pzUYQ1VMqVbUBiwK3VvfIe8wMOsjDWvGuymocrxyjF70WO/p615OCwunGVtGXam7cgTS7Zbo+LfRK84hjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:40:11.346770Z","bundle_sha256":"8e705cd98cdbffdc4a5bafb4551078176ffe567b084331020ecb308b20b59795"}}