{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XS3RF3WA7OTDB455KFOMIIZTXO","short_pith_number":"pith:XS3RF3WA","canonical_record":{"source":{"id":"1405.1249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-06T12:46:08Z","cross_cats_sorted":[],"title_canon_sha256":"fcf36387a5540faaf0e318038c1d2ed16e78672da9043bb9408b86db47740c77","abstract_canon_sha256":"bfb08a43fb2c1cd47c2a3109228793eaed69859c7ac4d79990090b69725b4ec8"},"schema_version":"1.0"},"canonical_sha256":"bcb712eec0fba630f3bd515cc42333bb8ec02a507558f72e38dd02862e434859","source":{"kind":"arxiv","id":"1405.1249","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1249","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1249v2","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1249","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"XS3RF3WA7OTD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XS3RF3WA7OTDB455","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XS3RF3WA","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XS3RF3WA7OTDB455KFOMIIZTXO","target":"record","payload":{"canonical_record":{"source":{"id":"1405.1249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-06T12:46:08Z","cross_cats_sorted":[],"title_canon_sha256":"fcf36387a5540faaf0e318038c1d2ed16e78672da9043bb9408b86db47740c77","abstract_canon_sha256":"bfb08a43fb2c1cd47c2a3109228793eaed69859c7ac4d79990090b69725b4ec8"},"schema_version":"1.0"},"canonical_sha256":"bcb712eec0fba630f3bd515cc42333bb8ec02a507558f72e38dd02862e434859","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:05.757204Z","signature_b64":"tJgHVsq74jK1lKtNrEID9Al8SI9NHe/SO4XANrMxrgdtoDs6GS0OGNIyAgylFBDwkbLgYyzqLb+bU0D9mMddCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb712eec0fba630f3bd515cc42333bb8ec02a507558f72e38dd02862e434859","last_reissued_at":"2026-05-18T02:52:05.756734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:05.756734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.1249","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":"2026-05-18T02:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWVstrFOW8bp8A2EuaC+7ybZQPV4TzCz1yh+z1T9dpR8Hxr0VEqs/VkTLZCQwiZVcAPhkX4TVRTKCvAK9ZLRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:13:08.669714Z"},"content_sha256":"3f8c0a5725a79c3898aa9c736c82774cfba2421547c4057dacfe9f18d3fcd7ce","schema_version":"1.0","event_id":"sha256:3f8c0a5725a79c3898aa9c736c82774cfba2421547c4057dacfe9f18d3fcd7ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XS3RF3WA7OTDB455KFOMIIZTXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Endomorphisms of Local Cohomology Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Waqas Mahmood, Zohaib Zahid","submitted_at":"2014-05-06T12:46:08Z","abstract_excerpt":"Let $I$ denote an ideal of a local ring $(R,\\mathfrak{m})$ of dimension $n$. Let $M$ denote a finitely generated $R$-module. We study the endomorphism ring of the local cohomology module $H^c_I(M), c = \\grade (I,M)$. In particular there is a natural homomorphism $\\Hom_{\\hat{R}^I}(\\hat{M}^I, \\hat{M}^I)\\to \\Hom_{R}(H^c_{I}(M),H^c_{I}(M))$, where $\\hat{\\cdot}^I$ denotes the $I$-adic completion functor. We prove sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J \\subset I$ with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1249","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":"2026-05-18T02:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GL3vu9UqhiZ1zqPnbqq/NGojBR7Og3N0kQZ6VLJH1f6M2wpLAQqgGZul9bpzY1/fs9U0V+/ZUTGRlCmlZgf1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:13:08.670066Z"},"content_sha256":"2317faa3e56d12d1e0dc11e361b43864ad22bbf11e774629e3591244052fbc98","schema_version":"1.0","event_id":"sha256:2317faa3e56d12d1e0dc11e361b43864ad22bbf11e774629e3591244052fbc98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XS3RF3WA7OTDB455KFOMIIZTXO/bundle.json","state_url":"https://pith.science/pith/XS3RF3WA7OTDB455KFOMIIZTXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XS3RF3WA7OTDB455KFOMIIZTXO/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":"2026-06-04T01:13:08Z","links":{"resolver":"https://pith.science/pith/XS3RF3WA7OTDB455KFOMIIZTXO","bundle":"https://pith.science/pith/XS3RF3WA7OTDB455KFOMIIZTXO/bundle.json","state":"https://pith.science/pith/XS3RF3WA7OTDB455KFOMIIZTXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XS3RF3WA7OTDB455KFOMIIZTXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XS3RF3WA7OTDB455KFOMIIZTXO","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":"bfb08a43fb2c1cd47c2a3109228793eaed69859c7ac4d79990090b69725b4ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-06T12:46:08Z","title_canon_sha256":"fcf36387a5540faaf0e318038c1d2ed16e78672da9043bb9408b86db47740c77"},"schema_version":"1.0","source":{"id":"1405.1249","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1249","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1249v2","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1249","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"XS3RF3WA7OTD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XS3RF3WA7OTDB455","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XS3RF3WA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2317faa3e56d12d1e0dc11e361b43864ad22bbf11e774629e3591244052fbc98","target":"graph","created_at":"2026-05-18T02:52:05Z","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 $I$ denote an ideal of a local ring $(R,\\mathfrak{m})$ of dimension $n$. Let $M$ denote a finitely generated $R$-module. We study the endomorphism ring of the local cohomology module $H^c_I(M), c = \\grade (I,M)$. In particular there is a natural homomorphism $\\Hom_{\\hat{R}^I}(\\hat{M}^I, \\hat{M}^I)\\to \\Hom_{R}(H^c_{I}(M),H^c_{I}(M))$, where $\\hat{\\cdot}^I$ denotes the $I$-adic completion functor. We prove sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J \\subset I$ with th","authors_text":"Waqas Mahmood, Zohaib Zahid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-06T12:46:08Z","title":"A Note on Endomorphisms of Local Cohomology Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1249","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":"sha256:3f8c0a5725a79c3898aa9c736c82774cfba2421547c4057dacfe9f18d3fcd7ce","target":"record","created_at":"2026-05-18T02:52:05Z","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":"bfb08a43fb2c1cd47c2a3109228793eaed69859c7ac4d79990090b69725b4ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-05-06T12:46:08Z","title_canon_sha256":"fcf36387a5540faaf0e318038c1d2ed16e78672da9043bb9408b86db47740c77"},"schema_version":"1.0","source":{"id":"1405.1249","kind":"arxiv","version":2}},"canonical_sha256":"bcb712eec0fba630f3bd515cc42333bb8ec02a507558f72e38dd02862e434859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcb712eec0fba630f3bd515cc42333bb8ec02a507558f72e38dd02862e434859","first_computed_at":"2026-05-18T02:52:05.756734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:05.756734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tJgHVsq74jK1lKtNrEID9Al8SI9NHe/SO4XANrMxrgdtoDs6GS0OGNIyAgylFBDwkbLgYyzqLb+bU0D9mMddCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:05.757204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1249","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f8c0a5725a79c3898aa9c736c82774cfba2421547c4057dacfe9f18d3fcd7ce","sha256:2317faa3e56d12d1e0dc11e361b43864ad22bbf11e774629e3591244052fbc98"],"state_sha256":"b181f661ffbb88ef9d0fd8847ef4698c2645c0b53851700ef682cea7bbb4ae00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XbFosmj+p/iB/lK0R2mBCAabDxGECdjOWdMm3SVA9tnZIoTZY31Gsbv+8mscvz1KuFxhm7AlTp2FvPAtIb/sAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:13:08.672004Z","bundle_sha256":"51222a189d1c7efa839dda27b0f04f8c815797588885a98ec298d257f1d76e30"}}