{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:X446CZ5OCFE4ZGNTEEFYRLDMBH","short_pith_number":"pith:X446CZ5O","canonical_record":{"source":{"id":"1207.2547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-11T06:37:00Z","cross_cats_sorted":[],"title_canon_sha256":"ba59f9fb6fe5e0c6df89f506dd3d8746fdb4eccdf848b80053bda3454bdecd0c","abstract_canon_sha256":"9db423bd1706659bff4dfb4ec14ed706266e5a49b807af3efa02c60f78ea44fd"},"schema_version":"1.0"},"canonical_sha256":"bf39e167ae1149cc99b3210b88ac6c09e933b4b1a7c177fc11d5733f6f7b19a7","source":{"kind":"arxiv","id":"1207.2547","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2547","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2547v2","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2547","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"X446CZ5OCFE4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X446CZ5OCFE4ZGNT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X446CZ5O","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:X446CZ5OCFE4ZGNTEEFYRLDMBH","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-11T06:37:00Z","cross_cats_sorted":[],"title_canon_sha256":"ba59f9fb6fe5e0c6df89f506dd3d8746fdb4eccdf848b80053bda3454bdecd0c","abstract_canon_sha256":"9db423bd1706659bff4dfb4ec14ed706266e5a49b807af3efa02c60f78ea44fd"},"schema_version":"1.0"},"canonical_sha256":"bf39e167ae1149cc99b3210b88ac6c09e933b4b1a7c177fc11d5733f6f7b19a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:04.407537Z","signature_b64":"A85HtSwCtNZlTk6nF51CdLIl2upnU8UDmr6I+VDeteBy8UKFGS6DvEhPiQx9ozss8nSFtjWCBJwaDtS8MjcxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf39e167ae1149cc99b3210b88ac6c09e933b4b1a7c177fc11d5733f6f7b19a7","last_reissued_at":"2026-05-18T02:55:04.407105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:04.407105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2547","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":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lKaOeR2GKhTmw5Iiszo62B+RCo1nwbU3TsrHesWpKGJnlXGxjjJrycB38t2fqdWQWaa6cGFMTBH4m3MovTJuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:14.407274Z"},"content_sha256":"74efda5eebac9550115e34fd18dc0839304332ea3a7df833791724bc1b2cc0a5","schema_version":"1.0","event_id":"sha256:74efda5eebac9550115e34fd18dc0839304332ea3a7df833791724bc1b2cc0a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:X446CZ5OCFE4ZGNTEEFYRLDMBH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coarsening of graded local cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Fred Rohrer","submitted_at":"2012-07-11T06:37:00Z","abstract_excerpt":"Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2547","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":"2026-05-18T02:55:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6b4na/gdNsWxCfOgXdzorLObtk42q2cMhttynzTSBjwTttHSKF9VebxFbuh/SkJLH/Lf6UiD3J9mBuJo1ZECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:22:14.407640Z"},"content_sha256":"a1109ebf5823b55717fbb0c90362c5f2c8aae56f42dbb7cbac1ca7d28f6375ba","schema_version":"1.0","event_id":"sha256:a1109ebf5823b55717fbb0c90362c5f2c8aae56f42dbb7cbac1ca7d28f6375ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/bundle.json","state_url":"https://pith.science/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/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":"2026-06-05T09:22:14Z","links":{"resolver":"https://pith.science/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH","bundle":"https://pith.science/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/bundle.json","state":"https://pith.science/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X446CZ5OCFE4ZGNTEEFYRLDMBH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X446CZ5OCFE4ZGNTEEFYRLDMBH","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":"9db423bd1706659bff4dfb4ec14ed706266e5a49b807af3efa02c60f78ea44fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-11T06:37:00Z","title_canon_sha256":"ba59f9fb6fe5e0c6df89f506dd3d8746fdb4eccdf848b80053bda3454bdecd0c"},"schema_version":"1.0","source":{"id":"1207.2547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2547","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2547v2","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2547","created_at":"2026-05-18T02:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"X446CZ5OCFE4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X446CZ5OCFE4ZGNT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X446CZ5O","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:a1109ebf5823b55717fbb0c90362c5f2c8aae56f42dbb7cbac1ca7d28f6375ba","target":"graph","created_at":"2026-05-18T02:55:04Z","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":"Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.","authors_text":"Fred Rohrer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-11T06:37:00Z","title":"Coarsening of graded local cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2547","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":"sha256:74efda5eebac9550115e34fd18dc0839304332ea3a7df833791724bc1b2cc0a5","target":"record","created_at":"2026-05-18T02:55:04Z","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":"9db423bd1706659bff4dfb4ec14ed706266e5a49b807af3efa02c60f78ea44fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-11T06:37:00Z","title_canon_sha256":"ba59f9fb6fe5e0c6df89f506dd3d8746fdb4eccdf848b80053bda3454bdecd0c"},"schema_version":"1.0","source":{"id":"1207.2547","kind":"arxiv","version":2}},"canonical_sha256":"bf39e167ae1149cc99b3210b88ac6c09e933b4b1a7c177fc11d5733f6f7b19a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf39e167ae1149cc99b3210b88ac6c09e933b4b1a7c177fc11d5733f6f7b19a7","first_computed_at":"2026-05-18T02:55:04.407105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:04.407105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A85HtSwCtNZlTk6nF51CdLIl2upnU8UDmr6I+VDeteBy8UKFGS6DvEhPiQx9ozss8nSFtjWCBJwaDtS8MjcxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:04.407537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74efda5eebac9550115e34fd18dc0839304332ea3a7df833791724bc1b2cc0a5","sha256:a1109ebf5823b55717fbb0c90362c5f2c8aae56f42dbb7cbac1ca7d28f6375ba"],"state_sha256":"6818c2fda4383748ad36df2138bdc185ec76d7467be6b2e2ed02c233d7c6a6d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F21AkhaeYOBO8+4sLfYehFgR75UUxSezTS+3I+H67aC6tQPULw4lgRx8TP+JbgZi1yDEDC7I9u/t4YXDW7OmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:22:14.409606Z","bundle_sha256":"5f8bd4586b0bcbe4452ff95498ced96d02c4da733bf09b32a201245ac0c0b316"}}