{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SMQ3IATNU6B3SUW7JNFC2PIVCI","short_pith_number":"pith:SMQ3IATN","canonical_record":{"source":{"id":"1707.00354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-02T20:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"b94be259a89837872050438a925e8e0c889b6c86ebea2d750dfa40b298ad62b5","abstract_canon_sha256":"2415e486a4576d842ea938ce489446c58a040b1f56afc6f7a81cd50f9ba65002"},"schema_version":"1.0"},"canonical_sha256":"9321b4026da783b952df4b4a2d3d151204ca46a4775a5ced2d5b56c749d74290","source":{"kind":"arxiv","id":"1707.00354","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00354","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00354v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00354","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"SMQ3IATNU6B3","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SMQ3IATNU6B3SUW7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SMQ3IATN","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SMQ3IATNU6B3SUW7JNFC2PIVCI","target":"record","payload":{"canonical_record":{"source":{"id":"1707.00354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-02T20:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"b94be259a89837872050438a925e8e0c889b6c86ebea2d750dfa40b298ad62b5","abstract_canon_sha256":"2415e486a4576d842ea938ce489446c58a040b1f56afc6f7a81cd50f9ba65002"},"schema_version":"1.0"},"canonical_sha256":"9321b4026da783b952df4b4a2d3d151204ca46a4775a5ced2d5b56c749d74290","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.579433Z","signature_b64":"YBTmyv+maqi1I9hFx65k+0/5ZGSc+YyDnuD4E8rJb9qlCUQpMKyCHneSZI9bbUjplRbfZfCC3MulGBeZnGzUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9321b4026da783b952df4b4a2d3d151204ca46a4775a5ced2d5b56c749d74290","last_reissued_at":"2026-05-17T23:43:18.578778Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.578778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.00354","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":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odbQB5/mgAi3Z07Y8kaoKoBgbVDp8o14C8io3DPV2EbMks8fI6fMM5vy6oFJFDWWf48aJFRU3iQuXLp9R95XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:33:11.858015Z"},"content_sha256":"9f50ce441f58e1f0fb21631e5ea02f47292b11cc7ed24a8d4912b0013ecc095a","schema_version":"1.0","event_id":"sha256:9f50ce441f58e1f0fb21631e5ea02f47292b11cc7ed24a8d4912b0013ecc095a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SMQ3IATNU6B3SUW7JNFC2PIVCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local cohomology and stratification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Vidit Nanda","submitted_at":"2017-07-02T20:56:42Z","abstract_excerpt":"We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a nested sequence of categories, each containing all the cells as its set of objects, with the property that two cells are isomorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00354","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":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGy/ljsfp0V3j5ORTqkg/BWSI5Sy7l+gMRXd/TtItW6krNf6kvNjcBGm4hy1FOEFbpluI5KZY0KDMbm/uSfoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:33:11.858375Z"},"content_sha256":"69470abac03d6e8508720c695f2a210683e4c76ba1a77c44c0bfe4701c46f398","schema_version":"1.0","event_id":"sha256:69470abac03d6e8508720c695f2a210683e4c76ba1a77c44c0bfe4701c46f398"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/bundle.json","state_url":"https://pith.science/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/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":"2026-06-25T09:33:11Z","links":{"resolver":"https://pith.science/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI","bundle":"https://pith.science/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/bundle.json","state":"https://pith.science/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMQ3IATNU6B3SUW7JNFC2PIVCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SMQ3IATNU6B3SUW7JNFC2PIVCI","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":"2415e486a4576d842ea938ce489446c58a040b1f56afc6f7a81cd50f9ba65002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-02T20:56:42Z","title_canon_sha256":"b94be259a89837872050438a925e8e0c889b6c86ebea2d750dfa40b298ad62b5"},"schema_version":"1.0","source":{"id":"1707.00354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00354","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00354v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00354","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"SMQ3IATNU6B3","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SMQ3IATNU6B3SUW7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SMQ3IATN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:69470abac03d6e8508720c695f2a210683e4c76ba1a77c44c0bfe4701c46f398","target":"graph","created_at":"2026-05-17T23:43:18Z","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":"We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a nested sequence of categories, each containing all the cells as its set of objects, with the property that two cells are isomorphi","authors_text":"Vidit Nanda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-02T20:56:42Z","title":"Local cohomology and stratification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00354","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":"sha256:9f50ce441f58e1f0fb21631e5ea02f47292b11cc7ed24a8d4912b0013ecc095a","target":"record","created_at":"2026-05-17T23:43:18Z","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":"2415e486a4576d842ea938ce489446c58a040b1f56afc6f7a81cd50f9ba65002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-02T20:56:42Z","title_canon_sha256":"b94be259a89837872050438a925e8e0c889b6c86ebea2d750dfa40b298ad62b5"},"schema_version":"1.0","source":{"id":"1707.00354","kind":"arxiv","version":2}},"canonical_sha256":"9321b4026da783b952df4b4a2d3d151204ca46a4775a5ced2d5b56c749d74290","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9321b4026da783b952df4b4a2d3d151204ca46a4775a5ced2d5b56c749d74290","first_computed_at":"2026-05-17T23:43:18.578778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.578778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBTmyv+maqi1I9hFx65k+0/5ZGSc+YyDnuD4E8rJb9qlCUQpMKyCHneSZI9bbUjplRbfZfCC3MulGBeZnGzUBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.579433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f50ce441f58e1f0fb21631e5ea02f47292b11cc7ed24a8d4912b0013ecc095a","sha256:69470abac03d6e8508720c695f2a210683e4c76ba1a77c44c0bfe4701c46f398"],"state_sha256":"1f7e45311828c3cfc712cbc3bfe1f01241847c900528082103619a9cc011bf67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOL2cxSCDcWV00/SpSMe8MrqyyMHBPyAEEXDMgWZbXiEnsPv1hBJpaVpaLb1Ec0L/MTzmRnVu+xavRBSS7yACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:33:11.860334Z","bundle_sha256":"c7a63ffb9dd0f680a33f34691ea9f7822196a5f3b2bd373deebde83782c47b23"}}