{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IY5A2FM3WWLMKT42LK6RNXI4I2","short_pith_number":"pith:IY5A2FM3","canonical_record":{"source":{"id":"1903.02668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-07T00:34:51Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"c00499e1e974042c37ba800d4def189b2a5ae9b97e7b9abf6f6fda6ca70297cb","abstract_canon_sha256":"a692eafc3a40261a13c15f4ffc4fad076ea21dbc4641129599a72fbf41340457"},"schema_version":"1.0"},"canonical_sha256":"463a0d159bb596c54f9a5abd16dd1c469b19e81aeb90f6a625299ce19b2674e4","source":{"kind":"arxiv","id":"1903.02668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02668","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02668v1","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02668","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"IY5A2FM3WWLM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IY5A2FM3WWLMKT42","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IY5A2FM3","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IY5A2FM3WWLMKT42LK6RNXI4I2","target":"record","payload":{"canonical_record":{"source":{"id":"1903.02668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-07T00:34:51Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"c00499e1e974042c37ba800d4def189b2a5ae9b97e7b9abf6f6fda6ca70297cb","abstract_canon_sha256":"a692eafc3a40261a13c15f4ffc4fad076ea21dbc4641129599a72fbf41340457"},"schema_version":"1.0"},"canonical_sha256":"463a0d159bb596c54f9a5abd16dd1c469b19e81aeb90f6a625299ce19b2674e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:51.515283Z","signature_b64":"soPQSO9Mj2pqHyQfl+UhefljRlwoMt96kmZc3INqlnzJaC5Bx+RFsNdSg+EICmr/juTCFFZB0WbOW0VG1DCMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"463a0d159bb596c54f9a5abd16dd1c469b19e81aeb90f6a625299ce19b2674e4","last_reissued_at":"2026-05-17T23:51:51.514568Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:51.514568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.02668","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":"2026-05-17T23:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YR1wNLTqoMTI2XsE0vnGJW4ELFtlk21FsHMXlHzocOWKoQq5k9XR/XEY0DXV5KHjHNrFIkfpswYdSQMgWr1CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:37.519401Z"},"content_sha256":"2a15bc05b8dde88a6ee09c32ba9956fc00bb5875daa43d0122f53baa90a8e388","schema_version":"1.0","event_id":"sha256:2a15bc05b8dde88a6ee09c32ba9956fc00bb5875daa43d0122f53baa90a8e388"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IY5A2FM3WWLMKT42LK6RNXI4I2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adelic cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AC","authors_text":"J.P.C.Greenlees","submitted_at":"2019-03-07T00:34:51Z","abstract_excerpt":"The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially ordered set with auxiliary structure which covers several examples of established interest in commutative algebra and stable equivariant homotopy theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02668","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":"2026-05-17T23:51:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TOXUtFfzYIcp+oE+4nzCtaQTP1/wnEMF9NfBDZl1IY8d7xe+B4mtQ+4zfoKt7++BGfZHNoDdPEw9/WLKLrqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:37.519743Z"},"content_sha256":"4f641eb80254d61df1338c00b02e2e2d826f08f042d59ca420dbcd00e6fc87cc","schema_version":"1.0","event_id":"sha256:4f641eb80254d61df1338c00b02e2e2d826f08f042d59ca420dbcd00e6fc87cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/bundle.json","state_url":"https://pith.science/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/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":"2026-06-27T10:55:37Z","links":{"resolver":"https://pith.science/pith/IY5A2FM3WWLMKT42LK6RNXI4I2","bundle":"https://pith.science/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/bundle.json","state":"https://pith.science/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IY5A2FM3WWLMKT42LK6RNXI4I2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IY5A2FM3WWLMKT42LK6RNXI4I2","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":"a692eafc3a40261a13c15f4ffc4fad076ea21dbc4641129599a72fbf41340457","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-07T00:34:51Z","title_canon_sha256":"c00499e1e974042c37ba800d4def189b2a5ae9b97e7b9abf6f6fda6ca70297cb"},"schema_version":"1.0","source":{"id":"1903.02668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02668","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02668v1","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02668","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"IY5A2FM3WWLM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IY5A2FM3WWLMKT42","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IY5A2FM3","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:4f641eb80254d61df1338c00b02e2e2d826f08f042d59ca420dbcd00e6fc87cc","target":"graph","created_at":"2026-05-17T23:51:51Z","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":"The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially ordered set with auxiliary structure which covers several examples of established interest in commutative algebra and stable equivariant homotopy theory.","authors_text":"J.P.C.Greenlees","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-07T00:34:51Z","title":"Adelic cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02668","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":"sha256:2a15bc05b8dde88a6ee09c32ba9956fc00bb5875daa43d0122f53baa90a8e388","target":"record","created_at":"2026-05-17T23:51:51Z","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":"a692eafc3a40261a13c15f4ffc4fad076ea21dbc4641129599a72fbf41340457","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-07T00:34:51Z","title_canon_sha256":"c00499e1e974042c37ba800d4def189b2a5ae9b97e7b9abf6f6fda6ca70297cb"},"schema_version":"1.0","source":{"id":"1903.02668","kind":"arxiv","version":1}},"canonical_sha256":"463a0d159bb596c54f9a5abd16dd1c469b19e81aeb90f6a625299ce19b2674e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463a0d159bb596c54f9a5abd16dd1c469b19e81aeb90f6a625299ce19b2674e4","first_computed_at":"2026-05-17T23:51:51.514568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:51.514568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"soPQSO9Mj2pqHyQfl+UhefljRlwoMt96kmZc3INqlnzJaC5Bx+RFsNdSg+EICmr/juTCFFZB0WbOW0VG1DCMCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:51.515283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a15bc05b8dde88a6ee09c32ba9956fc00bb5875daa43d0122f53baa90a8e388","sha256:4f641eb80254d61df1338c00b02e2e2d826f08f042d59ca420dbcd00e6fc87cc"],"state_sha256":"e01e6325c95ca434c55b31c874b1099efa316b5fd95fd2c4a2775ab3352fa3b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yRDXqbsie1pG3HfNepojr9aIboVS4nByt90WUF2RJGS2rTeR2RdfoVO8ergncvdyUHjRJZNv4w8MqwsSJ6s0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:55:37.521629Z","bundle_sha256":"9a3a2002122f36d63364890fa8732af18f18504151537368ac0c851df58b1bac"}}