{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:657RLFSB4GOJWYVNPVRYVU5YOS","short_pith_number":"pith:657RLFSB","canonical_record":{"source":{"id":"1902.02736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-07T17:23:18Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"894e7f7dbde94a08f65b6a9c1583b59e65a30e4977a6a04cb03c6653d59e8968","abstract_canon_sha256":"a9dc225aed32058ba1f52130164ed5f11e96a29f444e5bbea8f3e79bd5485c40"},"schema_version":"1.0"},"canonical_sha256":"f77f159641e19c9b62ad7d638ad3b874b14a7aeb2ca2ab0d70430b5b04f7d935","source":{"kind":"arxiv","id":"1902.02736","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02736","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02736v2","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02736","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"pith_short_12","alias_value":"657RLFSB4GOJ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"657RLFSB4GOJWYVN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"657RLFSB","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:657RLFSB4GOJWYVNPVRYVU5YOS","target":"record","payload":{"canonical_record":{"source":{"id":"1902.02736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-07T17:23:18Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"894e7f7dbde94a08f65b6a9c1583b59e65a30e4977a6a04cb03c6653d59e8968","abstract_canon_sha256":"a9dc225aed32058ba1f52130164ed5f11e96a29f444e5bbea8f3e79bd5485c40"},"schema_version":"1.0"},"canonical_sha256":"f77f159641e19c9b62ad7d638ad3b874b14a7aeb2ca2ab0d70430b5b04f7d935","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:30.594533Z","signature_b64":"e0sXgcGKKimEIL1gxpm2TQLccKEdNp34xtypHO6AJ1soQs5NzVpJsb2lU6x9YO6WoUIJfY9pE2Cj8uo20HqCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f77f159641e19c9b62ad7d638ad3b874b14a7aeb2ca2ab0d70430b5b04f7d935","last_reissued_at":"2026-05-17T23:48:30.593954Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:30.593954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.02736","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":"2026-05-17T23:48:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FjuhLH6zhP0ZcaWEopg6yP/Tkfc5iAhgqaeMEnx90FGC4NiWdzOxlU2drFKbuxtUqHVY9gb2ywkKq6l9HV2kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:33:00.580382Z"},"content_sha256":"a675d1c5436392ebe0a1b59b9d60d01ff91527cdcb97b5b2f4243383095b10bc","schema_version":"1.0","event_id":"sha256:a675d1c5436392ebe0a1b59b9d60d01ff91527cdcb97b5b2f4243383095b10bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:657RLFSB4GOJWYVNPVRYVU5YOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Cohomology of the Ordinals I: Basic Theory and Consistency Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson, Jeffrey Bergfalk","submitted_at":"2019-02-07T17:23:18Z","abstract_excerpt":"In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is \\v{C}ech cohomology. We show in particular that the \\v{C}ech cohomology groups of the ordinals articulate higher-dimensional generalizations of Todorcevic's walks and coherent sequences techniques, and begin to account for those techniques' `unreasonable effectiveness' on $\\omega_1$. This discussion occupies the first half of our paper and is written with a general mathematical audience in mind.\n  We turn in the paper's second half to more pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02736","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":"2026-05-17T23:48:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mj6FYFjRBuZmjn/1QYYS5xbEwO+NAtcpWoHBuPKNhzJwiQBYleKtCcRLDQs1fdOtH3tB9mwL2yXy8EHPztClCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:33:00.580738Z"},"content_sha256":"b4ce40e3e318a83446ba13ea278884da7bbb87eaff7c44294de0b879228cdbd1","schema_version":"1.0","event_id":"sha256:b4ce40e3e318a83446ba13ea278884da7bbb87eaff7c44294de0b879228cdbd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/657RLFSB4GOJWYVNPVRYVU5YOS/bundle.json","state_url":"https://pith.science/pith/657RLFSB4GOJWYVNPVRYVU5YOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/657RLFSB4GOJWYVNPVRYVU5YOS/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":"2026-06-20T07:33:00Z","links":{"resolver":"https://pith.science/pith/657RLFSB4GOJWYVNPVRYVU5YOS","bundle":"https://pith.science/pith/657RLFSB4GOJWYVNPVRYVU5YOS/bundle.json","state":"https://pith.science/pith/657RLFSB4GOJWYVNPVRYVU5YOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/657RLFSB4GOJWYVNPVRYVU5YOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:657RLFSB4GOJWYVNPVRYVU5YOS","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":"a9dc225aed32058ba1f52130164ed5f11e96a29f444e5bbea8f3e79bd5485c40","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-07T17:23:18Z","title_canon_sha256":"894e7f7dbde94a08f65b6a9c1583b59e65a30e4977a6a04cb03c6653d59e8968"},"schema_version":"1.0","source":{"id":"1902.02736","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02736","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02736v2","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02736","created_at":"2026-05-17T23:48:30Z"},{"alias_kind":"pith_short_12","alias_value":"657RLFSB4GOJ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"657RLFSB4GOJWYVN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"657RLFSB","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:b4ce40e3e318a83446ba13ea278884da7bbb87eaff7c44294de0b879228cdbd1","target":"graph","created_at":"2026-05-17T23:48:30Z","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":"In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is \\v{C}ech cohomology. We show in particular that the \\v{C}ech cohomology groups of the ordinals articulate higher-dimensional generalizations of Todorcevic's walks and coherent sequences techniques, and begin to account for those techniques' `unreasonable effectiveness' on $\\omega_1$. This discussion occupies the first half of our paper and is written with a general mathematical audience in mind.\n  We turn in the paper's second half to more pr","authors_text":"Chris Lambie-Hanson, Jeffrey Bergfalk","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-07T17:23:18Z","title":"The Cohomology of the Ordinals I: Basic Theory and Consistency Results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02736","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:a675d1c5436392ebe0a1b59b9d60d01ff91527cdcb97b5b2f4243383095b10bc","target":"record","created_at":"2026-05-17T23:48:30Z","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":"a9dc225aed32058ba1f52130164ed5f11e96a29f444e5bbea8f3e79bd5485c40","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-07T17:23:18Z","title_canon_sha256":"894e7f7dbde94a08f65b6a9c1583b59e65a30e4977a6a04cb03c6653d59e8968"},"schema_version":"1.0","source":{"id":"1902.02736","kind":"arxiv","version":2}},"canonical_sha256":"f77f159641e19c9b62ad7d638ad3b874b14a7aeb2ca2ab0d70430b5b04f7d935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f77f159641e19c9b62ad7d638ad3b874b14a7aeb2ca2ab0d70430b5b04f7d935","first_computed_at":"2026-05-17T23:48:30.593954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:30.593954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e0sXgcGKKimEIL1gxpm2TQLccKEdNp34xtypHO6AJ1soQs5NzVpJsb2lU6x9YO6WoUIJfY9pE2Cj8uo20HqCBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:30.594533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02736","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a675d1c5436392ebe0a1b59b9d60d01ff91527cdcb97b5b2f4243383095b10bc","sha256:b4ce40e3e318a83446ba13ea278884da7bbb87eaff7c44294de0b879228cdbd1"],"state_sha256":"f89199cfbfea9feb8c9ffe70b3d7f757f31c74c6acc46cbe41b72b64a7a81af6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecKRAu16fxC7MnMsF52jB4CpzBnzxV79LNh5iQ+RBRXgQV3NeH4Kv+Y2qAELE/KPuiJjqntc+cGOrxfwHExRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:33:00.582870Z","bundle_sha256":"1a9524f4ff079bd29e6a0c29ae0251435a415aee6da9258df81b51594e1db50b"}}