{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WW6HRY2IPPGAFQJNMMGJA6VAQ5","short_pith_number":"pith:WW6HRY2I","canonical_record":{"source":{"id":"math/0701077","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-01-03T17:36:14Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"179aed1750cf015c5e3dd8bd9a70c1769bac0141a0a7673ce1c744c810014859","abstract_canon_sha256":"fda3d63d2795cef84e8279c0a3f9f07455fa005464e69f3a5438d0047048188a"},"schema_version":"1.0"},"canonical_sha256":"b5bc78e3487bcc02c12d630c907aa08744f13671e7d62f9e596c8717d46b0bd1","source":{"kind":"arxiv","id":"math/0701077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701077","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701077v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701077","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"WW6HRY2IPPGA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WW6HRY2IPPGAFQJN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WW6HRY2I","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WW6HRY2IPPGAFQJNMMGJA6VAQ5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701077","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-01-03T17:36:14Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"179aed1750cf015c5e3dd8bd9a70c1769bac0141a0a7673ce1c744c810014859","abstract_canon_sha256":"fda3d63d2795cef84e8279c0a3f9f07455fa005464e69f3a5438d0047048188a"},"schema_version":"1.0"},"canonical_sha256":"b5bc78e3487bcc02c12d630c907aa08744f13671e7d62f9e596c8717d46b0bd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.331631Z","signature_b64":"V9xMlcqZ+Rtw6UjibQFv5IZnhSQ1f6JfKTUR/R/BZJAC2U4HeCjJGrrt52k9xv1nTthM6L7ATLQobHSF0ESgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5bc78e3487bcc02c12d630c907aa08744f13671e7d62f9e596c8717d46b0bd1","last_reissued_at":"2026-05-18T02:57:45.331067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.331067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701077","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WDTRl+qRT86Ly4+lujIRdyalDb0j/C51zlmaoMwcwnplh1qVcvFV1iErTDesUESJGD5AciabccxxVTkrOWlcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:55.221583Z"},"content_sha256":"96beb48e6e40dac6d1eaebb017abad92e9811a2055f567ffa75d6a03e786d4d4","schema_version":"1.0","event_id":"sha256:96beb48e6e40dac6d1eaebb017abad92e9811a2055f567ffa75d6a03e786d4d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WW6HRY2IPPGAFQJNMMGJA6VAQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axiomatic Characterization of Ordinary Differential Cohomology","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Dennis Sullivan, James Simons","submitted_at":"2007-01-03T17:36:14Z","abstract_excerpt":"Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group extensions of known functors. In one desciption these objects are extensions of integral cohomology by the quotient space of all differential forms by the subspace of closed forms with integral periods. In the other they are extensions of closed differential forms with integral periods by the cohomology with coefficients in the circle. These two series of shor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701077","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"trTR+Ms68JZWl/tXSnkfguimHDOekmMvVIKgzvzWEumBalVQsO/mJheLpgCDcwJi6TMvgQMPE++7ihwzpnGFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:55.222123Z"},"content_sha256":"7a5485855a5a659ee3508749549d6dcfb01bea5f44a055c48adb2467a025ecae","schema_version":"1.0","event_id":"sha256:7a5485855a5a659ee3508749549d6dcfb01bea5f44a055c48adb2467a025ecae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/bundle.json","state_url":"https://pith.science/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/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":"2026-06-04T04:22:55Z","links":{"resolver":"https://pith.science/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5","bundle":"https://pith.science/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/bundle.json","state":"https://pith.science/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WW6HRY2IPPGAFQJNMMGJA6VAQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WW6HRY2IPPGAFQJNMMGJA6VAQ5","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":"fda3d63d2795cef84e8279c0a3f9f07455fa005464e69f3a5438d0047048188a","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AT","submitted_at":"2007-01-03T17:36:14Z","title_canon_sha256":"179aed1750cf015c5e3dd8bd9a70c1769bac0141a0a7673ce1c744c810014859"},"schema_version":"1.0","source":{"id":"math/0701077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701077","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701077v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701077","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"WW6HRY2IPPGA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WW6HRY2IPPGAFQJN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WW6HRY2I","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7a5485855a5a659ee3508749549d6dcfb01bea5f44a055c48adb2467a025ecae","target":"graph","created_at":"2026-05-18T02:57:45Z","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":"Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group extensions of known functors. In one desciption these objects are extensions of integral cohomology by the quotient space of all differential forms by the subspace of closed forms with integral periods. In the other they are extensions of closed differential forms with integral periods by the cohomology with coefficients in the circle. These two series of shor","authors_text":"Dennis Sullivan, James Simons","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2007-01-03T17:36:14Z","title":"Axiomatic Characterization of Ordinary Differential Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701077","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":"sha256:96beb48e6e40dac6d1eaebb017abad92e9811a2055f567ffa75d6a03e786d4d4","target":"record","created_at":"2026-05-18T02:57:45Z","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":"fda3d63d2795cef84e8279c0a3f9f07455fa005464e69f3a5438d0047048188a","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AT","submitted_at":"2007-01-03T17:36:14Z","title_canon_sha256":"179aed1750cf015c5e3dd8bd9a70c1769bac0141a0a7673ce1c744c810014859"},"schema_version":"1.0","source":{"id":"math/0701077","kind":"arxiv","version":1}},"canonical_sha256":"b5bc78e3487bcc02c12d630c907aa08744f13671e7d62f9e596c8717d46b0bd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5bc78e3487bcc02c12d630c907aa08744f13671e7d62f9e596c8717d46b0bd1","first_computed_at":"2026-05-18T02:57:45.331067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.331067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9xMlcqZ+Rtw6UjibQFv5IZnhSQ1f6JfKTUR/R/BZJAC2U4HeCjJGrrt52k9xv1nTthM6L7ATLQobHSF0ESgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.331631Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96beb48e6e40dac6d1eaebb017abad92e9811a2055f567ffa75d6a03e786d4d4","sha256:7a5485855a5a659ee3508749549d6dcfb01bea5f44a055c48adb2467a025ecae"],"state_sha256":"2f2ef6768873d1667155e6ab12ad5f2a4bbf8ef77f93ee30cc95e26f8e83179e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MG+0xVrG1IWbZnNSqD2XCuvT+8IhbM8mzqM7WbzKyAvD4zxE0Yl4y6Ep0Z43MvJmTM9QGPSWkz17xuNfYQFCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:22:55.224933Z","bundle_sha256":"3a0dd9683ad68fcd084d34f3f8691dc120998896b05d63f89bcadaeade3e1424"}}