{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VBLFRWOOYGWC7GLNGVFD5QNMUJ","short_pith_number":"pith:VBLFRWOO","canonical_record":{"source":{"id":"0907.3508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-20T22:43:09Z","cross_cats_sorted":["hep-th","math.AT","math.KT"],"title_canon_sha256":"ca03c4a6c5d5c8ebc4ee4b038df7e8e7b1ca7ea46175d7de9445039c64323137","abstract_canon_sha256":"b175d12763763033bce92d8a3551888ffb29173a6db715361d73245e34e435f5"},"schema_version":"1.0"},"canonical_sha256":"a85658d9cec1ac2f996d354a3ec1aca26ad67ad126dcc3b1d1e6ae04371db3c1","source":{"kind":"arxiv","id":"0907.3508","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3508","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3508v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3508","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"VBLFRWOOYGWC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VBLFRWOOYGWC7GLN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VBLFRWOO","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VBLFRWOOYGWC7GLNGVFD5QNMUJ","target":"record","payload":{"canonical_record":{"source":{"id":"0907.3508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-20T22:43:09Z","cross_cats_sorted":["hep-th","math.AT","math.KT"],"title_canon_sha256":"ca03c4a6c5d5c8ebc4ee4b038df7e8e7b1ca7ea46175d7de9445039c64323137","abstract_canon_sha256":"b175d12763763033bce92d8a3551888ffb29173a6db715361d73245e34e435f5"},"schema_version":"1.0"},"canonical_sha256":"a85658d9cec1ac2f996d354a3ec1aca26ad67ad126dcc3b1d1e6ae04371db3c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.801637Z","signature_b64":"3f0Cz3sjvxt7I0TCWA3T0xzBVRsPC0gHvPd0MqB+E/r+FSW1WOmLlpKtLpx1+m2xoX1/MjKKfgfVKZTaHM0aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a85658d9cec1ac2f996d354a3ec1aca26ad67ad126dcc3b1d1e6ae04371db3c1","last_reissued_at":"2026-05-18T02:38:18.800960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.800960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.3508","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VS3T/PSMpTLm2JS+RgfdhHWtJlpx68Fs+JyMCpmcYACdt2IcDVmaf04fsQBkPaffWMo5DmmK2ti6DbQykzKlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:35:31.156127Z"},"content_sha256":"011906cbda524ad5c65de427e82ce2a16e8e81b65558083f7677345a255ee655","schema_version":"1.0","event_id":"sha256:011906cbda524ad5c65de427e82ce2a16e8e81b65558083f7677345a255ee655"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VBLFRWOOYGWC7GLNGVFD5QNMUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An index theorem in differential K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT","math.KT"],"primary_cat":"math.DG","authors_text":"Daniel S. Freed, John Lott","submitted_at":"2009-07-20T22:43:09Z","abstract_excerpt":"Let X --> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3508","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PdyqzjuXPutd86r5p5w9Xresn6Pi1FAWv1zYq0qD//+U1FSeV+plMlc45oZ6PMoJEOx42oKFdZLgczAteaIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:35:31.156499Z"},"content_sha256":"cfa8db72275bdb7dd967275ecc0ce3712bb1f16972ba9255736cf6afc09e638b","schema_version":"1.0","event_id":"sha256:cfa8db72275bdb7dd967275ecc0ce3712bb1f16972ba9255736cf6afc09e638b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/bundle.json","state_url":"https://pith.science/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/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":"2026-05-28T07:35:31Z","links":{"resolver":"https://pith.science/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ","bundle":"https://pith.science/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/bundle.json","state":"https://pith.science/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBLFRWOOYGWC7GLNGVFD5QNMUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VBLFRWOOYGWC7GLNGVFD5QNMUJ","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":"b175d12763763033bce92d8a3551888ffb29173a6db715361d73245e34e435f5","cross_cats_sorted":["hep-th","math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-20T22:43:09Z","title_canon_sha256":"ca03c4a6c5d5c8ebc4ee4b038df7e8e7b1ca7ea46175d7de9445039c64323137"},"schema_version":"1.0","source":{"id":"0907.3508","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.3508","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0907.3508v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.3508","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"VBLFRWOOYGWC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VBLFRWOOYGWC7GLN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VBLFRWOO","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:cfa8db72275bdb7dd967275ecc0ce3712bb1f16972ba9255736cf6afc09e638b","target":"graph","created_at":"2026-05-18T02:38:18Z","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":"Let X --> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same.","authors_text":"Daniel S. Freed, John Lott","cross_cats":["hep-th","math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-20T22:43:09Z","title":"An index theorem in differential K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3508","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":"sha256:011906cbda524ad5c65de427e82ce2a16e8e81b65558083f7677345a255ee655","target":"record","created_at":"2026-05-18T02:38:18Z","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":"b175d12763763033bce92d8a3551888ffb29173a6db715361d73245e34e435f5","cross_cats_sorted":["hep-th","math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-20T22:43:09Z","title_canon_sha256":"ca03c4a6c5d5c8ebc4ee4b038df7e8e7b1ca7ea46175d7de9445039c64323137"},"schema_version":"1.0","source":{"id":"0907.3508","kind":"arxiv","version":2}},"canonical_sha256":"a85658d9cec1ac2f996d354a3ec1aca26ad67ad126dcc3b1d1e6ae04371db3c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a85658d9cec1ac2f996d354a3ec1aca26ad67ad126dcc3b1d1e6ae04371db3c1","first_computed_at":"2026-05-18T02:38:18.800960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.800960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3f0Cz3sjvxt7I0TCWA3T0xzBVRsPC0gHvPd0MqB+E/r+FSW1WOmLlpKtLpx1+m2xoX1/MjKKfgfVKZTaHM0aCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.801637Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.3508","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:011906cbda524ad5c65de427e82ce2a16e8e81b65558083f7677345a255ee655","sha256:cfa8db72275bdb7dd967275ecc0ce3712bb1f16972ba9255736cf6afc09e638b"],"state_sha256":"0ed5f8a7a745d914c5844c75284e3d2252d30b390f7adbba294040c7da75152c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqdhjbQ0CqbGDjP0HtAvhG5OT9UDgy1+0RIcLDex+8A+QUr+QVNbzTIn6qLArVbNPYdMnJgEfhYBvj1VktJJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:35:31.158524Z","bundle_sha256":"ed1a65c9534153fdb3346f7baff059ca5898fa65b2ba56eded304c7cbb424828"}}