{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PZFETGKINFT7BMQWUBLGRNTVLG","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":"2244a69881e6a73c1d4b090b0bb1eac8561a978584db55a80d4314aa3fdd59a9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-30T07:03:25Z","title_canon_sha256":"84f4a6e4307938b11c67cda1afb8285007573369a441ea0014e1cf1b73a287a4"},"schema_version":"1.0","source":{"id":"0707.0046","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0046","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0046v4","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0046","created_at":"2026-05-18T04:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"PZFETGKINFT7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PZFETGKINFT7BMQW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PZFETGKI","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:971a3d5a4e2643c462408f68d80db8430c9d77b5e0603e5ed778c660d5b27904","target":"graph","created_at":"2026-05-18T04:41:06Z","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 construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-forward which satisfies functoriality, compatibility with pull-back diagrams, and projection and bordism formulas. We construct a multiplicative lift of the Chern character from smooth K-theory to smooth rational cohomology and verify that the cohomological version of the Atiyah-Singer index theorem for families lifts to smooth cohomology.","authors_text":"Thomas Schick (Georg-August-Universitaet Goettingen), Ulrich Bunke (Regensburg)","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-30T07:03:25Z","title":"Smooth K-Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0046","kind":"arxiv","version":4},"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":"sha256:126d5a93b2e53e66dde8bcb3d752ab1db1f43d400f0108313d4c6cbc8fadf1e2","target":"record","created_at":"2026-05-18T04:41:06Z","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":"2244a69881e6a73c1d4b090b0bb1eac8561a978584db55a80d4314aa3fdd59a9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-30T07:03:25Z","title_canon_sha256":"84f4a6e4307938b11c67cda1afb8285007573369a441ea0014e1cf1b73a287a4"},"schema_version":"1.0","source":{"id":"0707.0046","kind":"arxiv","version":4}},"canonical_sha256":"7e4a4999486967f0b216a05668b675598570f91a26baa9e3681f9f003308082f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e4a4999486967f0b216a05668b675598570f91a26baa9e3681f9f003308082f","first_computed_at":"2026-05-18T04:41:06.095928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:06.095928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wZyvAuR6TjvToU8gCz8aNlHnQMYX6CClzOAyIkUEO6ERi2dhw8McWuSCYY6uF3eEe8eO5VwxgRQepiZsM3/lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:06.096445Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.0046","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:126d5a93b2e53e66dde8bcb3d752ab1db1f43d400f0108313d4c6cbc8fadf1e2","sha256:971a3d5a4e2643c462408f68d80db8430c9d77b5e0603e5ed778c660d5b27904"],"state_sha256":"a75b64b8316f7a15da383b2c17c5b7185aaa8c886bb49b3745fa52b3ad29809b"}