{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JMT6EZCWWMPYKGNAH6LWASZM7M","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":"430aa78ba5874cc02c0f115fc6918a268f199a4eb385b034e78291f878091780","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-03-15T17:47:54Z","title_canon_sha256":"362ce79a3d99adaa52dac93ce32865a4ca691c53ee20c43d81c9c17051f79c88"},"schema_version":"1.0","source":{"id":"math/0703463","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703463","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703463v3","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703463","created_at":"2026-05-18T00:16:34Z"},{"alias_kind":"pith_short_12","alias_value":"JMT6EZCWWMPY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JMT6EZCWWMPYKGNA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JMT6EZCW","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:c31a31db4864fc895fa85e2f95cff83b9133282b8fd42eec02f6df9280f5da49","target":"graph","created_at":"2026-05-18T00:16:34Z","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":"Associated to a discrete group $G$, one has the topological category of finite dimensional (unitary) $G$-representations and (unitary) isomorphisms. Block sums provide this category with a permutative structure, and the associated $K$-theory spectrum is Carlsson's deformation $K$-theory of G. The goal of this paper is to examine the behavior of this functor on free products. Our main theorem shows the square of spectra associated to $G*H$ (considered as an amalgamated product over the trivial group) is homotopy cartesian. The proof uses a general result regarding group completions of homotopy ","authors_text":"Daniel A. Ramras","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-03-15T17:47:54Z","title":"Excision for deformation K-theory of free products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703463","kind":"arxiv","version":3},"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":"sha256:31d29494f90fccbedb40f60633831d022366f859e9db24fb94313b51ab52f784","target":"record","created_at":"2026-05-18T00:16:34Z","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":"430aa78ba5874cc02c0f115fc6918a268f199a4eb385b034e78291f878091780","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-03-15T17:47:54Z","title_canon_sha256":"362ce79a3d99adaa52dac93ce32865a4ca691c53ee20c43d81c9c17051f79c88"},"schema_version":"1.0","source":{"id":"math/0703463","kind":"arxiv","version":3}},"canonical_sha256":"4b27e26456b31f8519a03f97604b2cfb075191c7b820e5554e4a6bfd3c32f166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b27e26456b31f8519a03f97604b2cfb075191c7b820e5554e4a6bfd3c32f166","first_computed_at":"2026-05-18T00:16:34.346688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:34.346688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZaOGBzEYqy7sUrehzahUKy8nOWPVVvaj/77ZP811JA3QRiPn5RPnI6CKb1Jzu084tXkE+6VsyKkK3/M+41JDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:34.347077Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703463","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31d29494f90fccbedb40f60633831d022366f859e9db24fb94313b51ab52f784","sha256:c31a31db4864fc895fa85e2f95cff83b9133282b8fd42eec02f6df9280f5da49"],"state_sha256":"ccd41329a96a9954dd7f270edf18d127cf678f529c3d9f50f42da6b7b0abbaf2"}