{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2XKJWDALDYUNSND745U2Q6Z7DD","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":"76429ec9f1ff6fbbd6d05db02756dcbe149e1e0ad2e0ec78ae770625700ec95f","cross_cats_sorted":["math.FA","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-11-05T10:44:10Z","title_canon_sha256":"f78daa9e35d3ea31451def70976cb72c9b620b0baff4305af1d062eddbaf3957"},"schema_version":"1.0","source":{"id":"2411.02981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.02981","created_at":"2026-07-05T09:31:22Z"},{"alias_kind":"arxiv_version","alias_value":"2411.02981v1","created_at":"2026-07-05T09:31:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.02981","created_at":"2026-07-05T09:31:22Z"},{"alias_kind":"pith_short_12","alias_value":"2XKJWDALDYUN","created_at":"2026-07-05T09:31:22Z"},{"alias_kind":"pith_short_16","alias_value":"2XKJWDALDYUNSND7","created_at":"2026-07-05T09:31:22Z"},{"alias_kind":"pith_short_8","alias_value":"2XKJWDAL","created_at":"2026-07-05T09:31:22Z"}],"graph_snapshots":[{"event_id":"sha256:0361599879ff2fcc6f366185eafd28cdc16691c9297dd4abb68fe650b3107c4c","target":"graph","created_at":"2026-07-05T09:31:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.02981/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend our previous definition of K-theoretic invariants for operator systems based on hermitian forms to higher K-theoretical invariants. We realize the need for a positive parameter $\\delta$ as a measure for the spectral gap of the representatives for the K-theory classes. For each $\\delta$ and integer $p \\geq 0$ this gives operator system invariants $\\mathcal V_p^\\delta(-,n)$, indexed by the corresponding matrix size.\n  The corresponding direct system of these invariants has a direct limit that possesses a semigroup structure, and we define the $K_p^\\delta$-groups as the corresponding Gr","authors_text":"Walter D. van Suijlekom","cross_cats":["math.FA","math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-11-05T10:44:10Z","title":"Higher K-groups for operator systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02981","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":"sha256:9b75d9fc267a5d5276e33f0be67b75829d67d624c7aa00812136fb1b919ed810","target":"record","created_at":"2026-07-05T09:31:22Z","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":"76429ec9f1ff6fbbd6d05db02756dcbe149e1e0ad2e0ec78ae770625700ec95f","cross_cats_sorted":["math.FA","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2024-11-05T10:44:10Z","title_canon_sha256":"f78daa9e35d3ea31451def70976cb72c9b620b0baff4305af1d062eddbaf3957"},"schema_version":"1.0","source":{"id":"2411.02981","kind":"arxiv","version":1}},"canonical_sha256":"d5d49b0c0b1e28d9347fe769a87b3f18ca909f6a2d9ee6064678df8368cf1716","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5d49b0c0b1e28d9347fe769a87b3f18ca909f6a2d9ee6064678df8368cf1716","first_computed_at":"2026-07-05T09:31:22.997132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:31:22.997132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g6LODae5ahkJCin4W3d6Q4X3eIeCDKBdjZlQXH9uY4tvM6eUNFx9XyBVKiSdvJi830XTZBL1MxkivAeFBWqmCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:31:22.997603Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.02981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b75d9fc267a5d5276e33f0be67b75829d67d624c7aa00812136fb1b919ed810","sha256:0361599879ff2fcc6f366185eafd28cdc16691c9297dd4abb68fe650b3107c4c"],"state_sha256":"ea4b46782387732461cd74125ce4fa7203e51bcd962a709ea8800970dc89f622"}