{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UW3YN7TC5KJPR4UOELGASQCLDC","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":"151a6c7447bcb6641607669517201d66826794e58b7abad2bb6f30f0a8a041cc","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-01-16T16:21:01Z","title_canon_sha256":"ec51e1626a801b171404536409afa36099e8f9c924791638d511f17709f3ff33"},"schema_version":"1.0","source":{"id":"2501.09633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09633","created_at":"2026-07-05T10:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09633v1","created_at":"2026-07-05T10:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09633","created_at":"2026-07-05T10:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"UW3YN7TC5KJP","created_at":"2026-07-05T10:01:50Z"},{"alias_kind":"pith_short_16","alias_value":"UW3YN7TC5KJPR4UO","created_at":"2026-07-05T10:01:50Z"},{"alias_kind":"pith_short_8","alias_value":"UW3YN7TC","created_at":"2026-07-05T10:01:50Z"}],"graph_snapshots":[{"event_id":"sha256:88344aca703b2d5c4dbf6c06f450b38971584dd8ad5f36cd9cba209c4cc95792","target":"graph","created_at":"2026-07-05T10:01:50Z","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/2501.09633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we investigate the question of chromatic purity of L-theory. To do so, we utilize the theory of additive GW and L-theory in the language of Poincar\\'e categories as laid out in the series of papers by Calm\\`es et al. We apply this theory to chromatically localised L-theory at the prime $p=2$ and recover the L-theoretic analogues of chromatic purity for $E_1$-rings with involution. From this, we deduce that L-theory does not exhibit chromatic redshift. We deduce the higher chromatic vanishing of quadratic L-theory of arbitrary idempotent complete categories, thereby allowing the","authors_text":"Jordan Levin","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-01-16T16:21:01Z","title":"Chromatic Purity in Hermitian K-Theory at $p=2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09633","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:e6a5a6615d805530ee51d11edd9800a7d8f97a1ef6e9a8082f974e9ef35a271c","target":"record","created_at":"2026-07-05T10:01:50Z","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":"151a6c7447bcb6641607669517201d66826794e58b7abad2bb6f30f0a8a041cc","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-01-16T16:21:01Z","title_canon_sha256":"ec51e1626a801b171404536409afa36099e8f9c924791638d511f17709f3ff33"},"schema_version":"1.0","source":{"id":"2501.09633","kind":"arxiv","version":1}},"canonical_sha256":"a5b786fe62ea92f8f28e22cc09404b189d8e3b6f6be3a144b33799c5c299b419","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5b786fe62ea92f8f28e22cc09404b189d8e3b6f6be3a144b33799c5c299b419","first_computed_at":"2026-07-05T10:01:50.020996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:50.020996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"99sy4F3po8xkALQUi2B7Nhq5bMgAOp7l9WGza/HaLSM/ny1alBEsBy2zk9tusDZHlGyYSZoKnBzIcMdxkFgTDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:50.021429Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.09633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6a5a6615d805530ee51d11edd9800a7d8f97a1ef6e9a8082f974e9ef35a271c","sha256:88344aca703b2d5c4dbf6c06f450b38971584dd8ad5f36cd9cba209c4cc95792"],"state_sha256":"6b6429924f25d65f586e5206a288a30f57c4a9177102f32b2acd0382dbbb8a6f"}