{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DYRJGKY46OBNCKMRIASQ4EKDBG","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":"c7405e2dee7d931fe0b222661f63a5f41932d9c8f135dacc3ef0f906f0cb59ff","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-07-17T21:11:05Z","title_canon_sha256":"03cb96c9304bbca1e00e9b3ea08b4efbd184c21ebb9be2f22bfd403e7dc324a9"},"schema_version":"1.0","source":{"id":"2507.13537","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13537","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13537v2","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13537","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"DYRJGKY46OBN","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_16","alias_value":"DYRJGKY46OBNCKMR","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_8","alias_value":"DYRJGKY4","created_at":"2026-07-05T11:53:05Z"}],"graph_snapshots":[{"event_id":"sha256:62f2a3f23ceec648a75b6ba457195bd085c235f3a81dcbfd6459a95508a45df5","target":"graph","created_at":"2026-07-05T11:53:05Z","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/2507.13537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the functor sending a locally compact Hausdorff space $X$ to the $\\infty$-category of spectral sheaves $\\mathrm{Shv}(X; \\mathrm{Sp})$ is initial among all continuous six-functor formalisms on the category of locally compact Hausdorff spaces. Here, continuous six-functor formalisms are those valued in dualizable presentable stable $\\infty$-categories and satisfying canonical descent, profinite descent, and hyperdescent. As an application, we generalize Efimov's computation of the algebraic $K$-theory of sheaves to all localizing invariants on continuous six-functor formalisms. Our ","authors_text":"Qingchong Zhu","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-07-17T21:11:05Z","title":"Continuous six-functor formalism on locally compact Hausdorff spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13537","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:a23d056b6eb2ee72a86343bb16bf687dfa97fbd7e6f9a03ab917eeadd65675d8","target":"record","created_at":"2026-07-05T11:53:05Z","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":"c7405e2dee7d931fe0b222661f63a5f41932d9c8f135dacc3ef0f906f0cb59ff","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2025-07-17T21:11:05Z","title_canon_sha256":"03cb96c9304bbca1e00e9b3ea08b4efbd184c21ebb9be2f22bfd403e7dc324a9"},"schema_version":"1.0","source":{"id":"2507.13537","kind":"arxiv","version":2}},"canonical_sha256":"1e22932b1cf382d1299140250e114309b32747b90929ae1b187da213e02b09bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e22932b1cf382d1299140250e114309b32747b90929ae1b187da213e02b09bc","first_computed_at":"2026-07-05T11:53:05.404719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:53:05.404719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9/95ivBP0dVY90m7YYJ7Pvp39tsDnYbbjZjW8XlpKFoj20Xmnfz8/GXqLS7NL9XqypQEddGrVIksFFC1LBTCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:53:05.405171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13537","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a23d056b6eb2ee72a86343bb16bf687dfa97fbd7e6f9a03ab917eeadd65675d8","sha256:62f2a3f23ceec648a75b6ba457195bd085c235f3a81dcbfd6459a95508a45df5"],"state_sha256":"b6f0a9e39443d48db959614273ff879a23bb2956ff769e5be51d8483933e41a0"}