{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ALJ3FUWCCMFGQWGGWQRF35MASW","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":"2c4ac627beccb4a4049b5ee534881a4121a15aba69a79f07429b4e347d461970","cross_cats_sorted":["math.FA","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-09-30T09:12:39Z","title_canon_sha256":"9d864a989d3008a1bfb348a95ea6292e1a9682a359067c86308517b6334db982"},"schema_version":"1.0","source":{"id":"2509.25981","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.25981","created_at":"2026-07-09T01:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.25981v3","created_at":"2026-07-09T01:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.25981","created_at":"2026-07-09T01:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"ALJ3FUWCCMFG","created_at":"2026-07-09T01:19:37Z"},{"alias_kind":"pith_short_16","alias_value":"ALJ3FUWCCMFGQWGG","created_at":"2026-07-09T01:19:37Z"},{"alias_kind":"pith_short_8","alias_value":"ALJ3FUWC","created_at":"2026-07-09T01:19:37Z"}],"graph_snapshots":[{"event_id":"sha256:3ff02ba2a47b18574c46d235c9e9a1654c900906c53d9601990d20262d8296cf","target":"graph","created_at":"2026-07-09T01:19:37Z","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/2509.25981/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by applications to duality theorems for $p$-adic pro-\\'etale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full subcategories, both the category of (topologically) bounded algebraic Vector Spaces and the category of perfect complexes on the Fargues-Fontaine curve. Vector Spaces coming from $p$-adic pro-\\'etale cohomology of smooth partially proper rigid analytic varieties are examples of sheaves belonging to the former category.","authors_text":"Pierre Colmez, Wies{\\l}awa Nizio{\\l}","cross_cats":["math.FA","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-09-30T09:12:39Z","title":"Topological Vector Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.25981","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:d8833c12b2c97a9ded09cf793aba8b07696c4157551861d267d66f0d4ae89862","target":"record","created_at":"2026-07-09T01:19:37Z","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":"2c4ac627beccb4a4049b5ee534881a4121a15aba69a79f07429b4e347d461970","cross_cats_sorted":["math.FA","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-09-30T09:12:39Z","title_canon_sha256":"9d864a989d3008a1bfb348a95ea6292e1a9682a359067c86308517b6334db982"},"schema_version":"1.0","source":{"id":"2509.25981","kind":"arxiv","version":3}},"canonical_sha256":"02d3b2d2c2130a6858c6b4225df5809595645df89d59369d53a60d1d8a126b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d3b2d2c2130a6858c6b4225df5809595645df89d59369d53a60d1d8a126b17","first_computed_at":"2026-07-09T01:19:37.824309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:19:37.824309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfx/DZ/0M+4Z1rJAfTlYfT024pCgJ790DgZM31QmG5GWt4VuJkCb62PiOW9nMJaxc5mjVXNoD2+1mpgK4wtDBQ==","signature_status":"signed_v1","signed_at":"2026-07-09T01:19:37.824797Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.25981","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8833c12b2c97a9ded09cf793aba8b07696c4157551861d267d66f0d4ae89862","sha256:3ff02ba2a47b18574c46d235c9e9a1654c900906c53d9601990d20262d8296cf"],"state_sha256":"3f4d6de7957d66d158bc2f9585661e38dbf5d54cdf7bbdff3eff7646ba4b08df"}