{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CDFSTWHCXUROY5XA2XZUE2QO4F","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":"c83e0e2b26d55f8bdcbb59a440bdf7fa45488303d256f50055f32309d1a8681e","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-09-15T13:47:05Z","title_canon_sha256":"5ed9355166a63fa2d35f2e560485c42554c722c12a3685f2fdf98bcc57bbb127"},"schema_version":"1.0","source":{"id":"2509.11931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.11931","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2509.11931v2","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11931","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"CDFSTWHCXURO","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"CDFSTWHCXUROY5XA","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"CDFSTWHC","created_at":"2026-06-25T00:18:11Z"}],"graph_snapshots":[{"event_id":"sha256:b1aa580a75f0bb134bddf29b8dbee6a2442706bc39a9688fe2c649dc622cf514","target":"graph","created_at":"2026-06-25T00:18:11Z","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/2509.11931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for strongly continuous semigroups on Banach spaces.","authors_text":"Karsten Kruse","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-09-15T13:47:05Z","title":"Spectral theory for semigroups on locally convex spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11931","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":"sha256:19e7be57e80b2a25299cd9c5d1ce21b2848788ba5fbf8aa443ae960b725aab2d","target":"record","created_at":"2026-06-25T00:18:11Z","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":"c83e0e2b26d55f8bdcbb59a440bdf7fa45488303d256f50055f32309d1a8681e","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-09-15T13:47:05Z","title_canon_sha256":"5ed9355166a63fa2d35f2e560485c42554c722c12a3685f2fdf98bcc57bbb127"},"schema_version":"1.0","source":{"id":"2509.11931","kind":"arxiv","version":2}},"canonical_sha256":"10cb29d8e2bd22ec76e0d5f3426a0ee14110a659f073b06b779f6a72a1dbc1f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10cb29d8e2bd22ec76e0d5f3426a0ee14110a659f073b06b779f6a72a1dbc1f5","first_computed_at":"2026-06-25T00:18:11.598402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T00:18:11.598402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tnKA0uGZfEgAMFwmFaEQpuUreKBMTavqhSpznDebX2ps+8jfCW9PyDEzCAQN7qxia/PuHRiBTrX2IWxyv6s7CA==","signature_status":"signed_v1","signed_at":"2026-06-25T00:18:11.598971Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.11931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19e7be57e80b2a25299cd9c5d1ce21b2848788ba5fbf8aa443ae960b725aab2d","sha256:b1aa580a75f0bb134bddf29b8dbee6a2442706bc39a9688fe2c649dc622cf514"],"state_sha256":"5d0dbd0efcb7f247cf6e85276dfbf9f0d583ccb8bd123247f7e5e4057b1ad678"}