{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WHVK7AXDDEULZKFKAPWBOZTEUE","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":"4c4fa26abd6d11f0f8c086c7656fb31e526b07b56917a9ab5e7c3bad769abd51","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T17:29:01Z","title_canon_sha256":"c5a02f76176600264df7703addd5087aa0df758bb0e705cfc840b9a22f212af6"},"schema_version":"1.0","source":{"id":"2606.28284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28284","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28284v1","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28284","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_12","alias_value":"WHVK7AXDDEUL","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_16","alias_value":"WHVK7AXDDEULZKFK","created_at":"2026-06-29T01:15:11Z"},{"alias_kind":"pith_short_8","alias_value":"WHVK7AXD","created_at":"2026-06-29T01:15:11Z"}],"graph_snapshots":[{"event_id":"sha256:bf6a45c5180d2413aaf15ee7ba9652ac7f0bdc119b94261f9cbf78d89fb21b0b","target":"graph","created_at":"2026-06-29T01:15:11Z","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/2606.28284/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study commutative topological algebras naturally associated with translation-invariant reproducing kernel Hilbert spaces whose direct integral decomposition has one-dimensional fibers. Starting from the bounded algebra of translation-invariant operators, we pass to a common dense domain generated by reproducing kernels and identify the corresponding diagonalizable operators with multiplication by symbols in an intersection of weighted $L^2$-spaces. On the symbol side this gives a canonical space $\\mathcal F_0$ and a maximal multiplicative subalgebra $\\mathcal F_M$, which is a complete local","authors_text":"Miguel Angel Rodriguez Rodriguez","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T17:29:01Z","title":"Commutative topological algebras on translation-invariant reproducing kernel Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28284","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":"sha256:2de3c479ea687d8bbf85d3eaede21eda7f1d259d146049c85b401d14909aea3b","target":"record","created_at":"2026-06-29T01:15:11Z","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":"4c4fa26abd6d11f0f8c086c7656fb31e526b07b56917a9ab5e7c3bad769abd51","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-26T17:29:01Z","title_canon_sha256":"c5a02f76176600264df7703addd5087aa0df758bb0e705cfc840b9a22f212af6"},"schema_version":"1.0","source":{"id":"2606.28284","kind":"arxiv","version":1}},"canonical_sha256":"b1eaaf82e31928bca8aa03ec176664a1283610e2e96ace46d7ac0cae6e659db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1eaaf82e31928bca8aa03ec176664a1283610e2e96ace46d7ac0cae6e659db3","first_computed_at":"2026-06-29T01:15:11.972919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:15:11.972919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B0qDYP90aOCru06F4dwTHZ6GhQZ+JFJiyVevCfQgUQoXdvzbm3kQdjx1hXQwvauI+EyyVfueL7L4EivohmEmAw==","signature_status":"signed_v1","signed_at":"2026-06-29T01:15:11.973279Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2de3c479ea687d8bbf85d3eaede21eda7f1d259d146049c85b401d14909aea3b","sha256:bf6a45c5180d2413aaf15ee7ba9652ac7f0bdc119b94261f9cbf78d89fb21b0b"],"state_sha256":"9a25f6f887c3377d9d3956c6280809ffc00c8cdfc5e3eac84a3abb6237f76c4f"}