{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2IB6VG7LDAVTXE4WWPOP5BRYYT","short_pith_number":"pith:2IB6VG7L","schema_version":"1.0","canonical_sha256":"d203ea9beb182b3b9396b3dcfe8638c4de48bb3175ec7f56ee2c09df47b79fa0","source":{"kind":"arxiv","id":"2601.12044","version":2},"attestation_state":"computed","paper":{"title":"Endpoint Koopman Spectral Computation: $L^1$ Residual Bounds, $L^\\infty$ Instability, and Point-Spectral SCI Calibration Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","math.SP"],"primary_cat":"math.LO","authors_text":"Christopher Sorg","submitted_at":"2026-01-17T13:17:21Z","abstract_excerpt":"We study endpoint Koopman spectral computation from the viewpoint of the Solvability Complexity Index (SCI). Let \\((\\mathcal X,d)\\) be a compact metric space with finite Borel measure \\(\\omega\\), and let \\(\\mathcal K_F\\) be the Koopman operator associated with a continuous nonsingular map \\(F:\\mathcal X\\to\\mathcal X\\).\n  First, on \\(L^1(\\mathcal X,\\omega)\\), we record the endpoint residual upper-bound in the target-split form. The regularized compact fixed-\\(\\varepsilon\\) target $R_{\\mathrm{ap},\\varepsilon}(\\mathcal K_F)$ is separated from the closed fixed-\\(\\varepsilon\\) target $C_{\\mathrm{ap"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2601.12044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-01-17T13:17:21Z","cross_cats_sorted":["cs.NA","math.DS","math.NA","math.SP"],"title_canon_sha256":"defba7710ba515f1aff5df228515c4d4961ed6c707038e72e1d433e043dba575","abstract_canon_sha256":"d64854430e5505c48410e84aff4840156b413df244abb11d2cb22ec7b77ad246"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:02:30.904208Z","signature_b64":"w3q967Vkla+1DArHVw3T28CqroF0jZ2VEolQZ9tRxsbt1rlbaOXx5j019RrDgPaaibfJUUQhgMBY1TgO7ukiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d203ea9beb182b3b9396b3dcfe8638c4de48bb3175ec7f56ee2c09df47b79fa0","last_reissued_at":"2026-05-26T01:02:30.903296Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:02:30.903296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Endpoint Koopman Spectral Computation: $L^1$ Residual Bounds, $L^\\infty$ Instability, and Point-Spectral SCI Calibration Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","math.SP"],"primary_cat":"math.LO","authors_text":"Christopher Sorg","submitted_at":"2026-01-17T13:17:21Z","abstract_excerpt":"We study endpoint Koopman spectral computation from the viewpoint of the Solvability Complexity Index (SCI). Let \\((\\mathcal X,d)\\) be a compact metric space with finite Borel measure \\(\\omega\\), and let \\(\\mathcal K_F\\) be the Koopman operator associated with a continuous nonsingular map \\(F:\\mathcal X\\to\\mathcal X\\).\n  First, on \\(L^1(\\mathcal X,\\omega)\\), we record the endpoint residual upper-bound in the target-split form. The regularized compact fixed-\\(\\varepsilon\\) target $R_{\\mathrm{ap},\\varepsilon}(\\mathcal K_F)$ is separated from the closed fixed-\\(\\varepsilon\\) target $C_{\\mathrm{ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.12044","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.12044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2601.12044","created_at":"2026-05-26T01:02:30.903443+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.12044v2","created_at":"2026-05-26T01:02:30.903443+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.12044","created_at":"2026-05-26T01:02:30.903443+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IB6VG7LDAVT","created_at":"2026-05-26T01:02:30.903443+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IB6VG7LDAVTXE4W","created_at":"2026-05-26T01:02:30.903443+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IB6VG7L","created_at":"2026-05-26T01:02:30.903443+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT","json":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT.json","graph_json":"https://pith.science/api/pith-number/2IB6VG7LDAVTXE4WWPOP5BRYYT/graph.json","events_json":"https://pith.science/api/pith-number/2IB6VG7LDAVTXE4WWPOP5BRYYT/events.json","paper":"https://pith.science/paper/2IB6VG7L"},"agent_actions":{"view_html":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT","download_json":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT.json","view_paper":"https://pith.science/paper/2IB6VG7L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.12044&json=true","fetch_graph":"https://pith.science/api/pith-number/2IB6VG7LDAVTXE4WWPOP5BRYYT/graph.json","fetch_events":"https://pith.science/api/pith-number/2IB6VG7LDAVTXE4WWPOP5BRYYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT/action/storage_attestation","attest_author":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT/action/author_attestation","sign_citation":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT/action/citation_signature","submit_replication":"https://pith.science/pith/2IB6VG7LDAVTXE4WWPOP5BRYYT/action/replication_record"}},"created_at":"2026-05-26T01:02:30.903443+00:00","updated_at":"2026-05-26T01:02:30.903443+00:00"}