{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YSHNT7VOV2OIUD6OFS6GBXCUTZ","short_pith_number":"pith:YSHNT7VO","schema_version":"1.0","canonical_sha256":"c48ed9feaeae9c8a0fce2cbc60dc549e7aca0ded27f81e71aa99021c22d015b7","source":{"kind":"arxiv","id":"1502.03222","version":2},"attestation_state":"computed","paper":{"title":"Functional Calculus for definitizable self-adjoint linear relations on Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Kaltenb\\\"ack, Raphael Pruckner","submitted_at":"2015-02-11T08:57:10Z","abstract_excerpt":"In the present note a functional calculus $\\phi \\mapsto \\phi(A)$ for self-adjoint definitizable linear relation on Krein spaces is developed. This functional calculus is the proper analogue of $\\phi \\mapsto \\int \\phi \\, dE$ in the Hilbert space situation. It also comprises the Spectral Theorem for self-adjoint definitizable operators on Krein spaces showing the existence of spectral projections."},"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":"1502.03222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-11T08:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"cbe5dd0d216f02e26ca4a756e2c04297c61b63f8125670cb5062aae964dffb8e","abstract_canon_sha256":"75ac97698184221da19be75217a30038853044b2e597357ca2ee5e2e0068855e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.350624Z","signature_b64":"chSZa1maC3GW36A7YDgBmRRZDcsLgJM1uSsPznxa4RUQSDbvu2m+I55+T5cCpE52vDkaRce015pxySktR0zaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c48ed9feaeae9c8a0fce2cbc60dc549e7aca0ded27f81e71aa99021c22d015b7","last_reissued_at":"2026-05-18T01:31:11.349872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.349872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional Calculus for definitizable self-adjoint linear relations on Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Kaltenb\\\"ack, Raphael Pruckner","submitted_at":"2015-02-11T08:57:10Z","abstract_excerpt":"In the present note a functional calculus $\\phi \\mapsto \\phi(A)$ for self-adjoint definitizable linear relation on Krein spaces is developed. This functional calculus is the proper analogue of $\\phi \\mapsto \\int \\phi \\, dE$ in the Hilbert space situation. It also comprises the Spectral Theorem for self-adjoint definitizable operators on Krein spaces showing the existence of spectral projections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03222","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":""},"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":"1502.03222","created_at":"2026-05-18T01:31:11.349999+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.03222v2","created_at":"2026-05-18T01:31:11.349999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03222","created_at":"2026-05-18T01:31:11.349999+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSHNT7VOV2OI","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSHNT7VOV2OIUD6O","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSHNT7VO","created_at":"2026-05-18T12:29:52.810259+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/YSHNT7VOV2OIUD6OFS6GBXCUTZ","json":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ.json","graph_json":"https://pith.science/api/pith-number/YSHNT7VOV2OIUD6OFS6GBXCUTZ/graph.json","events_json":"https://pith.science/api/pith-number/YSHNT7VOV2OIUD6OFS6GBXCUTZ/events.json","paper":"https://pith.science/paper/YSHNT7VO"},"agent_actions":{"view_html":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ","download_json":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ.json","view_paper":"https://pith.science/paper/YSHNT7VO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.03222&json=true","fetch_graph":"https://pith.science/api/pith-number/YSHNT7VOV2OIUD6OFS6GBXCUTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YSHNT7VOV2OIUD6OFS6GBXCUTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ/action/storage_attestation","attest_author":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ/action/author_attestation","sign_citation":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ/action/citation_signature","submit_replication":"https://pith.science/pith/YSHNT7VOV2OIUD6OFS6GBXCUTZ/action/replication_record"}},"created_at":"2026-05-18T01:31:11.349999+00:00","updated_at":"2026-05-18T01:31:11.349999+00:00"}