{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FNP5CJ5VGNW44ETXSI7R7G4IVN","short_pith_number":"pith:FNP5CJ5V","canonical_record":{"source":{"id":"2503.16239","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-03-20T15:37:00Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"0eafecbfdf7860bf6ebcef047b75a1d8beaca7219569248ee2e7420b55c4be04","abstract_canon_sha256":"a942771ee4bb4f6662488bd3cf472a72b2e940ec4761fd4f52813fed1aabcaa8"},"schema_version":"1.0"},"canonical_sha256":"2b5fd127b5336dce1277923f1f9b88ab6543872aa5ee433915e213efa6dc695b","source":{"kind":"arxiv","id":"2503.16239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16239","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16239v1","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16239","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"FNP5CJ5VGNW4","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_16","alias_value":"FNP5CJ5VGNW44ETX","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_8","alias_value":"FNP5CJ5V","created_at":"2026-07-05T10:36:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FNP5CJ5VGNW44ETXSI7R7G4IVN","target":"record","payload":{"canonical_record":{"source":{"id":"2503.16239","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-03-20T15:37:00Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"0eafecbfdf7860bf6ebcef047b75a1d8beaca7219569248ee2e7420b55c4be04","abstract_canon_sha256":"a942771ee4bb4f6662488bd3cf472a72b2e940ec4761fd4f52813fed1aabcaa8"},"schema_version":"1.0"},"canonical_sha256":"2b5fd127b5336dce1277923f1f9b88ab6543872aa5ee433915e213efa6dc695b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:08.603134Z","signature_b64":"QKXB3ZCOHVtWKC9wSpJSnf5bKep+16tmDKaql86VaOXpliKi8t19d0irseV4Xjdhcjh3EXXWzRyMfPrpku+sDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b5fd127b5336dce1277923f1f9b88ab6543872aa5ee433915e213efa6dc695b","last_reissued_at":"2026-07-05T10:36:08.602578Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:08.602578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.16239","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"31y0qtkqpzCEjaywbvBgQE6lRNAQAbbD9MJgZS4WC16bWw7Oj3mOIXi9QcmMD8SMjsPXnDnVJTb0oOFkrojsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:47:59.136516Z"},"content_sha256":"747c54486e85ae5864481b1c624357d9fe1d453d8e041c7128fcdb0507abb62e","schema_version":"1.0","event_id":"sha256:747c54486e85ae5864481b1c624357d9fe1d453d8e041c7128fcdb0507abb62e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FNP5CJ5VGNW44ETXSI7R7G4IVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Double Operator Integrals: Finite Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Shih-Yu Chang","submitted_at":"2025-03-20T15:37:00Z","abstract_excerpt":"The Double Operator Integral (DOI) framework provides a powerful tool for analyzing perturbations and interactions between self-adjoint operators in functional analysis and spectral theory. However, most existing DOI formulations rely on self-adjointness (Hermitian) or unitary assumptions, limiting their applicability to non-Hermitian settings. Motivated by advancements in non-Hermitian physics and operator theory, this paper introduces Generalized Double Operator Integrals (GDOIs), extending DOI theory to arbitrary non-Hermitian and non-normal matrices. We establish key algebraic properties o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16239","kind":"arxiv","version":1},"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/2503.16239/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MucpZTRpGhOMlDN5vUYB72tTggQIKMu7QYr/sNmpyRTtAXIE0RWYovl3K+x5OCsN82vm/WW+H0QW0OkfCUi5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:47:59.137377Z"},"content_sha256":"b86ab39f7fbcfa950ae6cee0fd5e4d7049e13e4d4e8adb973066ac98e433dd87","schema_version":"1.0","event_id":"sha256:b86ab39f7fbcfa950ae6cee0fd5e4d7049e13e4d4e8adb973066ac98e433dd87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/bundle.json","state_url":"https://pith.science/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T21:47:59Z","links":{"resolver":"https://pith.science/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN","bundle":"https://pith.science/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/bundle.json","state":"https://pith.science/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNP5CJ5VGNW44ETXSI7R7G4IVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FNP5CJ5VGNW44ETXSI7R7G4IVN","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":"a942771ee4bb4f6662488bd3cf472a72b2e940ec4761fd4f52813fed1aabcaa8","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-03-20T15:37:00Z","title_canon_sha256":"0eafecbfdf7860bf6ebcef047b75a1d8beaca7219569248ee2e7420b55c4be04"},"schema_version":"1.0","source":{"id":"2503.16239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16239","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16239v1","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16239","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"FNP5CJ5VGNW4","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_16","alias_value":"FNP5CJ5VGNW44ETX","created_at":"2026-07-05T10:36:08Z"},{"alias_kind":"pith_short_8","alias_value":"FNP5CJ5V","created_at":"2026-07-05T10:36:08Z"}],"graph_snapshots":[{"event_id":"sha256:b86ab39f7fbcfa950ae6cee0fd5e4d7049e13e4d4e8adb973066ac98e433dd87","target":"graph","created_at":"2026-07-05T10:36:08Z","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/2503.16239/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Double Operator Integral (DOI) framework provides a powerful tool for analyzing perturbations and interactions between self-adjoint operators in functional analysis and spectral theory. However, most existing DOI formulations rely on self-adjointness (Hermitian) or unitary assumptions, limiting their applicability to non-Hermitian settings. Motivated by advancements in non-Hermitian physics and operator theory, this paper introduces Generalized Double Operator Integrals (GDOIs), extending DOI theory to arbitrary non-Hermitian and non-normal matrices. We establish key algebraic properties o","authors_text":"Shih-Yu Chang","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-03-20T15:37:00Z","title":"Generalized Double Operator Integrals: Finite Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16239","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":"sha256:747c54486e85ae5864481b1c624357d9fe1d453d8e041c7128fcdb0507abb62e","target":"record","created_at":"2026-07-05T10:36:08Z","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":"a942771ee4bb4f6662488bd3cf472a72b2e940ec4761fd4f52813fed1aabcaa8","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-03-20T15:37:00Z","title_canon_sha256":"0eafecbfdf7860bf6ebcef047b75a1d8beaca7219569248ee2e7420b55c4be04"},"schema_version":"1.0","source":{"id":"2503.16239","kind":"arxiv","version":1}},"canonical_sha256":"2b5fd127b5336dce1277923f1f9b88ab6543872aa5ee433915e213efa6dc695b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b5fd127b5336dce1277923f1f9b88ab6543872aa5ee433915e213efa6dc695b","first_computed_at":"2026-07-05T10:36:08.602578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:36:08.602578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKXB3ZCOHVtWKC9wSpJSnf5bKep+16tmDKaql86VaOXpliKi8t19d0irseV4Xjdhcjh3EXXWzRyMfPrpku+sDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:36:08.603134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.16239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:747c54486e85ae5864481b1c624357d9fe1d453d8e041c7128fcdb0507abb62e","sha256:b86ab39f7fbcfa950ae6cee0fd5e4d7049e13e4d4e8adb973066ac98e433dd87"],"state_sha256":"b90c98164da566900a7876c39e6f5df5a540af44807da0a2b9a9cd2a54a35077"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B17eTNEIidqgPdsM3EONxg9OYKy6leOFTlUn6RMx3MZO1jXu4f4vMxK1yRvw1Pmml0n2cJ0YkVWzDi7sQI+VDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:47:59.145451Z","bundle_sha256":"81bcf7dfbaeb4c57b7753955300b12d720dfe749fe9b006c164b27a46cb2790c"}}