{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2SUKYZZ3I4ETYMIISWX6UHC67E","short_pith_number":"pith:2SUKYZZ3","canonical_record":{"source":{"id":"1305.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-05-14T10:38:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a7675f735156b500482e97dd66fb81994ca131c7e87d552981a27f29b36539cc","abstract_canon_sha256":"621ef7192d29162fd42f0c99ddf483b529975e76921b4aefae9a42ee7c60d817"},"schema_version":"1.0"},"canonical_sha256":"d4a8ac673b47093c310895afea1c5ef9086364d21d7d36ea3b23ce6ab0e03e1e","source":{"kind":"arxiv","id":"1305.3100","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3100","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3100v2","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3100","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"2SUKYZZ3I4ET","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2SUKYZZ3I4ETYMII","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2SUKYZZ3","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2SUKYZZ3I4ETYMIISWX6UHC67E","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-05-14T10:38:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a7675f735156b500482e97dd66fb81994ca131c7e87d552981a27f29b36539cc","abstract_canon_sha256":"621ef7192d29162fd42f0c99ddf483b529975e76921b4aefae9a42ee7c60d817"},"schema_version":"1.0"},"canonical_sha256":"d4a8ac673b47093c310895afea1c5ef9086364d21d7d36ea3b23ce6ab0e03e1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:54.473612Z","signature_b64":"ulhoyBXDAgZc0+ZtGaUmfC+7tFR8xtRQ7SYvA6mVBwXCxvsqChpbmww2agSDSbQrDOtu1Eh6tyJE50z09TOhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4a8ac673b47093c310895afea1c5ef9086364d21d7d36ea3b23ce6ab0e03e1e","last_reissued_at":"2026-05-18T01:38:54.472923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:54.472923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3100","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uFXG7BZiUWM3WhZtFJWWjYpLn8931pSDQmq9U3qRF4eE3dhcwvECtJX6jbA0IDTVh1v9HOz9fqzqMWXMoWAfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:21:00.736516Z"},"content_sha256":"732f5206b6af406d6970c8a4a24b68fde2561f3dcbe707a15cc1f91d03f1f672","schema_version":"1.0","event_id":"sha256:732f5206b6af406d6970c8a4a24b68fde2561f3dcbe707a15cc1f91d03f1f672"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2SUKYZZ3I4ETYMIISWX6UHC67E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse uniqueness results for one-dimensional weighted Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Aleksey Kostenko, Gerald Teschl, Jonathan Eckhardt","submitted_at":"2013-05-14T10:38:51Z","abstract_excerpt":"Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one regular endpoint. Moreover, our result also improves the currently known results for canonical (Hamiltonian) systems. If one endpoint is limit circle case, we also establish corresponding two-spectra re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3100","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujHv+uX7MlwkMlaIy20GoPRFfI+zvgEZgfOAbtY8HL65sn/Rlyq8PvVcADcNAvIvvia13hTubn8haJEEaNiuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:21:00.737163Z"},"content_sha256":"6bef4a3c3c02a289bc072fc60fd2afbd88b9acc0aadc21fd2c7315544201131e","schema_version":"1.0","event_id":"sha256:6bef4a3c3c02a289bc072fc60fd2afbd88b9acc0aadc21fd2c7315544201131e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/bundle.json","state_url":"https://pith.science/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/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":"2026-06-07T08:21:00Z","links":{"resolver":"https://pith.science/pith/2SUKYZZ3I4ETYMIISWX6UHC67E","bundle":"https://pith.science/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/bundle.json","state":"https://pith.science/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SUKYZZ3I4ETYMIISWX6UHC67E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2SUKYZZ3I4ETYMIISWX6UHC67E","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":"621ef7192d29162fd42f0c99ddf483b529975e76921b4aefae9a42ee7c60d817","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-05-14T10:38:51Z","title_canon_sha256":"a7675f735156b500482e97dd66fb81994ca131c7e87d552981a27f29b36539cc"},"schema_version":"1.0","source":{"id":"1305.3100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3100","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3100v2","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3100","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"2SUKYZZ3I4ET","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2SUKYZZ3I4ETYMII","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2SUKYZZ3","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:6bef4a3c3c02a289bc072fc60fd2afbd88b9acc0aadc21fd2c7315544201131e","target":"graph","created_at":"2026-05-18T01:38:54Z","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"},"paper":{"abstract_excerpt":"Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one regular endpoint. Moreover, our result also improves the currently known results for canonical (Hamiltonian) systems. If one endpoint is limit circle case, we also establish corresponding two-spectra re","authors_text":"Aleksey Kostenko, Gerald Teschl, Jonathan Eckhardt","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-05-14T10:38:51Z","title":"Inverse uniqueness results for one-dimensional weighted Dirac operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3100","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":"sha256:732f5206b6af406d6970c8a4a24b68fde2561f3dcbe707a15cc1f91d03f1f672","target":"record","created_at":"2026-05-18T01:38:54Z","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":"621ef7192d29162fd42f0c99ddf483b529975e76921b4aefae9a42ee7c60d817","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-05-14T10:38:51Z","title_canon_sha256":"a7675f735156b500482e97dd66fb81994ca131c7e87d552981a27f29b36539cc"},"schema_version":"1.0","source":{"id":"1305.3100","kind":"arxiv","version":2}},"canonical_sha256":"d4a8ac673b47093c310895afea1c5ef9086364d21d7d36ea3b23ce6ab0e03e1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4a8ac673b47093c310895afea1c5ef9086364d21d7d36ea3b23ce6ab0e03e1e","first_computed_at":"2026-05-18T01:38:54.472923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:54.472923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ulhoyBXDAgZc0+ZtGaUmfC+7tFR8xtRQ7SYvA6mVBwXCxvsqChpbmww2agSDSbQrDOtu1Eh6tyJE50z09TOhBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:54.473612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:732f5206b6af406d6970c8a4a24b68fde2561f3dcbe707a15cc1f91d03f1f672","sha256:6bef4a3c3c02a289bc072fc60fd2afbd88b9acc0aadc21fd2c7315544201131e"],"state_sha256":"0c84dd6bc97b6cff5b9cffe9ab6cee4e1a250427366b6c554fb38da084e6e5ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJWwIFJtcZzkK70czWn6denl/N8X3Lo5iYvaXoEUrOc5EjvLzhV87Fj/TvaSzjrciUfiK9a4l1mHSBX8p4R6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:21:00.740796Z","bundle_sha256":"d6ad3fb3e9df993b4adcd4e9523d57d4a36989f62c626aa98ce5052f3d0abef0"}}