{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:A42U667KK767CDFDOP7X2V462U","short_pith_number":"pith:A42U667K","canonical_record":{"source":{"id":"1105.6355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-31T18:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"5dc3ad9df888a1a0371fdfcb5ea338264ed07bd9c90e302c60cfe277818dbbd4","abstract_canon_sha256":"5e0182e3eeb3b572308eb476c52a8fd840053a1dfea3e3e0ab598ccfd3f5081e"},"schema_version":"1.0"},"canonical_sha256":"07354f7bea57fdf10ca373ff7d579ed526b310fc4dfdd719dee5b32564ce9724","source":{"kind":"arxiv","id":"1105.6355","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6355","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6355v2","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6355","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"A42U667KK767","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A42U667KK767CDFD","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A42U667K","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:A42U667KK767CDFDOP7X2V462U","target":"record","payload":{"canonical_record":{"source":{"id":"1105.6355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-31T18:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"5dc3ad9df888a1a0371fdfcb5ea338264ed07bd9c90e302c60cfe277818dbbd4","abstract_canon_sha256":"5e0182e3eeb3b572308eb476c52a8fd840053a1dfea3e3e0ab598ccfd3f5081e"},"schema_version":"1.0"},"canonical_sha256":"07354f7bea57fdf10ca373ff7d579ed526b310fc4dfdd719dee5b32564ce9724","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.198392Z","signature_b64":"BVDssDvtCjxgIlD3R1ZYK4HY4bRNRwOnFHIyZceFB36nrSq5CvGtMV2wNm4xZ9GVvyi4Ulby+cztE4g78qroDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07354f7bea57fdf10ca373ff7d579ed526b310fc4dfdd719dee5b32564ce9724","last_reissued_at":"2026-05-18T03:02:44.197691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.197691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.6355","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avwYGY6SyXTrgDl15RyIqX6wInMB4Ur//Bcn+5cTCI5e8rsHJzlo6phqcZOulZwx70QDD/hj0QKM7/NoUij7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:40:16.118829Z"},"content_sha256":"165e7671c511d0d89f14fc02de51a862faf8ca8ca88ef51cb5a0f64d4be12c80","schema_version":"1.0","event_id":"sha256:165e7671c511d0d89f14fc02de51a862faf8ca8ca88ef51cb5a0f64d4be12c80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:A42U667KK767CDFDOP7X2V462U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse uniqueness results for Schr\\\"odinger operators using de Branges theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jonathan Eckhardt","submitted_at":"2011-05-31T18:20:15Z","abstract_excerpt":"We utilize the theory of de Branges spaces to show when certain Schr\\\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness theorem for perturbed spherical Schr\\\"odinger operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6355","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGDT/waUSFlYWyxQFS50dVf3XuCMEss6vBhZq4IZbbkP5sXLcyegirlHOlhif3nsN9uZme9cTw7GhPlrFG87DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:40:16.119498Z"},"content_sha256":"89110b5ae63ece3ab5544e4bb9c702b4e74780b21aaad6d57d1f7c46103f881b","schema_version":"1.0","event_id":"sha256:89110b5ae63ece3ab5544e4bb9c702b4e74780b21aaad6d57d1f7c46103f881b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A42U667KK767CDFDOP7X2V462U/bundle.json","state_url":"https://pith.science/pith/A42U667KK767CDFDOP7X2V462U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A42U667KK767CDFDOP7X2V462U/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":"2026-06-11T17:40:16Z","links":{"resolver":"https://pith.science/pith/A42U667KK767CDFDOP7X2V462U","bundle":"https://pith.science/pith/A42U667KK767CDFDOP7X2V462U/bundle.json","state":"https://pith.science/pith/A42U667KK767CDFDOP7X2V462U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A42U667KK767CDFDOP7X2V462U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A42U667KK767CDFDOP7X2V462U","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":"5e0182e3eeb3b572308eb476c52a8fd840053a1dfea3e3e0ab598ccfd3f5081e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-31T18:20:15Z","title_canon_sha256":"5dc3ad9df888a1a0371fdfcb5ea338264ed07bd9c90e302c60cfe277818dbbd4"},"schema_version":"1.0","source":{"id":"1105.6355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6355","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6355v2","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6355","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"A42U667KK767","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A42U667KK767CDFD","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A42U667K","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:89110b5ae63ece3ab5544e4bb9c702b4e74780b21aaad6d57d1f7c46103f881b","target":"graph","created_at":"2026-05-18T03:02:44Z","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":"We utilize the theory of de Branges spaces to show when certain Schr\\\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness theorem for perturbed spherical Schr\\\"odinger operators.","authors_text":"Jonathan Eckhardt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-31T18:20:15Z","title":"Inverse uniqueness results for Schr\\\"odinger operators using de Branges theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6355","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":"sha256:165e7671c511d0d89f14fc02de51a862faf8ca8ca88ef51cb5a0f64d4be12c80","target":"record","created_at":"2026-05-18T03:02:44Z","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":"5e0182e3eeb3b572308eb476c52a8fd840053a1dfea3e3e0ab598ccfd3f5081e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-05-31T18:20:15Z","title_canon_sha256":"5dc3ad9df888a1a0371fdfcb5ea338264ed07bd9c90e302c60cfe277818dbbd4"},"schema_version":"1.0","source":{"id":"1105.6355","kind":"arxiv","version":2}},"canonical_sha256":"07354f7bea57fdf10ca373ff7d579ed526b310fc4dfdd719dee5b32564ce9724","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07354f7bea57fdf10ca373ff7d579ed526b310fc4dfdd719dee5b32564ce9724","first_computed_at":"2026-05-18T03:02:44.197691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:44.197691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVDssDvtCjxgIlD3R1ZYK4HY4bRNRwOnFHIyZceFB36nrSq5CvGtMV2wNm4xZ9GVvyi4Ulby+cztE4g78qroDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:44.198392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:165e7671c511d0d89f14fc02de51a862faf8ca8ca88ef51cb5a0f64d4be12c80","sha256:89110b5ae63ece3ab5544e4bb9c702b4e74780b21aaad6d57d1f7c46103f881b"],"state_sha256":"318fee142bf4432d3a1aad9478d9f0b6efc35693a364feeeb05637fed7a4eae3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1gH0Z4jVzeQC1jDwCDVDNr12MPuvS2jlQsz253wE6C+pzrkxfSy8BzEHbnveUU+t5Dos6ySqVAusUUMOZyCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:40:16.123929Z","bundle_sha256":"f88c9ad14f6754e5fd79f9c115d0c80eeb689a7fccf5381c59ea938d343f4845"}}