{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GGBTASASFID5MTBTRUCQCFQLIX","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":"42b677e679ee20ab8623c5ffb733f086f4c0ba4dd58d28b569bd490840dd636c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-30T14:41:32Z","title_canon_sha256":"11e3bc3bdbf95b6dd268d70b5eeedb338c01fd6f7069a7c91d306d341b942e6a"},"schema_version":"1.0","source":{"id":"2507.22723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.22723","created_at":"2026-07-05T11:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"2507.22723v1","created_at":"2026-07-05T11:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.22723","created_at":"2026-07-05T11:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"GGBTASASFID5","created_at":"2026-07-05T11:45:47Z"},{"alias_kind":"pith_short_16","alias_value":"GGBTASASFID5MTBT","created_at":"2026-07-05T11:45:47Z"},{"alias_kind":"pith_short_8","alias_value":"GGBTASAS","created_at":"2026-07-05T11:45:47Z"}],"graph_snapshots":[{"event_id":"sha256:235d92aab4e8ab5d477ca6504110cabc977e218bfbe6ce205fce927a5dc3e8a3","target":"graph","created_at":"2026-07-05T11:45:47Z","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/2507.22723/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by inverse problems with a single passive measurement, we introduce and analyze a new class of inverse spectral problems on closed Riemannian manifolds. Specifically, we establish two general uniqueness results for the recovery of a potential in the stationary Schr\\\"odinger operator from partial spectral data, which consists of a possibly sparse subset of its eigenvalues and the restrictions of the corresponding eigenfunctions to a nonempty open subset of the manifold. Crucially, the eigenfunctions are not assumed to be orthogonal, and no information about global norming constants is","authors_text":"Ali Feizmohammadi, Katya Krupchyk","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-30T14:41:32Z","title":"Inverse spectral problems with sparse data and applications to passive imaging on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22723","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:b146672b11216f3a5329a59a50429ce0aab9fcd93cd3c2a0b1d628763f3987f1","target":"record","created_at":"2026-07-05T11:45:47Z","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":"42b677e679ee20ab8623c5ffb733f086f4c0ba4dd58d28b569bd490840dd636c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-30T14:41:32Z","title_canon_sha256":"11e3bc3bdbf95b6dd268d70b5eeedb338c01fd6f7069a7c91d306d341b942e6a"},"schema_version":"1.0","source":{"id":"2507.22723","kind":"arxiv","version":1}},"canonical_sha256":"31833048122a07d64c338d0501160b45f40b6b6764b8a2d086e9b841f328798e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31833048122a07d64c338d0501160b45f40b6b6764b8a2d086e9b841f328798e","first_computed_at":"2026-07-05T11:45:47.901063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:47.901063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r64A8HuGVFiXtkRu6xWWgWzoWTkqecSp2+ZdDoSusrG7QscsfXdeGCFZyHGUTmIBIF7lbH+JCCyfZp6+X4c0Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:47.901603Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.22723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b146672b11216f3a5329a59a50429ce0aab9fcd93cd3c2a0b1d628763f3987f1","sha256:235d92aab4e8ab5d477ca6504110cabc977e218bfbe6ce205fce927a5dc3e8a3"],"state_sha256":"83fdcf80eb0758bf8123e796c6df50e1db1571f1924d383cef1a5258582eabc5"}