{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NBK3ECXVR4TGGHTEX5KRSTM7XS","short_pith_number":"pith:NBK3ECXV","schema_version":"1.0","canonical_sha256":"6855b20af58f26631e64bf55194d9fbcb47de1337e496f744986f1f9d390f393","source":{"kind":"arxiv","id":"2607.26705","version":1},"attestation_state":"computed","paper":{"title":"Dynamical phase retrieval for Schr{\\\"o}dinger evolution on finite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.CA","authors_text":"Azita Mayeli (CUNY), Philippe Jaming (IMB)","submitted_at":"2026-07-29T09:51:24Z","abstract_excerpt":"We study dynamical phase retrieval for Schr\\''odinger evolutions on finite connected graphs. Let \\[ H\\_Q=\\Delta\\_G+Q \\] be a graph Schr\\''odinger operator with a real diagonal potential. We investigate when phaseless data obtained from the associated Schr\\''odinger evolution \\[ |e^{-itH\\_Q}u\\_0(j)|, \\qquad 0\\leq t\\leq T,\\ j\\in V, \\] determines the initial state $u\\_0\\in\\C^V$ up to a global phase. We give a uniqueness criterion in terms of the eigenvalues and eigenvectors of $H\\_Q$. The assumptions are a $B\\_2$ condition on the spectrum, meaning that the sums $\\lambda\\_j+\\lambda\\_k$ determine t"},"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":"2607.26705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-29T09:51:24Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"5593ee944636972433458c67257bc8ccb453cdc5dbb975d43cff86e6e037d3a4","abstract_canon_sha256":"cd1270a028a199f18e56bb8bc12fe41f093bf74277bd4bbf094836e33f897ad0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6855b20af58f26631e64bf55194d9fbcb47de1337e496f744986f1f9d390f393","last_reissued_at":"2026-07-30T01:21:59.146725Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:21:59.146725Z"},"graph_snapshot":{"paper":{"title":"Dynamical phase retrieval for Schr{\\\"o}dinger evolution on finite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.CA","authors_text":"Azita Mayeli (CUNY), Philippe Jaming (IMB)","submitted_at":"2026-07-29T09:51:24Z","abstract_excerpt":"We study dynamical phase retrieval for Schr\\''odinger evolutions on finite connected graphs. Let \\[ H\\_Q=\\Delta\\_G+Q \\] be a graph Schr\\''odinger operator with a real diagonal potential. We investigate when phaseless data obtained from the associated Schr\\''odinger evolution \\[ |e^{-itH\\_Q}u\\_0(j)|, \\qquad 0\\leq t\\leq T,\\ j\\in V, \\] determines the initial state $u\\_0\\in\\C^V$ up to a global phase. We give a uniqueness criterion in terms of the eigenvalues and eigenvectors of $H\\_Q$. The assumptions are a $B\\_2$ condition on the spectrum, meaning that the sums $\\lambda\\_j+\\lambda\\_k$ determine t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26705","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/2607.26705/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.26705","created_at":"2026-07-30T01:21:59.151851+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.26705v1","created_at":"2026-07-30T01:21:59.151851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26705","created_at":"2026-07-30T01:21:59.151851+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBK3ECXVR4TG","created_at":"2026-07-30T01:21:59.151851+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBK3ECXVR4TGGHTE","created_at":"2026-07-30T01:21:59.151851+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBK3ECXV","created_at":"2026-07-30T01:21:59.151851+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/NBK3ECXVR4TGGHTEX5KRSTM7XS","json":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS.json","graph_json":"https://pith.science/api/pith-number/NBK3ECXVR4TGGHTEX5KRSTM7XS/graph.json","events_json":"https://pith.science/api/pith-number/NBK3ECXVR4TGGHTEX5KRSTM7XS/events.json","paper":"https://pith.science/paper/NBK3ECXV"},"agent_actions":{"view_html":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS","download_json":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS.json","view_paper":"https://pith.science/paper/NBK3ECXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.26705&json=true","fetch_graph":"https://pith.science/api/pith-number/NBK3ECXVR4TGGHTEX5KRSTM7XS/graph.json","fetch_events":"https://pith.science/api/pith-number/NBK3ECXVR4TGGHTEX5KRSTM7XS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS/action/storage_attestation","attest_author":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS/action/author_attestation","sign_citation":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS/action/citation_signature","submit_replication":"https://pith.science/pith/NBK3ECXVR4TGGHTEX5KRSTM7XS/action/replication_record"}},"created_at":"2026-07-30T01:21:59.151851+00:00","updated_at":"2026-07-30T01:21:59.151851+00:00"}