{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ISOTYAW2CBPVSXP3Z6HM265ABQ","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":"70edf73336f59ca38f1a27b4c1ed4fc186782f5269283495c612123aee70258f","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-08-16T16:26:40Z","title_canon_sha256":"31eb209fa18843f7c9465e342340cb7fd5b1fdcb2a197dc69d62198941cae9f2"},"schema_version":"1.0","source":{"id":"math/0408209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408209","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408209v1","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408209","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"ISOTYAW2CBPV","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"ISOTYAW2CBPVSXP3","created_at":"2026-06-03T22:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"ISOTYAW2","created_at":"2026-06-03T22:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:29643cb9b1165853a6e40b5d67af94171046c171c2fe4da24d9ce77423b9a4a3","target":"graph","created_at":"2026-06-03T22:06:15Z","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/math/0408209/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of theoretical and computational issues. The problem of finding small subsurface inclusions from surface scattering data is solved by the Hybrid Stochastic-Deterministic minimization algorithm. A similar approach is used to determine layers in a particle from the scattering data. The Inverse potential scattering problem for spherically symmetric potentials and fixed-en","authors_text":"Alexander G. Ramm, Semion Gutman","cross_cats":["cs.NA","math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2004-08-16T16:26:40Z","title":"Optimization methods in direct and inverse scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408209","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:d872facfa75afd18164b8568b9ece29a5d50969ef5bb2ab9d94fe4a7f1cb2548","target":"record","created_at":"2026-06-03T22:06:15Z","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":"70edf73336f59ca38f1a27b4c1ed4fc186782f5269283495c612123aee70258f","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"","primary_cat":"math.NA","submitted_at":"2004-08-16T16:26:40Z","title_canon_sha256":"31eb209fa18843f7c9465e342340cb7fd5b1fdcb2a197dc69d62198941cae9f2"},"schema_version":"1.0","source":{"id":"math/0408209","kind":"arxiv","version":1}},"canonical_sha256":"449d3c02da105f595dfbcf8ecd7ba00c25e5d2ce5e3b163675a531148390dd9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"449d3c02da105f595dfbcf8ecd7ba00c25e5d2ce5e3b163675a531148390dd9f","first_computed_at":"2026-06-03T22:06:15.558045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:15.558045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDvVRGUStnDQA7aGHsDC3e96Fc9PoL+z2pdZy0Gw+6mSRzYQFXcVY+Co0R5ijd4v5Ati0O0vQ9C1uZE6+V3bCA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:15.558504Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d872facfa75afd18164b8568b9ece29a5d50969ef5bb2ab9d94fe4a7f1cb2548","sha256:29643cb9b1165853a6e40b5d67af94171046c171c2fe4da24d9ce77423b9a4a3"],"state_sha256":"509816fdf58237c487663d52120f8d11f1745b5cb5736e172b38d77a1a696b01"}