{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:RXQVEPEEJG5RGGKQYGY6AJIDCI","short_pith_number":"pith:RXQVEPEE","canonical_record":{"source":{"id":"math-ph/0010035","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2000-10-23T18:14:22Z","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"title_canon_sha256":"7166be83f7c521bc8ac38e1dab3ce6c16c89007b86b605017c8cf2c84b42e066","abstract_canon_sha256":"afb6501aaecdeb3717a482af395d5e690aabb5ae8c283fe0bfc98c8eb32484f5"},"schema_version":"1.0"},"canonical_sha256":"8de1523c8449bb131950c1b1e02503123f45411b5449ec2da79bf7af7dec8bf8","source":{"kind":"arxiv","id":"math-ph/0010035","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0010035","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0010035v2","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0010035","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"RXQVEPEEJG5R","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"RXQVEPEEJG5RGGKQ","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"RXQVEPEE","created_at":"2026-06-03T22:06:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:RXQVEPEEJG5RGGKQYGY6AJIDCI","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0010035","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2000-10-23T18:14:22Z","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"title_canon_sha256":"7166be83f7c521bc8ac38e1dab3ce6c16c89007b86b605017c8cf2c84b42e066","abstract_canon_sha256":"afb6501aaecdeb3717a482af395d5e690aabb5ae8c283fe0bfc98c8eb32484f5"},"schema_version":"1.0"},"canonical_sha256":"8de1523c8449bb131950c1b1e02503123f45411b5449ec2da79bf7af7dec8bf8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:14.132717Z","signature_b64":"bH+fOv0pp9aWCabNtK7o2aORpjKuphNfk5CzQL/q70lp1OTDX2YHRNkJ5YUbosO+3DVMQ6RcX1g3jvjUUpAZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8de1523c8449bb131950c1b1e02503123f45411b5449ec2da79bf7af7dec8bf8","last_reissued_at":"2026-06-03T22:06:14.132264Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:14.132264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0010035","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":"2026-06-03T22:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qb9hv5ZOa9Ryg/OW61pTy+i9AodqojFokxcSiEVBbKIMTVAmg8x+a37ZUhEjd3phWipt5P1BbvNrDxVekg3DCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:39:46.187202Z"},"content_sha256":"c1f1b35c2469cfd366cb2cbd1b678b6034c8f8410f78446fe3f9e83ff5d80729","schema_version":"1.0","event_id":"sha256:c1f1b35c2469cfd366cb2cbd1b678b6034c8f8410f78446fe3f9e83ff5d80729"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:RXQVEPEEJG5RGGKQYGY6AJIDCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem","license":"","headline":"","cross_cats":["cs.NA","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Alexander G. Ramm, Semion Gutman","submitted_at":"2000-10-23T18:14:22Z","abstract_excerpt":"A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this inverse problem to an identification of the positions of the small scatterers. These positions are found by a global minimization search. Such a search is implemented by a novel Hybrid Stochastic-Deterministic Minimization method. The method combines random tries and a deterministic minimization. The effectiveness of this approach is illustrated by numerical e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0010035","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0010035/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GIjEuuNEp0rvOz2LupM0D8P6SIADDt8A/aVIBCmmpoLPMC/psuCNOeMwY0uDl+6Sm/pbS43RkNFuvgwHmE9+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T17:39:46.187589Z"},"content_sha256":"5678757592a162a59ba52ba2af7744b8c2f227b5b5e11440d626c24e6eabe17f","schema_version":"1.0","event_id":"sha256:5678757592a162a59ba52ba2af7744b8c2f227b5b5e11440d626c24e6eabe17f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/bundle.json","state_url":"https://pith.science/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/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":"2026-06-27T17:39:46Z","links":{"resolver":"https://pith.science/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI","bundle":"https://pith.science/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/bundle.json","state":"https://pith.science/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXQVEPEEJG5RGGKQYGY6AJIDCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:RXQVEPEEJG5RGGKQYGY6AJIDCI","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":"afb6501aaecdeb3717a482af395d5e690aabb5ae8c283fe0bfc98c8eb32484f5","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2000-10-23T18:14:22Z","title_canon_sha256":"7166be83f7c521bc8ac38e1dab3ce6c16c89007b86b605017c8cf2c84b42e066"},"schema_version":"1.0","source":{"id":"math-ph/0010035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0010035","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0010035v2","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0010035","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"RXQVEPEEJG5R","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"RXQVEPEEJG5RGGKQ","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"RXQVEPEE","created_at":"2026-06-03T22:06:14Z"}],"graph_snapshots":[{"event_id":"sha256:5678757592a162a59ba52ba2af7744b8c2f227b5b5e11440d626c24e6eabe17f","target":"graph","created_at":"2026-06-03T22:06:14Z","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-ph/0010035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A method for the identification of small inhomogeneities from a surface data is presented in the framework of an inverse scattering problem for the Helmholtz equation. Using the assumptions of smallness of the scatterers one reduces this inverse problem to an identification of the positions of the small scatterers. These positions are found by a global minimization search. Such a search is implemented by a novel Hybrid Stochastic-Deterministic Minimization method. The method combines random tries and a deterministic minimization. The effectiveness of this approach is illustrated by numerical e","authors_text":"Alexander G. Ramm, Semion Gutman","cross_cats":["cs.NA","math.MP","math.NA"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2000-10-23T18:14:22Z","title":"Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0010035","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:c1f1b35c2469cfd366cb2cbd1b678b6034c8f8410f78446fe3f9e83ff5d80729","target":"record","created_at":"2026-06-03T22:06:14Z","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":"afb6501aaecdeb3717a482af395d5e690aabb5ae8c283fe0bfc98c8eb32484f5","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2000-10-23T18:14:22Z","title_canon_sha256":"7166be83f7c521bc8ac38e1dab3ce6c16c89007b86b605017c8cf2c84b42e066"},"schema_version":"1.0","source":{"id":"math-ph/0010035","kind":"arxiv","version":2}},"canonical_sha256":"8de1523c8449bb131950c1b1e02503123f45411b5449ec2da79bf7af7dec8bf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de1523c8449bb131950c1b1e02503123f45411b5449ec2da79bf7af7dec8bf8","first_computed_at":"2026-06-03T22:06:14.132264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:14.132264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bH+fOv0pp9aWCabNtK7o2aORpjKuphNfk5CzQL/q70lp1OTDX2YHRNkJ5YUbosO+3DVMQ6RcX1g3jvjUUpAZDg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:14.132717Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0010035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1f1b35c2469cfd366cb2cbd1b678b6034c8f8410f78446fe3f9e83ff5d80729","sha256:5678757592a162a59ba52ba2af7744b8c2f227b5b5e11440d626c24e6eabe17f"],"state_sha256":"c493a67e4f17b960a26a8955e6cbcbf2f9d27c3cce018fe7c29ec5990bbfc4df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RKmIwdnRinyK6k/EBWaWM9557MqlO76hwhGkHI1uhy5v1QfwGrYiZzIIQRwn6OS8SkLt8IVllWn1SrpPJVVHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T17:39:46.189520Z","bundle_sha256":"399529ab25936a01c2e3872f2fe275207745034b120cabd8a53686b18c109575"}}