{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:624OPEVXX3HASTUMZQWJF54GJJ","short_pith_number":"pith:624OPEVX","canonical_record":{"source":{"id":"0910.5731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-29T20:20:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"138aa272d85bb73d009afd87ed2879eb838115fb977a262644dd402fe7422676","abstract_canon_sha256":"72c17c88ad066838b3e9fb889520a37d704a1f073cfea517ee084d96f890c7c6"},"schema_version":"1.0"},"canonical_sha256":"f6b8e792b7bece094e8ccc2c92f7864a7d2e34fc09652e7b75067404a600b868","source":{"kind":"arxiv","id":"0910.5731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5731","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5731v1","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5731","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"pith_short_12","alias_value":"624OPEVXX3HA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"624OPEVXX3HASTUM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"624OPEVX","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:624OPEVXX3HASTUMZQWJF54GJJ","target":"record","payload":{"canonical_record":{"source":{"id":"0910.5731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-29T20:20:51Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"138aa272d85bb73d009afd87ed2879eb838115fb977a262644dd402fe7422676","abstract_canon_sha256":"72c17c88ad066838b3e9fb889520a37d704a1f073cfea517ee084d96f890c7c6"},"schema_version":"1.0"},"canonical_sha256":"f6b8e792b7bece094e8ccc2c92f7864a7d2e34fc09652e7b75067404a600b868","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:01.597867Z","signature_b64":"ynBUU1cLNxcEQBONgbxGm2fsewwkg6tsqxWH60DR0FCdATyVlAhxRwiC+y60gkkhoYLQWR98G1qCoex4fdGxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b8e792b7bece094e8ccc2c92f7864a7d2e34fc09652e7b75067404a600b868","last_reissued_at":"2026-05-18T02:11:01.596900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:01.596900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.5731","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:11:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZEzOL8MUzsUUw9GGDjN2LTG7cZHfNeoBJPQ1brkxcEYK+1iCmonIv5RXUXOVmiDXwP7AcXDpJSW5HpaqMcjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:59:40.249984Z"},"content_sha256":"40f9a4445b76403341663d04329e5f6a7decb728806ddd3737d4767def0d37dd","schema_version":"1.0","event_id":"sha256:40f9a4445b76403341663d04329e5f6a7decb728806ddd3737d4767def0d37dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:624OPEVXX3HASTUMZQWJF54GJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness theorem for inverse scattering problem with non-overdetermined data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.G. Ramm","submitted_at":"2009-10-29T20:20:51Z","abstract_excerpt":"Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\\in H^\\ell_0(B_a)$, $B_a:=\\{x: |x|\\leq a, x\\in R^3$ . It is proved that the scattering data $A(-\\beta,\\beta,k)$ $\\forall \\beta\\in S^2$, $\\forall k>0$ determine $q$ uniquely. here $A(\\beta,\\alpha,k)$ is the scattering amplitude, corresponding to the potential $q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5731","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":""},"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":"2026-05-18T02:11:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"br2lEy483ElPeykVr1BOh2Ms7Mk3456WSLlnyJhK6zd3Smp/fw9SfrLL4cBISzAWZ7Ti3XjxLhrSV3ATy1DhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:59:40.250353Z"},"content_sha256":"2e063fdd26fd585603643c6e22c8630eb174a30154a8b83aeb561b4bac4799df","schema_version":"1.0","event_id":"sha256:2e063fdd26fd585603643c6e22c8630eb174a30154a8b83aeb561b4bac4799df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/624OPEVXX3HASTUMZQWJF54GJJ/bundle.json","state_url":"https://pith.science/pith/624OPEVXX3HASTUMZQWJF54GJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/624OPEVXX3HASTUMZQWJF54GJJ/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":"2026-06-26T01:59:40Z","links":{"resolver":"https://pith.science/pith/624OPEVXX3HASTUMZQWJF54GJJ","bundle":"https://pith.science/pith/624OPEVXX3HASTUMZQWJF54GJJ/bundle.json","state":"https://pith.science/pith/624OPEVXX3HASTUMZQWJF54GJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/624OPEVXX3HASTUMZQWJF54GJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:624OPEVXX3HASTUMZQWJF54GJJ","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":"72c17c88ad066838b3e9fb889520a37d704a1f073cfea517ee084d96f890c7c6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-29T20:20:51Z","title_canon_sha256":"138aa272d85bb73d009afd87ed2879eb838115fb977a262644dd402fe7422676"},"schema_version":"1.0","source":{"id":"0910.5731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5731","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5731v1","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5731","created_at":"2026-05-18T02:11:01Z"},{"alias_kind":"pith_short_12","alias_value":"624OPEVXX3HA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"624OPEVXX3HASTUM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"624OPEVX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:2e063fdd26fd585603643c6e22c8630eb174a30154a8b83aeb561b4bac4799df","target":"graph","created_at":"2026-05-18T02:11:01Z","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":"Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\\in H^\\ell_0(B_a)$, $B_a:=\\{x: |x|\\leq a, x\\in R^3$ . It is proved that the scattering data $A(-\\beta,\\beta,k)$ $\\forall \\beta\\in S^2$, $\\forall k>0$ determine $q$ uniquely. here $A(\\beta,\\alpha,k)$ is the scattering amplitude, corresponding to the potential $q$.","authors_text":"A.G. Ramm","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-29T20:20:51Z","title":"Uniqueness theorem for inverse scattering problem with non-overdetermined data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5731","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":"sha256:40f9a4445b76403341663d04329e5f6a7decb728806ddd3737d4767def0d37dd","target":"record","created_at":"2026-05-18T02:11:01Z","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":"72c17c88ad066838b3e9fb889520a37d704a1f073cfea517ee084d96f890c7c6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-29T20:20:51Z","title_canon_sha256":"138aa272d85bb73d009afd87ed2879eb838115fb977a262644dd402fe7422676"},"schema_version":"1.0","source":{"id":"0910.5731","kind":"arxiv","version":1}},"canonical_sha256":"f6b8e792b7bece094e8ccc2c92f7864a7d2e34fc09652e7b75067404a600b868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b8e792b7bece094e8ccc2c92f7864a7d2e34fc09652e7b75067404a600b868","first_computed_at":"2026-05-18T02:11:01.596900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:01.596900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynBUU1cLNxcEQBONgbxGm2fsewwkg6tsqxWH60DR0FCdATyVlAhxRwiC+y60gkkhoYLQWR98G1qCoex4fdGxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:01.597867Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40f9a4445b76403341663d04329e5f6a7decb728806ddd3737d4767def0d37dd","sha256:2e063fdd26fd585603643c6e22c8630eb174a30154a8b83aeb561b4bac4799df"],"state_sha256":"0250a564e729fd1e8135010774844c7fd21f0027d2421a9dcd6463311104f84f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVtLq9sh+2cPQUlX6AC6Cm/nNlQNa60Nq03ZcyBhtiKEuh9Z+vSuNLkSkrvKDzpUANZ1iD9IGMUfBXpi2pAyDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:59:40.252293Z","bundle_sha256":"0853ceae3b64534f3416a09d045ba6b1b19abccf2a2488c0345b065bc84d2276"}}