{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HNOMLOY3KPXW4JSTDYZAUSSBCR","short_pith_number":"pith:HNOMLOY3","canonical_record":{"source":{"id":"1302.5000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-02T16:00:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"451b104e087e20d6028170e702318a22969484bcf74c4bf3ec58b6048bb0d423","abstract_canon_sha256":"4a8a76f4bcae30ef384f37b70afda8719e63a92b666ebcc5e07cb72179c7e1ca"},"schema_version":"1.0"},"canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","source":{"kind":"arxiv","id":"1302.5000","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5000","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5000v1","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5000","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"HNOMLOY3KPXW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HNOMLOY3KPXW4JST","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HNOMLOY3","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HNOMLOY3KPXW4JSTDYZAUSSBCR","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-02T16:00:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"451b104e087e20d6028170e702318a22969484bcf74c4bf3ec58b6048bb0d423","abstract_canon_sha256":"4a8a76f4bcae30ef384f37b70afda8719e63a92b666ebcc5e07cb72179c7e1ca"},"schema_version":"1.0"},"canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:00.459789Z","signature_b64":"iMVRwALSHfOmqQuEuBBXMlPfpaqAgAfUuHwKl2ZHGabkTOyoEtMQBhxhmPVVF/F61oAqDo0RIpHKc13qySuHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","last_reissued_at":"2026-05-18T03:33:00.458936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:00.458936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5000","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":"2026-05-18T03:33:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXHhluV57QH5skr+PRODw6YifjUpPFXsSsPndi1dTpVzJRen7Vfs4IMwP53aO3nyPd15ByrWfBnEoZUI4E7KBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:43:35.023555Z"},"content_sha256":"963daf4e0beac1336176f009dc8b2ed1f4cfa56a6844de7c9c5a139c677b85e0","schema_version":"1.0","event_id":"sha256:963daf4e0beac1336176f009dc8b2ed1f4cfa56a6844de7c9c5a139c677b85e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HNOMLOY3KPXW4JSTDYZAUSSBCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse scattering with the data at fixed energy and fixed incident direction","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":"2013-02-02T16:00:30Z","abstract_excerpt":"Consider the Schr\\\"odinger operator $-\\nabla^2+q$ $ $q$, $q=q(x), x \\in \\mathbf{R}^3$. Let $A(\\beta,\\alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $\\alpha \\in S^2$ be the incident direction, $\\beta \\in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $\\mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $\\alpha=\\alpha_0$ is fixed. Then the scattering data are $A(\\beta)= A(\\beta,\\alpha_0, k_0)=A_q(\\beta)$ is a function on $S^2$. The following invers$ \\textit{IP: Given an arbitrary $f \\in L^2(S^2)$ and an arbitrary small number $$ $q \\in C_0^{\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5000","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":"2026-05-18T03:33:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RZmpp4i2eS+CTadFC8FzkJox4iF9bdMhKt5KqO0T/n1oO2mBADnMoJh18jozTGqfKXMnETmRtcRD6KaS9dMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:43:35.024211Z"},"content_sha256":"1b2b4d64aa4134eb200dc9bfb127b8e014d928edf53e447350e41ae0bffc5086","schema_version":"1.0","event_id":"sha256:1b2b4d64aa4134eb200dc9bfb127b8e014d928edf53e447350e41ae0bffc5086"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/bundle.json","state_url":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/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":"2026-05-25T17:43:35Z","links":{"resolver":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR","bundle":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/bundle.json","state":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HNOMLOY3KPXW4JSTDYZAUSSBCR","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":"4a8a76f4bcae30ef384f37b70afda8719e63a92b666ebcc5e07cb72179c7e1ca","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-02T16:00:30Z","title_canon_sha256":"451b104e087e20d6028170e702318a22969484bcf74c4bf3ec58b6048bb0d423"},"schema_version":"1.0","source":{"id":"1302.5000","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5000","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5000v1","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5000","created_at":"2026-05-18T03:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"HNOMLOY3KPXW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HNOMLOY3KPXW4JST","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HNOMLOY3","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:1b2b4d64aa4134eb200dc9bfb127b8e014d928edf53e447350e41ae0bffc5086","target":"graph","created_at":"2026-05-18T03:33:00Z","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":"Consider the Schr\\\"odinger operator $-\\nabla^2+q$ $ $q$, $q=q(x), x \\in \\mathbf{R}^3$. Let $A(\\beta,\\alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $\\alpha \\in S^2$ be the incident direction, $\\beta \\in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $\\mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $\\alpha=\\alpha_0$ is fixed. Then the scattering data are $A(\\beta)= A(\\beta,\\alpha_0, k_0)=A_q(\\beta)$ is a function on $S^2$. The following invers$ \\textit{IP: Given an arbitrary $f \\in L^2(S^2)$ and an arbitrary small number $$ $q \\in C_0^{\\inft","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":"2013-02-02T16:00:30Z","title":"Inverse scattering with the data at fixed energy and fixed incident direction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5000","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":"sha256:963daf4e0beac1336176f009dc8b2ed1f4cfa56a6844de7c9c5a139c677b85e0","target":"record","created_at":"2026-05-18T03:33:00Z","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":"4a8a76f4bcae30ef384f37b70afda8719e63a92b666ebcc5e07cb72179c7e1ca","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-02T16:00:30Z","title_canon_sha256":"451b104e087e20d6028170e702318a22969484bcf74c4bf3ec58b6048bb0d423"},"schema_version":"1.0","source":{"id":"1302.5000","kind":"arxiv","version":1}},"canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","first_computed_at":"2026-05-18T03:33:00.458936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:00.458936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iMVRwALSHfOmqQuEuBBXMlPfpaqAgAfUuHwKl2ZHGabkTOyoEtMQBhxhmPVVF/F61oAqDo0RIpHKc13qySuHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:00.459789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5000","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:963daf4e0beac1336176f009dc8b2ed1f4cfa56a6844de7c9c5a139c677b85e0","sha256:1b2b4d64aa4134eb200dc9bfb127b8e014d928edf53e447350e41ae0bffc5086"],"state_sha256":"312231ac3f056cf3c6e2740389ef6a7c5927adf7db037d132940dc55453cef7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPT0Vj8GlXC9a3WZXnntGoG07smkj/NexTJ5SyyIvHXKRtVpUjb97ZfU3cTqtz9m7HOvvn15RhHj+5Qrp+aRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:43:35.027827Z","bundle_sha256":"11bad37a7c620cf7010fbdd62bcc08f03aed9f8aaa756495871166c6159c09f9"}}