{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NXKZDWQCLOUTLX7DSDSDXY5CMJ","short_pith_number":"pith:NXKZDWQC","canonical_record":{"source":{"id":"0912.4429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-12-22T15:50:19Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"dbaeb184859878b0625a8c39e9b3413f8e6f6013fd56af5f5602c92d5c7cc6cf","abstract_canon_sha256":"ab40fb97fe485ee1e577522fa352186502c6bfd483349e38a5c2b25fb7bfe3a1"},"schema_version":"1.0"},"canonical_sha256":"6dd591da025ba935dfe390e43be3a26259ea7acd0b9a4c83dde21811daca2424","source":{"kind":"arxiv","id":"0912.4429","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4429","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4429v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4429","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"NXKZDWQCLOUT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"NXKZDWQCLOUTLX7D","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"NXKZDWQC","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NXKZDWQCLOUTLX7DSDSDXY5CMJ","target":"record","payload":{"canonical_record":{"source":{"id":"0912.4429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-12-22T15:50:19Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"dbaeb184859878b0625a8c39e9b3413f8e6f6013fd56af5f5602c92d5c7cc6cf","abstract_canon_sha256":"ab40fb97fe485ee1e577522fa352186502c6bfd483349e38a5c2b25fb7bfe3a1"},"schema_version":"1.0"},"canonical_sha256":"6dd591da025ba935dfe390e43be3a26259ea7acd0b9a4c83dde21811daca2424","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.808479Z","signature_b64":"O5yfT/MLcx6TVFgt7VlLkofQnqoRbYaCspexBH9uSt6mJwMUrS4FZZX9MQSfwX2ticwN7V8vkSQp+dAMbitgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dd591da025ba935dfe390e43be3a26259ea7acd0b9a4c83dde21811daca2424","last_reissued_at":"2026-05-18T04:41:54.807795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.807795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.4429","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtOqidGFPotVZFMSj92376gHsPyEMVEe4EMYC8UmEMI9FNRWS6lU+fuKg3sST7iLI1S8iK8CbnmSCDAar/ckAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:53:01.599544Z"},"content_sha256":"2071affc35372395fb0a9e3a2ade34dbf42aa6bbcb5665830356f5a6243e7ed9","schema_version":"1.0","event_id":"sha256:2071affc35372395fb0a9e3a2ade34dbf42aa6bbcb5665830356f5a6243e7ed9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NXKZDWQCLOUTLX7DSDSDXY5CMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Approximations in a Path-Integral Description of Potential Scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"nucl-th","authors_text":"J. Carron, R. Rosenfelder","submitted_at":"2009-12-22T15:50:19Z","abstract_excerpt":"Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4429","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":""},"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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQW9BiknSbC5cyk8VlrojpGfye6bG9idJYdMv4kqEZfdbfkm3Su3KL1QqOG46/EkdGpsBfR3c0Q2Xx43VVMTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:53:01.599893Z"},"content_sha256":"78d8cbb43dda4290d4b44013e38407a8d1902b8b9d4728b4ae3c574f51a7f7c1","schema_version":"1.0","event_id":"sha256:78d8cbb43dda4290d4b44013e38407a8d1902b8b9d4728b4ae3c574f51a7f7c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/bundle.json","state_url":"https://pith.science/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/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":"2026-05-19T20:53:01Z","links":{"resolver":"https://pith.science/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ","bundle":"https://pith.science/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/bundle.json","state":"https://pith.science/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXKZDWQCLOUTLX7DSDSDXY5CMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NXKZDWQCLOUTLX7DSDSDXY5CMJ","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":"ab40fb97fe485ee1e577522fa352186502c6bfd483349e38a5c2b25fb7bfe3a1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-12-22T15:50:19Z","title_canon_sha256":"dbaeb184859878b0625a8c39e9b3413f8e6f6013fd56af5f5602c92d5c7cc6cf"},"schema_version":"1.0","source":{"id":"0912.4429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4429","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4429v2","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4429","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"NXKZDWQCLOUT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"NXKZDWQCLOUTLX7D","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"NXKZDWQC","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:78d8cbb43dda4290d4b44013e38407a8d1902b8b9d4728b4ae3c574f51a7f7c1","target":"graph","created_at":"2026-05-18T04:41:54Z","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":"Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to th","authors_text":"J. Carron, R. Rosenfelder","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-12-22T15:50:19Z","title":"Variational Approximations in a Path-Integral Description of Potential Scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4429","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":"sha256:2071affc35372395fb0a9e3a2ade34dbf42aa6bbcb5665830356f5a6243e7ed9","target":"record","created_at":"2026-05-18T04:41:54Z","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":"ab40fb97fe485ee1e577522fa352186502c6bfd483349e38a5c2b25fb7bfe3a1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-12-22T15:50:19Z","title_canon_sha256":"dbaeb184859878b0625a8c39e9b3413f8e6f6013fd56af5f5602c92d5c7cc6cf"},"schema_version":"1.0","source":{"id":"0912.4429","kind":"arxiv","version":2}},"canonical_sha256":"6dd591da025ba935dfe390e43be3a26259ea7acd0b9a4c83dde21811daca2424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd591da025ba935dfe390e43be3a26259ea7acd0b9a4c83dde21811daca2424","first_computed_at":"2026-05-18T04:41:54.807795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.807795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5yfT/MLcx6TVFgt7VlLkofQnqoRbYaCspexBH9uSt6mJwMUrS4FZZX9MQSfwX2ticwN7V8vkSQp+dAMbitgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.808479Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.4429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2071affc35372395fb0a9e3a2ade34dbf42aa6bbcb5665830356f5a6243e7ed9","sha256:78d8cbb43dda4290d4b44013e38407a8d1902b8b9d4728b4ae3c574f51a7f7c1"],"state_sha256":"236c680b73055ecad8607d9298346df2d5b197809921ea61984f09d9d82ab131"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+9ur9a1zoqsVPVPOI1qJt+a7fQ4n26sWZFY/1Nbni4XIgrefGlmLXm/yqeEB5fQsW9YubeG555K5wvj7YFrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T20:53:01.602329Z","bundle_sha256":"956fc6988866fcfa291909992a5e535cd863b3ec8f9670ec1d321c9a3f79d4d8"}}