{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:ABNSSKETP63X2ICDZZFXH5TZVE","short_pith_number":"pith:ABNSSKET","canonical_record":{"source":{"id":"math-ph/0012046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2000-12-28T10:45:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3f4ca10718230478e2c34ccbd1af5c66bae961db7d1a9eef8e5e218436961a7","abstract_canon_sha256":"7ea91fab2c039d18f7d0ba20227dcaff3eb2628c541230eb5d4725c06aa7ba1b"},"schema_version":"1.0"},"canonical_sha256":"005b2928937fb77d2043ce4b73f679a92c26f0c1a9c292ea261f655cde5cdc71","source":{"kind":"arxiv","id":"math-ph/0012046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0012046","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0012046v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0012046","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"ABNSSKETP63X","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ABNSSKETP63X2ICD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ABNSSKET","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:ABNSSKETP63X2ICDZZFXH5TZVE","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0012046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2000-12-28T10:45:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3f4ca10718230478e2c34ccbd1af5c66bae961db7d1a9eef8e5e218436961a7","abstract_canon_sha256":"7ea91fab2c039d18f7d0ba20227dcaff3eb2628c541230eb5d4725c06aa7ba1b"},"schema_version":"1.0"},"canonical_sha256":"005b2928937fb77d2043ce4b73f679a92c26f0c1a9c292ea261f655cde5cdc71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:32.108884Z","signature_b64":"rgn0SH0IRlmDEeiY4WtHuO3IK412ojhutB69+GgKw0SQi/1XEza/bj7Ynkdl1RtC3xdYzbiKb0Y/JyxlePnPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005b2928937fb77d2043ce4b73f679a92c26f0c1a9c292ea261f655cde5cdc71","last_reissued_at":"2026-05-18T01:05:32.108296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:32.108296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0012046","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7uxrrgMJpUaKq1unJTqqWOoVaRIfi6Lx9bPZZCLh8KOMvj1qkSMG2gVyCUeFA8+W6AXWcWgmkQFp964Wf6FjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:23:32.462203Z"},"content_sha256":"388babd0f277dab2b7e1c91c1932faa3931102ae34cbe3d54e6d079a69d0833c","schema_version":"1.0","event_id":"sha256:388babd0f277dab2b7e1c91c1932faa3931102ae34cbe3d54e6d079a69d0833c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:ABNSSKETP63X2ICDZZFXH5TZVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.V. Shapovalov(Tomsk State University), A.Yu. Trifonov(Tomsk Polytechnic University), Mathematics), V.V. Belov (Moscow Institute of Electronics","submitted_at":"2000-12-28T10:45:38Z","abstract_excerpt":"The general construction of quasi-classically concentrated solutions to the Hartree-type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter \\h (\\h\\to0), are constructed with a power accuracy of O(\\h^{N/2}), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for middle or centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of quasi-classically "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0012046","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyeOROt+joflWGc0TuqPJ3qrUZm/fZXUSnj1+fVPXDB9X5q5JveEy51oeWsZRlQz842sgMlHg9g/fiq11/tLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:23:32.462566Z"},"content_sha256":"73b5588bd757ed60b479a5fa17056ef9dfeb7d8cc43546fcbcf6b08ab0ff14f5","schema_version":"1.0","event_id":"sha256:73b5588bd757ed60b479a5fa17056ef9dfeb7d8cc43546fcbcf6b08ab0ff14f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABNSSKETP63X2ICDZZFXH5TZVE/bundle.json","state_url":"https://pith.science/pith/ABNSSKETP63X2ICDZZFXH5TZVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABNSSKETP63X2ICDZZFXH5TZVE/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":"2026-06-03T00:23:32Z","links":{"resolver":"https://pith.science/pith/ABNSSKETP63X2ICDZZFXH5TZVE","bundle":"https://pith.science/pith/ABNSSKETP63X2ICDZZFXH5TZVE/bundle.json","state":"https://pith.science/pith/ABNSSKETP63X2ICDZZFXH5TZVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABNSSKETP63X2ICDZZFXH5TZVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:ABNSSKETP63X2ICDZZFXH5TZVE","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":"7ea91fab2c039d18f7d0ba20227dcaff3eb2628c541230eb5d4725c06aa7ba1b","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2000-12-28T10:45:38Z","title_canon_sha256":"a3f4ca10718230478e2c34ccbd1af5c66bae961db7d1a9eef8e5e218436961a7"},"schema_version":"1.0","source":{"id":"math-ph/0012046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0012046","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0012046v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0012046","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"ABNSSKETP63X","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ABNSSKETP63X2ICD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ABNSSKET","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:73b5588bd757ed60b479a5fa17056ef9dfeb7d8cc43546fcbcf6b08ab0ff14f5","target":"graph","created_at":"2026-05-18T01:05:32Z","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":"The general construction of quasi-classically concentrated solutions to the Hartree-type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter \\h (\\h\\to0), are constructed with a power accuracy of O(\\h^{N/2}), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for middle or centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of quasi-classically ","authors_text":"A.V. Shapovalov(Tomsk State University), A.Yu. Trifonov(Tomsk Polytechnic University), Mathematics), V.V. Belov (Moscow Institute of Electronics","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2000-12-28T10:45:38Z","title":"The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0012046","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":"sha256:388babd0f277dab2b7e1c91c1932faa3931102ae34cbe3d54e6d079a69d0833c","target":"record","created_at":"2026-05-18T01:05:32Z","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":"7ea91fab2c039d18f7d0ba20227dcaff3eb2628c541230eb5d4725c06aa7ba1b","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2000-12-28T10:45:38Z","title_canon_sha256":"a3f4ca10718230478e2c34ccbd1af5c66bae961db7d1a9eef8e5e218436961a7"},"schema_version":"1.0","source":{"id":"math-ph/0012046","kind":"arxiv","version":1}},"canonical_sha256":"005b2928937fb77d2043ce4b73f679a92c26f0c1a9c292ea261f655cde5cdc71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"005b2928937fb77d2043ce4b73f679a92c26f0c1a9c292ea261f655cde5cdc71","first_computed_at":"2026-05-18T01:05:32.108296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:32.108296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgn0SH0IRlmDEeiY4WtHuO3IK412ojhutB69+GgKw0SQi/1XEza/bj7Ynkdl1RtC3xdYzbiKb0Y/JyxlePnPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:32.108884Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0012046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:388babd0f277dab2b7e1c91c1932faa3931102ae34cbe3d54e6d079a69d0833c","sha256:73b5588bd757ed60b479a5fa17056ef9dfeb7d8cc43546fcbcf6b08ab0ff14f5"],"state_sha256":"b29ecb811ee974ccdd7cbcee6d91b62a5fe81639aae97ce3e7f98b2abc8a3c8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ooUBVn3MEQIMsb84O5EcKs64AGsUrKmeDR1IgyJrd5CDaAZVKlBPruQR2al8Ugeer3+iLpy5KsB5Rc8J8z/kCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:23:32.464982Z","bundle_sha256":"87935141f915904eea2eb595348d86a7e5c6624cb56fed4a55f1237a9aaa0303"}}