{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BWKBYBB66QM2SXRBUBKKUUFCST","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":"278f1272513395fe00b5069ae490db3f8ca6fa4f409e04284f5d4cc89cdf7c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-13T02:01:23Z","title_canon_sha256":"eb8a2b70ff133cf6a7e9c43232e0cf4528a7897bc4aa3294e457e01ca5ac1c0d"},"schema_version":"1.0","source":{"id":"1312.3688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3688","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3688v1","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3688","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"BWKBYBB66QM2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BWKBYBB66QM2SXRB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BWKBYBB6","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:b0de2fc1f8c19227b10501b916778d770b7b0306250bde83a90eda92408e9fb4","target":"graph","created_at":"2026-05-18T03:04:47Z","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":"One of important problems in mathematical physics concerns derivation of point dynamics from field equations. The most common approach to this problem is based on WKB method. Here we describe a different method based on the concept of trajectory of concentration. When we applied this method to nonlinear Klein-Gordon equation, we derived relativistic Newton's law and Einstein's formula for inertial mass. Here we apply the same approach to nonlinear Schrodinger equation and derive non-relativistic Newton's law for the trajectory of concentration.","authors_text":"Alexander Figotin, Anatoli Babin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-13T02:01:23Z","title":"Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3688","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":"sha256:2c3c5ee22c902ae425d535bb312339c7499f0656262468b96903918190781a20","target":"record","created_at":"2026-05-18T03:04:47Z","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":"278f1272513395fe00b5069ae490db3f8ca6fa4f409e04284f5d4cc89cdf7c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-13T02:01:23Z","title_canon_sha256":"eb8a2b70ff133cf6a7e9c43232e0cf4528a7897bc4aa3294e457e01ca5ac1c0d"},"schema_version":"1.0","source":{"id":"1312.3688","kind":"arxiv","version":1}},"canonical_sha256":"0d941c043ef419a95e21a054aa50a294e9b5fd977c3122608e461997469eab34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d941c043ef419a95e21a054aa50a294e9b5fd977c3122608e461997469eab34","first_computed_at":"2026-05-18T03:04:47.936682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:47.936682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3hvHNQg5R+qpGQRcBxBOMxLu4diZq9WhHZacJXE25o+9GVHUTWyKVJ2ftUTwjS+FURq25+fLCF2pzNFfPAINAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:47.937242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c3c5ee22c902ae425d535bb312339c7499f0656262468b96903918190781a20","sha256:b0de2fc1f8c19227b10501b916778d770b7b0306250bde83a90eda92408e9fb4"],"state_sha256":"a039edaedf99271968251d9f9eb01df04aeaa55176d904ec5319ad1130f7ef43"}