{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EMECQHKGYGBBLQINCVAFFSO6JD","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":"3c7ed18e28d0ef0c37fa9bf4ea854aac0cfd4b5d16f7c3d4621ddaa53f668585","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-11T14:57:57Z","title_canon_sha256":"6fccff9d4c53131ba9ab92e9db0391670417aebf321bc373ff5db36b88287eab"},"schema_version":"1.0","source":{"id":"2509.09518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09518","created_at":"2026-07-05T12:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09518v1","created_at":"2026-07-05T12:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09518","created_at":"2026-07-05T12:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"EMECQHKGYGBB","created_at":"2026-07-05T12:09:37Z"},{"alias_kind":"pith_short_16","alias_value":"EMECQHKGYGBBLQIN","created_at":"2026-07-05T12:09:37Z"},{"alias_kind":"pith_short_8","alias_value":"EMECQHKG","created_at":"2026-07-05T12:09:37Z"}],"graph_snapshots":[{"event_id":"sha256:452f6e085004cb5aa7337d60304a33ce5daf5083e64a9dd24ac6772e5b1426e3","target":"graph","created_at":"2026-07-05T12:09:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.09518/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the more technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with time-dependent coefficients, focusing on the Klein--Gordon equation. Two asymptotic regimes in phase space are relevant to the non-relativistic limit: one corresponding to what physicists call ``natural'' units, in which the PDE is approximable by the free Klein--Gordon equation, and a low-frequency regime in which the equation is approximable by the usual Schrodinger equation. Combining the analyses in the two regim","authors_text":"Andras Vasy, Andrew Hassell, Ethan Sussman, Qiuye Jia","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-11T14:57:57Z","title":"Microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09518","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":"sha256:12dd9678a82d169068a2c9f00c9357330d2c29ec2a54dd9b1844cb9a9fa075b9","target":"record","created_at":"2026-07-05T12:09:37Z","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":"3c7ed18e28d0ef0c37fa9bf4ea854aac0cfd4b5d16f7c3d4621ddaa53f668585","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-11T14:57:57Z","title_canon_sha256":"6fccff9d4c53131ba9ab92e9db0391670417aebf321bc373ff5db36b88287eab"},"schema_version":"1.0","source":{"id":"2509.09518","kind":"arxiv","version":1}},"canonical_sha256":"2308281d46c18215c10d154052c9de48db0e2e177e57dd027bb5ce426acc3d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2308281d46c18215c10d154052c9de48db0e2e177e57dd027bb5ce426acc3d5d","first_computed_at":"2026-07-05T12:09:37.395200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:37.395200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HX3WMJD6tdXZyq/FVBYAmpD7MRKWGvIu0A5jdh+RtfMlJ0vZALrjw5PHssTfRd2Mxh8swGPI6DqlkPX3Il8YDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:37.395749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.09518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12dd9678a82d169068a2c9f00c9357330d2c29ec2a54dd9b1844cb9a9fa075b9","sha256:452f6e085004cb5aa7337d60304a33ce5daf5083e64a9dd24ac6772e5b1426e3"],"state_sha256":"330ce90b024a9f5d64e1af01f97b4976c97f66591e34ccf61bdbfa7480d236c5"}