{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VZDUVIPJBNJJTZPO7ZJ24PLJFA","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":"b37ce8014844618a7f8fb0b15addf60c429cc9fe308828efc859809dc3422a01","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-11T15:45:57Z","title_canon_sha256":"81f485b7fb9bf372f529611355581b22c82f2ed68a569d79b0d0c72b0c60dd31"},"schema_version":"1.0","source":{"id":"1101.2145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2145","created_at":"2026-05-18T02:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2145v2","created_at":"2026-05-18T02:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2145","created_at":"2026-05-18T02:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"VZDUVIPJBNJJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZDUVIPJBNJJTZPO","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZDUVIPJ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:d4b193aa9091a42f360c92081e8b8ab27a0e369f779f1281a49c9ab69b4cb4e9","target":"graph","created_at":"2026-05-18T02:03:42Z","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":"We study the scattering theory for charged Klein-Gordon equations: \\[\\{{array}{l} (\\p_{t}- \\i v(x))^{2}\\phi(t,x) \\epsilon^{2}(x, D_{x})\\phi(t,x)=0,[2mm] \\phi(0, x)= f_{0}, [2mm] \\i^{-1} \\p_{t}\\phi(0, x)= f_{1}, {array}. \\] where: \\[\\epsilon^{2}(x, D_{x})= \\sum_{1\\leq j, k\\leq n}(\\p_{x_{j}} \\i b_{j}(x))A^{jk}(x)(\\p_{x_{k}} \\i b_{k}(x))+ m^{2}(x),\\] describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: \\[ h[f, f]:= \\int_{\\rr^","authors_text":"Christian G\\'erard (LM-Orsay)","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-11T15:45:57Z","title":"Scattering theory for Klein-Gordon equations with non-positive energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2145","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":"sha256:7ecfb288c7f7c783ea71467f90b5629c397034f42cf0eb531a269639ad226331","target":"record","created_at":"2026-05-18T02:03:42Z","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":"b37ce8014844618a7f8fb0b15addf60c429cc9fe308828efc859809dc3422a01","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-11T15:45:57Z","title_canon_sha256":"81f485b7fb9bf372f529611355581b22c82f2ed68a569d79b0d0c72b0c60dd31"},"schema_version":"1.0","source":{"id":"1101.2145","kind":"arxiv","version":2}},"canonical_sha256":"ae474aa1e90b5299e5eefe53ae3d6928358ff1b9309b7fb47ed834b17fd5b905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae474aa1e90b5299e5eefe53ae3d6928358ff1b9309b7fb47ed834b17fd5b905","first_computed_at":"2026-05-18T02:03:42.976775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:42.976775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ubpX47f+e/VdZ0PAf0D4U7v9rF/jB5kxYhjDt+5XwJoZ0qqpz1lOYN89MnNqjfhTV8oOrQ2Uc7paEysJZvjVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:42.977146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ecfb288c7f7c783ea71467f90b5629c397034f42cf0eb531a269639ad226331","sha256:d4b193aa9091a42f360c92081e8b8ab27a0e369f779f1281a49c9ab69b4cb4e9"],"state_sha256":"8d9f5f2ebbdfdf885d3095ff5233d9add5565593b663fe07469b2317ca0963b5"}