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We also show that if the grid ratio is $dt/dx=1/\\sqrt{n}$, then there is the discrete analog of the charge which is conserved.\n  We prove the existence and uniqueness of solutions to t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.3032","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-18T06:56:25Z","cross_cats_sorted":["math-ph","math.MP","math.NA"],"title_canon_sha256":"d8bd0552277634458269a361b7cd3da3955c7a484cc9d359ccc98e6d42f54886","abstract_canon_sha256":"7849889cc1a43f41db67d5f39ba282afdc85e589f16f118e1bf42a2390997192"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:47.158190Z","signature_b64":"sacOhfksk71VaQifVSNMkRAsInZSi4ghZO0LXTZDOm7ympgxpi0w4cBlvVkXVQEoJ9kkWqbxcUZgIpR0Wh6DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a44929485142a97336b389bf8451e05bba0d690b32141af19e62d1f60b9e0f8","last_reissued_at":"2026-05-18T02:05:47.157496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:47.157496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.AP","authors_text":"Alexander Komech, Andrew Comech","submitted_at":"2010-08-18T06:56:25Z","abstract_excerpt":"We consider the problem of discretization for the U(1)-invariant nonlinear wave equations in any dimension. 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