{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M7V5U77URHFGP5AIS3BNV6BMJT","short_pith_number":"pith:M7V5U77U","canonical_record":{"source":{"id":"1208.6410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"34a6a77078aa182298267dfd339a502cd9ff9a8d1b30a2f3ec9becd4f585d6cf","abstract_canon_sha256":"a6f8dbbdf4578cd1e7a0f69ed596e2780360467af60c6fecd83744563f73545f"},"schema_version":"1.0"},"canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","source":{"kind":"arxiv","id":"1208.6410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6410","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6410v1","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6410","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"M7V5U77URHFG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7V5U77URHFGP5AI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7V5U77U","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M7V5U77URHFGP5AIS3BNV6BMJT","target":"record","payload":{"canonical_record":{"source":{"id":"1208.6410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"34a6a77078aa182298267dfd339a502cd9ff9a8d1b30a2f3ec9becd4f585d6cf","abstract_canon_sha256":"a6f8dbbdf4578cd1e7a0f69ed596e2780360467af60c6fecd83744563f73545f"},"schema_version":"1.0"},"canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:33.227106Z","signature_b64":"1DxGZMfGUgFjoc6pCbmXMfUuiRvKJbwwcyIGTxL0LfWHG1M29hPrHheqXR6attIEx5IKxDXu+YnDIUdD68MnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","last_reissued_at":"2026-05-18T03:46:33.226072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:33.226072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.6410","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":"2026-05-18T03:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYV/u1LUERmoU+veM/vfxufioKdQEvHNy+czzNvXs9+RxJnuTn27heOasDz2npNO/rKpEx7JEWvGTN/9x69lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:37:28.754646Z"},"content_sha256":"c2351c3b697618e8446940af7dc4c6c44010374eb15d7455f92e913eed002ab5","schema_version":"1.0","event_id":"sha256:c2351c3b697618e8446940af7dc4c6c44010374eb15d7455f92e913eed002ab5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M7V5U77URHFGP5AIS3BNV6BMJT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Helge Holden, Nils Henrik Risebro, Ujjwal Koley","submitted_at":"2012-08-31T07:26:10Z","abstract_excerpt":"We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\\in H^3(\\R)$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is smaller, $u_0\\in L^2(\\R)$, then the scheme converges strongly in $L^2(0,T;L^2_{\\mathrm{loc}}(\\R))$ to a weak solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6410","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":"2026-05-18T03:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"77TAXbskCJJHI9TlVSH0Oc6mdHf5P4ZGDBpcWzUAJ29BChEjT4x0SQkBkPHt7Q45x0IGr2zX1YLr2K0Vmz0nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:37:28.755170Z"},"content_sha256":"706859fb0a9447efd0496a41965755e857e9d0b04521f0a9769e9c9f6eaffbc8","schema_version":"1.0","event_id":"sha256:706859fb0a9447efd0496a41965755e857e9d0b04521f0a9769e9c9f6eaffbc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/bundle.json","state_url":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7V5U77URHFGP5AIS3BNV6BMJT/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":"2026-05-27T01:37:28Z","links":{"resolver":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT","bundle":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/bundle.json","state":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7V5U77URHFGP5AIS3BNV6BMJT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M7V5U77URHFGP5AIS3BNV6BMJT","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":"a6f8dbbdf4578cd1e7a0f69ed596e2780360467af60c6fecd83744563f73545f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","title_canon_sha256":"34a6a77078aa182298267dfd339a502cd9ff9a8d1b30a2f3ec9becd4f585d6cf"},"schema_version":"1.0","source":{"id":"1208.6410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6410","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6410v1","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6410","created_at":"2026-05-18T03:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"M7V5U77URHFG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7V5U77URHFGP5AI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7V5U77U","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:706859fb0a9447efd0496a41965755e857e9d0b04521f0a9769e9c9f6eaffbc8","target":"graph","created_at":"2026-05-18T03:46:33Z","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 prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\\in H^3(\\R)$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is smaller, $u_0\\in L^2(\\R)$, then the scheme converges strongly in $L^2(0,T;L^2_{\\mathrm{loc}}(\\R))$ to a weak solution.","authors_text":"Helge Holden, Nils Henrik Risebro, Ujjwal Koley","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","title":"Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6410","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:c2351c3b697618e8446940af7dc4c6c44010374eb15d7455f92e913eed002ab5","target":"record","created_at":"2026-05-18T03:46:33Z","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":"a6f8dbbdf4578cd1e7a0f69ed596e2780360467af60c6fecd83744563f73545f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","title_canon_sha256":"34a6a77078aa182298267dfd339a502cd9ff9a8d1b30a2f3ec9becd4f585d6cf"},"schema_version":"1.0","source":{"id":"1208.6410","kind":"arxiv","version":1}},"canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","first_computed_at":"2026-05-18T03:46:33.226072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:33.226072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1DxGZMfGUgFjoc6pCbmXMfUuiRvKJbwwcyIGTxL0LfWHG1M29hPrHheqXR6attIEx5IKxDXu+YnDIUdD68MnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:33.227106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2351c3b697618e8446940af7dc4c6c44010374eb15d7455f92e913eed002ab5","sha256:706859fb0a9447efd0496a41965755e857e9d0b04521f0a9769e9c9f6eaffbc8"],"state_sha256":"cd5ebdfaba1131908fc6b976ab36d45c3337e1bff2902f55e257945d75f1f789"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXbjOR00oCJZ3Kl7YxZE6C5tN2/N2aniQiaAvgg/7PfrUYkZetG8x5sTeoSOnxgMQ66MeUNQ469RLMeZ0AwXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:37:28.757591Z","bundle_sha256":"b77f54d128b834a4ab9a97b6f43dbd028562477c31afa7a10aa04d8720c85215"}}