{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XL2OEXQJQUNRZB2KM2DIIB4JJ3","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":"a39d91fa3bea7259a12fc8dfffd6aba185f169235bc3c3e52bb1d0b485423e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-10T07:49:57Z","title_canon_sha256":"16459deea679e38a61aa190fffce41d3d3ec41bae198c8cdec60466d4f1f92bc"},"schema_version":"1.0","source":{"id":"1802.03539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03539","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03539v1","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03539","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"XL2OEXQJQUNR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XL2OEXQJQUNRZB2K","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XL2OEXQJ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:f590d00949c276a726fcbb5ca63d9ac77398d1fffe1edba7a9d9b8b2e8fe672f","target":"graph","created_at":"2026-05-18T00:23:51Z","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":"The modified Hunter--Saxton equation models the propagation of short capillary-gravity waves. As it involves a mixed derivative, its initial value problem on the periodic domain is much more complicated than the standard evolutionary equations. Although its local well-posedness has recently been proved, the behavior of its solution is yet to be investigated. In this paper, to develop a reliable numerical method for this problem, we derive a conservative finite difference scheme. Then, we rigorously prove not only its stability in the sense of the uniform norm but also its uniform convergence t","authors_text":"Shun Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-10T07:49:57Z","title":"Stability and convergence of a conservative finite difference scheme for the modified Hunter--Saxton equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03539","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:b20ff9d788a751c2389094152f93568e6af5156f0a9c2d7cfe25a6f6f8754110","target":"record","created_at":"2026-05-18T00:23:51Z","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":"a39d91fa3bea7259a12fc8dfffd6aba185f169235bc3c3e52bb1d0b485423e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-10T07:49:57Z","title_canon_sha256":"16459deea679e38a61aa190fffce41d3d3ec41bae198c8cdec60466d4f1f92bc"},"schema_version":"1.0","source":{"id":"1802.03539","kind":"arxiv","version":1}},"canonical_sha256":"baf4e25e09851b1c874a66868407894ec16578480c41d2f42e93018942800bfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf4e25e09851b1c874a66868407894ec16578480c41d2f42e93018942800bfb","first_computed_at":"2026-05-18T00:23:51.247962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:51.247962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prNfhZG9css/hDnKOcax3N2C/UA7LQ51kEzu2aSnJps9SZJvpBsJoZCUOUwJJkh16QhpEb7OxaZtYMpl/rZsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:51.248448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b20ff9d788a751c2389094152f93568e6af5156f0a9c2d7cfe25a6f6f8754110","sha256:f590d00949c276a726fcbb5ca63d9ac77398d1fffe1edba7a9d9b8b2e8fe672f"],"state_sha256":"473776f69d2d8da9a65e3a41b599bd64ad0a31d550f053314f06769856d29c2f"}