{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BTPXTPH3QTUKXSFN5ALDCOTFD2","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":"7b6e34cd2833f840436833e8cbcdfdc3f2bdc86b133ae9c408192931e0cee2f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-12T07:29:26Z","title_canon_sha256":"21fc83be904b7b5f564c0a08a7321491cfcaa0e7b433d8bbd0d564554ada922f"},"schema_version":"1.0","source":{"id":"1704.03645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03645","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03645v2","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03645","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"BTPXTPH3QTUK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BTPXTPH3QTUKXSFN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BTPXTPH3","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:7bcb71ae7796352a33c2bb3042f1a805428a6d75b85db87c6234116271054089","target":"graph","created_at":"2026-05-18T00:28:25Z","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":"Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper, we aim at the unified framework of numerical methods for such PDEs. However, due to the presence of the mixed derivative, we cannot discuss numerical methods without some appropriate reformulation, which is mathematically challenging itself. Therefore, we first propose a novel procedure for the reformulation of target PDEs into a standard form of evolutiona","authors_text":"Shun Sato, Takayasu Matsuo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-12T07:29:26Z","title":"On Spatial Discretization of Evolutionary Differential Equations on the Periodic Domain with a Mixed Derivative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03645","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":"sha256:73f94ccc818d5694a9c6b9c35836a2f763b95a070444367b0716e635e3c4407c","target":"record","created_at":"2026-05-18T00:28:25Z","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":"7b6e34cd2833f840436833e8cbcdfdc3f2bdc86b133ae9c408192931e0cee2f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-12T07:29:26Z","title_canon_sha256":"21fc83be904b7b5f564c0a08a7321491cfcaa0e7b433d8bbd0d564554ada922f"},"schema_version":"1.0","source":{"id":"1704.03645","kind":"arxiv","version":2}},"canonical_sha256":"0cdf79bcfb84e8abc8ade816313a651ea43ceb9bdd1cfbd33b586181c3106541","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cdf79bcfb84e8abc8ade816313a651ea43ceb9bdd1cfbd33b586181c3106541","first_computed_at":"2026-05-18T00:28:25.517857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:25.517857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ZHR/J/RLs8faXYThMxhEy1YMnMp76nwqT5OJrN1Zt1B1nLJC+SbWWuSKUKoykp2s5Wb1NJTzQvr06VpM3t8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:25.518380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73f94ccc818d5694a9c6b9c35836a2f763b95a070444367b0716e635e3c4407c","sha256:7bcb71ae7796352a33c2bb3042f1a805428a6d75b85db87c6234116271054089"],"state_sha256":"ececb5ab3fc601ecf4d1dd30ac56a3cc2db5666ec5500cd70194441963dc5975"}