{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HOQ5Y5OS4K6WAQCKN3S5VPZZF6","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":"a612b3195ebc059bb90d50fb192e526846129213d660a96bc0753e840c8dded6","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-31T17:55:44Z","title_canon_sha256":"b5e1554211d55ae64711160ee3b2aa0667a8cc2a342cb96ca741da76c9dc9854"},"schema_version":"1.0","source":{"id":"1005.5712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5712","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5712v1","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5712","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_12","alias_value":"HOQ5Y5OS4K6W","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_16","alias_value":"HOQ5Y5OS4K6WAQCK","created_at":"2026-06-03T23:06:37Z"},{"alias_kind":"pith_short_8","alias_value":"HOQ5Y5OS","created_at":"2026-06-03T23:06:37Z"}],"graph_snapshots":[{"event_id":"sha256:0a499fc0eba6daca1ea8db95a0e42dab309ecde0ccef00801bd96859f9ecc8d3","target":"graph","created_at":"2026-06-03T23:06:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1005.5712/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study, we use a simple boundary value problem for a one-dimensional parabolic equation to discuss the selection of an approximation with respect to time. We consider the pure diffusion equation, the pure convective transport equation and combined convection-diffusion phenomena. Requirements for the unconditionally stable finite difference schemes are formulated tha","authors_text":"Petr N. Vabishchevich","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-31T17:55:44Z","title":"SM stability for time-dependent problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5712","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":"sha256:5d524a4ca60b6b5c9b0d300b7941039c022f8b163325f5d26264e619c2fbb379","target":"record","created_at":"2026-06-03T23:06:37Z","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":"a612b3195ebc059bb90d50fb192e526846129213d660a96bc0753e840c8dded6","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2010-05-31T17:55:44Z","title_canon_sha256":"b5e1554211d55ae64711160ee3b2aa0667a8cc2a342cb96ca741da76c9dc9854"},"schema_version":"1.0","source":{"id":"1005.5712","kind":"arxiv","version":1}},"canonical_sha256":"3ba1dc75d2e2bd60404a6ee5dabf392f813e0f8e360397b6732e30bd86362090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ba1dc75d2e2bd60404a6ee5dabf392f813e0f8e360397b6732e30bd86362090","first_computed_at":"2026-06-03T23:06:37.854259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:37.854259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGiaGMFpjqd83HtLnXJCtQ9kCTyMPyOy2dCPrsy/1NWaVEN2YX9BK48pvATX+oMLVnuIcFpzYTxWuQpyRsKiCw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:37.854689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d524a4ca60b6b5c9b0d300b7941039c022f8b163325f5d26264e619c2fbb379","sha256:0a499fc0eba6daca1ea8db95a0e42dab309ecde0ccef00801bd96859f9ecc8d3"],"state_sha256":"ae7db0655cf41fa6e456264f493c40d6fd4cb31c31e3730f319fffd5a7350efb"}