{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VO2A5OBDTYFOJIV4PJXUVCXMIV","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":"86c518c7dc52b967d014bf9781fa7581e6b41f4422210b0e6cfd61f83f06b0d6","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-01-14T22:14:24Z","title_canon_sha256":"a70d7e07d89aaf4e7ef5fa0858856791132a3d23e30afccf42ccb18712544b89"},"schema_version":"1.0","source":{"id":"2601.09900","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.09900","created_at":"2026-06-09T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2601.09900v4","created_at":"2026-06-09T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.09900","created_at":"2026-06-09T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"VO2A5OBDTYFO","created_at":"2026-06-09T01:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"VO2A5OBDTYFOJIV4","created_at":"2026-06-09T01:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"VO2A5OBD","created_at":"2026-06-09T01:05:12Z"}],"graph_snapshots":[{"event_id":"sha256:bb41cd9ab296a36dea22cd450a02bddfbb846274541201dc5c24d739e11c261b","target":"graph","created_at":"2026-06-09T01:05:12Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We select one scheme and prove its second-order consistency and convergence. By modifying this scheme, we also obtain a numerical scheme with zero local truncation error for ODEs whose solution trajectories are ellipses."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The quasi-Fermat theorem and quasi-Mean Value Theorem hold for the newly defined specular differentiation operator and can be used to derive the truncation error bounds without additional restrictions on the solution."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Introduces specular differentiation to create second-order consistent numerical schemes for ODE IVPs, including a modified version with zero local truncation error on elliptical trajectories."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Specular differentiation defines nonlinear numerical schemes for first-order ODE initial value problems with proven second-order accuracy and exact integration along ellipses."}],"snapshot_sha256":"a07c47602e617c9bb686567b0c697c20b8cef0138136fea1affe26899b466ab8"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.09900/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary differential equations. Based on numerical simulations, we select one scheme and prove its second-order consistency and convergence. By modifying this scheme, we also obtain a numerical scheme with zero local truncation error for ODEs whose solution trajectories are ellipses.","authors_text":"Kiyuob Jung","cross_cats":["cs.NA"],"headline":"Specular differentiation defines nonlinear numerical schemes for first-order ODE initial value problems with proven second-order accuracy and exact integration along ellipses.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-01-14T22:14:24Z","title":"Nonlinear numerical schemes using specular differentiation for initial value problems of first-order ordinary differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.09900","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-16T13:48:00.327433Z","id":"d4c514f6-505c-478a-bf55-efeb92c0e203","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces specular differentiation to create second-order consistent numerical schemes for ODE IVPs, including a modified version with zero local truncation error on elliptical trajectories.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Specular differentiation defines nonlinear numerical schemes for first-order ODE initial value problems with proven second-order accuracy and exact integration along ellipses.","strongest_claim":"We select one scheme and prove its second-order consistency and convergence. By modifying this scheme, we also obtain a numerical scheme with zero local truncation error for ODEs whose solution trajectories are ellipses.","weakest_assumption":"The quasi-Fermat theorem and quasi-Mean Value Theorem hold for the newly defined specular differentiation operator and can be used to derive the truncation error bounds without additional restrictions on the solution."}},"verdict_id":"d4c514f6-505c-478a-bf55-efeb92c0e203"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:75e6d93aaad5443858dbaaa4a21574ddd60620f9256e0f9ba0f7c11a26f785f4","target":"record","created_at":"2026-06-09T01:05:12Z","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":"86c518c7dc52b967d014bf9781fa7581e6b41f4422210b0e6cfd61f83f06b0d6","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-01-14T22:14:24Z","title_canon_sha256":"a70d7e07d89aaf4e7ef5fa0858856791132a3d23e30afccf42ccb18712544b89"},"schema_version":"1.0","source":{"id":"2601.09900","kind":"arxiv","version":4}},"canonical_sha256":"abb40eb8239e0ae4a2bc7a6f4a8aec454c4974d3d55402e986657153697ed347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abb40eb8239e0ae4a2bc7a6f4a8aec454c4974d3d55402e986657153697ed347","first_computed_at":"2026-06-09T01:05:12.761287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:12.761287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b6g0/0Qc0M2vLnyLO0IIem0ybr0KTBEwKYp1BXUwNgBe2y63K/p7jjlpsBRv0hUdwDXwwr0tff1YcUTB3ok0Dw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:12.761780Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.09900","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75e6d93aaad5443858dbaaa4a21574ddd60620f9256e0f9ba0f7c11a26f785f4","sha256:bb41cd9ab296a36dea22cd450a02bddfbb846274541201dc5c24d739e11c261b"],"state_sha256":"0b5102d619847b8f57cc6f9878c7a3e4b1e8efab76a74cdd7043368bcb7f2db2"}