{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LG2TOSSF4JV4HJ4UVK2ALQK4VG","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":"ff2edbe159670f765cde0d27695c0a4a788d8796f41d2d616199d7411c97c91b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-01T17:53:07Z","title_canon_sha256":"ec881d5ae84845cbe67843be517a96278fd3c9c86f789b0a31666aa8e496fa85"},"schema_version":"1.0","source":{"id":"2412.00910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.00910","created_at":"2026-07-05T09:42:50Z"},{"alias_kind":"arxiv_version","alias_value":"2412.00910v1","created_at":"2026-07-05T09:42:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.00910","created_at":"2026-07-05T09:42:50Z"},{"alias_kind":"pith_short_12","alias_value":"LG2TOSSF4JV4","created_at":"2026-07-05T09:42:50Z"},{"alias_kind":"pith_short_16","alias_value":"LG2TOSSF4JV4HJ4U","created_at":"2026-07-05T09:42:50Z"},{"alias_kind":"pith_short_8","alias_value":"LG2TOSSF","created_at":"2026-07-05T09:42:50Z"}],"graph_snapshots":[{"event_id":"sha256:e176e7f27df128177e6218dfeb1a4fd76bf2587bedf646de75d3c6c00f325d0a","target":"graph","created_at":"2026-07-05T09:42:50Z","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/2412.00910/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to derive a time evolution equation followed by the half-spins, in the moving frame provided by the Lax pair. We then rewrite this formula using a Toeplitz operator and $G$, the adjoint of the operator of multiplication by $x$ on the Hardy space $L_+^2(\\mathbb{R})$.","authors_text":"Gaspard Ohlmann","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-01T17:53:07Z","title":"Half-Wave Maps: Explicit Formulas for Rational Functions with Simple Poles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00910","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":"sha256:9fb06509f400aeeec75529602f6b9ccb3592a3a1e21f75ee78da5af39a4b5d95","target":"record","created_at":"2026-07-05T09:42:50Z","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":"ff2edbe159670f765cde0d27695c0a4a788d8796f41d2d616199d7411c97c91b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-01T17:53:07Z","title_canon_sha256":"ec881d5ae84845cbe67843be517a96278fd3c9c86f789b0a31666aa8e496fa85"},"schema_version":"1.0","source":{"id":"2412.00910","kind":"arxiv","version":1}},"canonical_sha256":"59b5374a45e26bc3a794aab405c15ca9b46838e34d6fb4f1fa523aded1f74f57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59b5374a45e26bc3a794aab405c15ca9b46838e34d6fb4f1fa523aded1f74f57","first_computed_at":"2026-07-05T09:42:50.312810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:50.312810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BULT/q4OSSTtjVeHOjEBqg5DRePtrGvrjRQA3coc/Q9HQ+IErtosF8Nh9DAg9zzjONS+g5xIQ6alnHc3/RE+DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:50.313311Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.00910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fb06509f400aeeec75529602f6b9ccb3592a3a1e21f75ee78da5af39a4b5d95","sha256:e176e7f27df128177e6218dfeb1a4fd76bf2587bedf646de75d3c6c00f325d0a"],"state_sha256":"610f8a1fb104b2e1f9b774d24cb7b9184fc348077d102c8c6f8b5851040f1c28"}