{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2MF5ZIOAQ3B5BKXSKP5JYBITOC","short_pith_number":"pith:2MF5ZIOA","canonical_record":{"source":{"id":"1707.05028","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T07:50:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"082a27b4e566cc637515dba8184f67e0e491ecb332bc5b6e828303193153a450","abstract_canon_sha256":"5f0bc5d4d350aad824733796af71baac766e2cf0f89a8dd6a6971046a27facc8"},"schema_version":"1.0"},"canonical_sha256":"d30bdca1c086c3d0aaf253fa9c051370a4ebb79cd7d8c4bf55b17d877f6af629","source":{"kind":"arxiv","id":"1707.05028","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05028","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05028v2","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05028","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"2MF5ZIOAQ3B5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2MF5ZIOAQ3B5BKXS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2MF5ZIOA","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2MF5ZIOAQ3B5BKXSKP5JYBITOC","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05028","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T07:50:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"082a27b4e566cc637515dba8184f67e0e491ecb332bc5b6e828303193153a450","abstract_canon_sha256":"5f0bc5d4d350aad824733796af71baac766e2cf0f89a8dd6a6971046a27facc8"},"schema_version":"1.0"},"canonical_sha256":"d30bdca1c086c3d0aaf253fa9c051370a4ebb79cd7d8c4bf55b17d877f6af629","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:35.061665Z","signature_b64":"5VrLkk61oieeKFmFIU8sge0F71d0nj/VeM4ThGEq5pQiB65grzA7UHvWc7+jOk0Ubm3mAxhwcXD1EaRg6f8zCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d30bdca1c086c3d0aaf253fa9c051370a4ebb79cd7d8c4bf55b17d877f6af629","last_reissued_at":"2026-05-18T00:23:35.061028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:35.061028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05028","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROpkcRs6zdaGNoL/yyWPCugar4pDvjlVprm5B3Uzei31I3EV+nW1zPKYIiVPu62PO46GFfMxFWHDqxfQolYJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T10:57:01.995574Z"},"content_sha256":"1850db301e71ba5d838a833feb2a621c62583e107eb4eb30e98fc99bee7db00a","schema_version":"1.0","event_id":"sha256:1850db301e71ba5d838a833feb2a621c62583e107eb4eb30e98fc99bee7db00a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2MF5ZIOAQ3B5BKXSKP5JYBITOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Lax Pair Structure for the Half-Wave Maps Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Patrick G\\'erard","submitted_at":"2017-07-17T07:50:13Z","abstract_excerpt":"We consider the half-wave maps equation $$ \\partial_t \\vec{S} = \\vec{S} \\wedge |\\nabla| \\vec{S}, $$ where $\\vec{S}= \\vec{S}(t,x)$ takes values on the two-dimensional unit sphere $\\mathbb{S}^2$ and $x \\in \\mathbb{R}$ (real line case) or $x \\in \\mathbb{T}$ (periodic case). This an energy-critical Hamiltonian evolution equation recently introduced in \\cite{LS,Zh}, which formally arises as an effective evolution equation in the classical and continuum limit of Haldane-Shastry quantum spin chains. We prove that the half-wave maps equation admits a Lax pair and we discuss some analytic consequences "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05028","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nC+HnLL7VK/jkwkrMadH5I5rEMxVt2Jghyv5/UrJ3/bm5y6UmnHupahqhMWr0yAdPTfDUpTYGF68BlB0R64tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T10:57:01.995952Z"},"content_sha256":"de9fc2c95674c5e3d320444d0b63353322fc567c2fc7266f147168e9655fbbda","schema_version":"1.0","event_id":"sha256:de9fc2c95674c5e3d320444d0b63353322fc567c2fc7266f147168e9655fbbda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/bundle.json","state_url":"https://pith.science/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T10:57:01Z","links":{"resolver":"https://pith.science/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC","bundle":"https://pith.science/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/bundle.json","state":"https://pith.science/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MF5ZIOAQ3B5BKXSKP5JYBITOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2MF5ZIOAQ3B5BKXSKP5JYBITOC","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":"5f0bc5d4d350aad824733796af71baac766e2cf0f89a8dd6a6971046a27facc8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T07:50:13Z","title_canon_sha256":"082a27b4e566cc637515dba8184f67e0e491ecb332bc5b6e828303193153a450"},"schema_version":"1.0","source":{"id":"1707.05028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05028","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05028v2","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05028","created_at":"2026-05-18T00:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"2MF5ZIOAQ3B5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2MF5ZIOAQ3B5BKXS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2MF5ZIOA","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:de9fc2c95674c5e3d320444d0b63353322fc567c2fc7266f147168e9655fbbda","target":"graph","created_at":"2026-05-18T00:23:35Z","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":"We consider the half-wave maps equation $$ \\partial_t \\vec{S} = \\vec{S} \\wedge |\\nabla| \\vec{S}, $$ where $\\vec{S}= \\vec{S}(t,x)$ takes values on the two-dimensional unit sphere $\\mathbb{S}^2$ and $x \\in \\mathbb{R}$ (real line case) or $x \\in \\mathbb{T}$ (periodic case). This an energy-critical Hamiltonian evolution equation recently introduced in \\cite{LS,Zh}, which formally arises as an effective evolution equation in the classical and continuum limit of Haldane-Shastry quantum spin chains. We prove that the half-wave maps equation admits a Lax pair and we discuss some analytic consequences ","authors_text":"Enno Lenzmann, Patrick G\\'erard","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T07:50:13Z","title":"A Lax Pair Structure for the Half-Wave Maps Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05028","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":"sha256:1850db301e71ba5d838a833feb2a621c62583e107eb4eb30e98fc99bee7db00a","target":"record","created_at":"2026-05-18T00:23:35Z","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":"5f0bc5d4d350aad824733796af71baac766e2cf0f89a8dd6a6971046a27facc8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T07:50:13Z","title_canon_sha256":"082a27b4e566cc637515dba8184f67e0e491ecb332bc5b6e828303193153a450"},"schema_version":"1.0","source":{"id":"1707.05028","kind":"arxiv","version":2}},"canonical_sha256":"d30bdca1c086c3d0aaf253fa9c051370a4ebb79cd7d8c4bf55b17d877f6af629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d30bdca1c086c3d0aaf253fa9c051370a4ebb79cd7d8c4bf55b17d877f6af629","first_computed_at":"2026-05-18T00:23:35.061028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:35.061028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VrLkk61oieeKFmFIU8sge0F71d0nj/VeM4ThGEq5pQiB65grzA7UHvWc7+jOk0Ubm3mAxhwcXD1EaRg6f8zCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:35.061665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1850db301e71ba5d838a833feb2a621c62583e107eb4eb30e98fc99bee7db00a","sha256:de9fc2c95674c5e3d320444d0b63353322fc567c2fc7266f147168e9655fbbda"],"state_sha256":"3ec0f1e16197e29292e388697304e0fcb526ef094b7b3f344730bb6bea2f5f4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ToaguHOJUbi7QiDZCxF7XyMwEjVgrd7nl9Hanut/65SNNQ5FSHt39aDrBgPTG3mkk5dkX1zNkpSElPfDrqY7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T10:57:01.998417Z","bundle_sha256":"3096206e3b43047a3e31f4d66ad0dff4b7ff6be52684f26b7bbfd081d3ece969"}}