{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2LWGIR7KQVRQAJ4N3TT5FMMFLT","short_pith_number":"pith:2LWGIR7K","schema_version":"1.0","canonical_sha256":"d2ec6447ea856300278ddce7d2b1855cef2bd334399aee5e4792f5f21cc81c58","source":{"kind":"arxiv","id":"1701.03629","version":1},"attestation_state":"computed","paper":{"title":"Nondegeneracy of half-harmonic maps from $\\mathbb{R}$ into $\\mathbb{S}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. Wei, Y. Sire, Y. Zheng","submitted_at":"2017-01-13T11:18:43Z","abstract_excerpt":"We prove that the standard half-harmonic map $U:\\mathbb{R}\\to\\mathbb{S}^1$ defined by \\begin{equation*} x\\to \\begin{pmatrix}\n  \\frac{x^2-1}{x^2+1}\n  \\frac{-2x}{x^2+1} \\end{pmatrix} \\end{equation*} is nondegenerate in the sense that all bounded solutions of the linearized half-harmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation and rotation) of $U$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.03629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T11:18:43Z","cross_cats_sorted":[],"title_canon_sha256":"73e7845125d5982ab7ac47aba83ac376ded3d92425a4c5ff09de50d7376fdad0","abstract_canon_sha256":"fc565891dc6b4f8a4cf318b6d6a8306085037e034bd6cc7e8f87dc5f59517b51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:54.309619Z","signature_b64":"Qx+hrN+8eGlSSHe/ZJoCBR88JrFGpzw9v5EVoZBKu/AIj9UNwMHdFs+sIYxV5fXmaly/CSNd6oudeCsY11DdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2ec6447ea856300278ddce7d2b1855cef2bd334399aee5e4792f5f21cc81c58","last_reissued_at":"2026-05-18T00:52:54.309143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:54.309143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nondegeneracy of half-harmonic maps from $\\mathbb{R}$ into $\\mathbb{S}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. Wei, Y. Sire, Y. Zheng","submitted_at":"2017-01-13T11:18:43Z","abstract_excerpt":"We prove that the standard half-harmonic map $U:\\mathbb{R}\\to\\mathbb{S}^1$ defined by \\begin{equation*} x\\to \\begin{pmatrix}\n  \\frac{x^2-1}{x^2+1}\n  \\frac{-2x}{x^2+1} \\end{pmatrix} \\end{equation*} is nondegenerate in the sense that all bounded solutions of the linearized half-harmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation and rotation) of $U$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03629","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.03629","created_at":"2026-05-18T00:52:54.309213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.03629v1","created_at":"2026-05-18T00:52:54.309213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03629","created_at":"2026-05-18T00:52:54.309213+00:00"},{"alias_kind":"pith_short_12","alias_value":"2LWGIR7KQVRQ","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2LWGIR7KQVRQAJ4N","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2LWGIR7K","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT","json":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT.json","graph_json":"https://pith.science/api/pith-number/2LWGIR7KQVRQAJ4N3TT5FMMFLT/graph.json","events_json":"https://pith.science/api/pith-number/2LWGIR7KQVRQAJ4N3TT5FMMFLT/events.json","paper":"https://pith.science/paper/2LWGIR7K"},"agent_actions":{"view_html":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT","download_json":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT.json","view_paper":"https://pith.science/paper/2LWGIR7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.03629&json=true","fetch_graph":"https://pith.science/api/pith-number/2LWGIR7KQVRQAJ4N3TT5FMMFLT/graph.json","fetch_events":"https://pith.science/api/pith-number/2LWGIR7KQVRQAJ4N3TT5FMMFLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT/action/storage_attestation","attest_author":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT/action/author_attestation","sign_citation":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT/action/citation_signature","submit_replication":"https://pith.science/pith/2LWGIR7KQVRQAJ4N3TT5FMMFLT/action/replication_record"}},"created_at":"2026-05-18T00:52:54.309213+00:00","updated_at":"2026-05-18T00:52:54.309213+00:00"}