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Mironov, Dafeng Zuo","submitted_at":"2013-05-27T16:10:36Z","abstract_excerpt":"The Halphen operator is a third-order operator of the form $$\n  L_3=\\partial_x^3-g(g+2)\\wp(x)\\partial_x-\\frac{1}{2}g(g+2)\\wp'(x), $$ where $g\\ne 2\\,\\mbox{mod(3)}$, the Weierstrass $\\wp$-function satisfies the equation $$\n  (\\wp'(x))^2=4\\wp^3(x)-g_2\\wp(x)-g_3. $$ In the equianharmonic case, i.e., $g_2=0$ the Halphen operator commutes with some ordinary differential operator $L_n$ of order $n\\ne 0\\,\\mbox{mod(3)}.$ In this paper we find the spectral curve of the pair $L_3,L_n$."},"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":"1305.6267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-27T16:10:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"da5642ae7892c3de2cbfd281e77fb89e84a108d001436d677fe218f7c379f589","abstract_canon_sha256":"39f9290958bdb984b1119343f0b44f262213bbaffae3435fa6072b5c4f50c5c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:36.024852Z","signature_b64":"WcuKAt8mPdzEH9xIWtwWpd5Lwgz1DqhMCVuT3ajkHeK6nzgw5Buij6Np36sOBRPo3gitYmV2LyoW2MHpwEZaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b510df5032d25d2e628ebc40afcd90b1933fa2e1cd189f40eca85c69b03b965","last_reissued_at":"2026-05-18T01:34:36.024038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:36.024038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Curve of the Halphen Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrey E. Mironov, Dafeng Zuo","submitted_at":"2013-05-27T16:10:36Z","abstract_excerpt":"The Halphen operator is a third-order operator of the form $$\n  L_3=\\partial_x^3-g(g+2)\\wp(x)\\partial_x-\\frac{1}{2}g(g+2)\\wp'(x), $$ where $g\\ne 2\\,\\mbox{mod(3)}$, the Weierstrass $\\wp$-function satisfies the equation $$\n  (\\wp'(x))^2=4\\wp^3(x)-g_2\\wp(x)-g_3. $$ In the equianharmonic case, i.e., $g_2=0$ the Halphen operator commutes with some ordinary differential operator $L_n$ of order $n\\ne 0\\,\\mbox{mod(3)}.$ In this paper we find the spectral curve of the pair $L_3,L_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6267","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.6267","created_at":"2026-05-18T01:34:36.024175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6267v2","created_at":"2026-05-18T01:34:36.024175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6267","created_at":"2026-05-18T01:34:36.024175+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNIQ35IDFUS5","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNIQ35IDFUS5FZRI","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNIQ35ID","created_at":"2026-05-18T12:27:46.883200+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/HNIQ35IDFUS5FZRI5PCAV7GZBM","json":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM.json","graph_json":"https://pith.science/api/pith-number/HNIQ35IDFUS5FZRI5PCAV7GZBM/graph.json","events_json":"https://pith.science/api/pith-number/HNIQ35IDFUS5FZRI5PCAV7GZBM/events.json","paper":"https://pith.science/paper/HNIQ35ID"},"agent_actions":{"view_html":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM","download_json":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM.json","view_paper":"https://pith.science/paper/HNIQ35ID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6267&json=true","fetch_graph":"https://pith.science/api/pith-number/HNIQ35IDFUS5FZRI5PCAV7GZBM/graph.json","fetch_events":"https://pith.science/api/pith-number/HNIQ35IDFUS5FZRI5PCAV7GZBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM/action/storage_attestation","attest_author":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM/action/author_attestation","sign_citation":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM/action/citation_signature","submit_replication":"https://pith.science/pith/HNIQ35IDFUS5FZRI5PCAV7GZBM/action/replication_record"}},"created_at":"2026-05-18T01:34:36.024175+00:00","updated_at":"2026-05-18T01:34:36.024175+00:00"}