Pith Number

pith:3JAUXWFG

pith:2026:3JAUXWFGDPD6YXVVO6QYADBTG3

not attested not anchored not stored refs pending

A theory of generalized Lam\'e curves

Chin-Lung Wang, Po-Sheng Wu, You-Cheng Chou

Generalized Lamé curves parametrize quasi-periodic solutions to elliptic equations with multiple poles and prove the Treibich conjecture for up to four symmetric pairs.

arxiv:2604.21880 v2 · 2026-04-23 · math.AG · math.CA

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Claims

C1strongest claim

We prove the Treibich conjecture stated for r=2 extra symmetric pairs, as well as its generalizations for r ≤ 4. We construct the generalized Lamé curve Y_n(p;τ) which lies in an affine bundle over Sym^n E and parametrizes generalized Hermite-Halphen ansatz solutions, and we prove that the log-free curve V_n(p;τ) is a reduced curve.

C2weakest assumption

The restriction to the locus admitting solutions with quasi-periodic properties is sufficient to construct the generalized Lamé curve and to allow continuous deformation to the classical Lamé equation; if this locus is empty or the ansatz misses essential solutions for general pole configurations, the parametrization and deformation claims fail.

C3one line summary

Generalized Lamé curves are built to parametrize quasi-periodic solutions of Lamé equations with multiple singularities on elliptic curves, together with a proof of the Treibich conjecture for up to four extra symmetric pairs.

Receipt and verification

First computed	2026-06-03T01:05:50.588832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da414bd8a61bc7ec5eb577a1800c3336efe828885356ed29ba19284f6ecdec70

Aliases

arxiv: 2604.21880 · arxiv_version: 2604.21880v2 · doi: 10.48550/arxiv.2604.21880 · pith_short_12: 3JAUXWFGDPD6 · pith_short_16: 3JAUXWFGDPD6YXVV · pith_short_8: 3JAUXWFG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3JAUXWFGDPD6YXVVO6QYADBTG3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: da414bd8a61bc7ec5eb577a1800c3336efe828885356ed29ba19284f6ecdec70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f57175116f7940738aa5d824329e7122cf475bea7a848245430ccd86c0290a2b",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-23T17:23:20Z",
    "title_canon_sha256": "9e86185d2a8b36ba59dd9729fa8d38ca7088cbf7494d755f408e05f9c85ce264"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.21880",
    "kind": "arxiv",
    "version": 2
  }
}