Pith Number

pith:WP342Q76

pith:2026:WP342Q76CWVFS6OBXIPTDKJTCP

not attested not anchored not stored refs resolved

A Degree-Two Hilbert--P\'olya Realisation by Causal Riemann-Surface Operators

Kejun Liu

J-self-adjoint analytic pencils on square-root Riemann surfaces recover the local Euler factors of an elliptic L-function at Langlands degree two.

arxiv:2605.17645 v1 · 2026-05-17 · math.NT · math-ph · math.MP · math.SP

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For the N=2 canonical case, the spectral curve is the elliptic curve E_0: y^2 = x^3 + 8x (LMFDB 256b2, conductor 256) and the local Euler factors of L(E_0,s) are recovered by an explicit off-shell basepoint in the resolvent. The basepoint is real because the Hasse-Weil bound supplies the needed inequality.

C2weakest assumption

The assumption that the fractional kernel being the Laplace transform of a causal response, together with the J-self-adjoint analytic pencil condition, forces the branch-point cover on which the RSCO pencil lives and permits recovery of the local Euler factors via the resolvent basepoint (with Hasse-Weil supplying reality).

C3one line summary

The paper gives a local Hilbert-Pólya realization for elliptic L-functions at degree two via causal Riemann-surface operators, recovering local Euler factors for the curve y² = x³ + 8x and extending to a family through quadratic matching.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] Symmetry , volume =

[2] Yakaboylu, Enderalp , title =. J. Phys. A: Math. Theor. , volume =

[3] Connes, Alain and Moscovici, Henri , title =. Proc. Natl. Acad. Sci. USA , volume =

[4] and Snaith, Nina C

[5] and Sarnak, Peter , title =

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:50.342705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3f7cd43fe15aa5979c1ba1f31a93313c9f66bf7e25e715901a3aa6b04188526

Aliases

arxiv: 2605.17645 · arxiv_version: 2605.17645v1 · doi: 10.48550/arxiv.2605.17645 · pith_short_12: WP342Q76CWVF · pith_short_16: WP342Q76CWVFS6OB · pith_short_8: WP342Q76

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WP342Q76CWVFS6OBXIPTDKJTCP \
  | 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: b3f7cd43fe15aa5979c1ba1f31a93313c9f66bf7e25e715901a3aa6b04188526

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bb45c017cd7b15f98781fac358c02b2c699ce4ef7c3df10fae4a5ae126ac3ad",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-17T20:46:30Z",
    "title_canon_sha256": "b89c37b10f27a2a61747aa2ffc22ae7d4a103b83598917784cba50f2701b9bb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17645",
    "kind": "arxiv",
    "version": 1
  }
}