Pith Number

pith:VMTHLZPR

pith:2026:VMTHLZPROMXB63BGDXQ7WWP44R

not attested not anchored not stored refs pending

Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 4: contribution of non-elliptic parts

Yuhao Cheng

arxiv:2605.20719 v1 · 2026-05-20 · math.NT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMTHLZPROMXB63BGDXQ7WWP44R}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-05-21T01:04:50.638435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab2675e5f1732e1f6c261de1fb59fce451d73f00c616ab1419dae52223864075

Aliases

arxiv: 2605.20719 · arxiv_version: 2605.20719v1 · doi: 10.48550/arxiv.2605.20719 · pith_short_12: VMTHLZPROMXB · pith_short_16: VMTHLZPROMXB63BG · pith_short_8: VMTHLZPR

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/VMTHLZPROMXB63BGDXQ7WWP44R \
  | 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: ab2675e5f1732e1f6c261de1fb59fce451d73f00c616ab1419dae52223864075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4412df39a140ee59694d7f3dea141a8be7dff0d7f618f9a8172417daa80735bd",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-20T05:20:00Z",
    "title_canon_sha256": "30ee7d6c6acdaef56ae727aabc4de220d1970722b3b3e5bfa6698bbb58dc69bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20719",
    "kind": "arxiv",
    "version": 1
  }
}