Pith Number

pith:DCHKTWYR

pith:2025:DCHKTWYRCHODWWD3WWUCG3W24Q

not attested not anchored not stored refs pending

Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect

Zhao Xu

arxiv:2509.05968 v1 · 2025-09-07 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DCHKTWYRCHODWWD3WWUCG3W24Q}

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	2026-07-05T12:06:27.431732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

188ea9db1111dc3b587bb5a8236edae4095f235d2587f2d385a41ebb93963064

Aliases

arxiv: 2509.05968 · arxiv_version: 2509.05968v1 · doi: 10.48550/arxiv.2509.05968 · pith_short_12: DCHKTWYRCHOD · pith_short_16: DCHKTWYRCHODWWD3 · pith_short_8: DCHKTWYR

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/DCHKTWYRCHODWWD3WWUCG3W24Q \
  | 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: 188ea9db1111dc3b587bb5a8236edae4095f235d2587f2d385a41ebb93963064

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bba59c8a8eaf0fdc007f109a6d38d2cf78b377b862d88f5cf7ea94943981bbe",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-07T08:18:58Z",
    "title_canon_sha256": "e94158bae9b249257bfa25967d7065c34e0b612311c58b15f69ff467cb17304e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05968",
    "kind": "arxiv",
    "version": 1
  }
}