Pith Number

pith:7DUU7WVX

pith:2012:7DUU7WVX4YDXBHJJHDIK4XPDMM

not attested not anchored not stored refs pending

Sato-Tate theorem for families and low-lying zeros of automorphic $L$-functions

Nicolas Templier, Sug Woo Shin

arxiv:1208.1945 v3 · 2012-08-09 · math.NT · math.LO · 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{7DUU7WVX4YDXBHJJHDIK4XPDMM}

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	2026-05-18T02:35:52.665182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8e94fdab7e607709d2938d0ae5de36324f4fc6f277d963a803942ed2b9fc438

Aliases

arxiv: 1208.1945 · arxiv_version: 1208.1945v3 · doi: 10.48550/arxiv.1208.1945 · pith_short_12: 7DUU7WVX4YDX · pith_short_16: 7DUU7WVX4YDXBHJJ · pith_short_8: 7DUU7WVX

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/7DUU7WVX4YDXBHJJHDIK4XPDMM \
  | 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: f8e94fdab7e607709d2938d0ae5de36324f4fc6f277d963a803942ed2b9fc438

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caeabd99c8770c1486c934612d920dc2e06ac1b1156dd97c3145b313f8768de9",
    "cross_cats_sorted": [
      "math.LO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-09T15:19:07Z",
    "title_canon_sha256": "f5e2646ab6327c30955302fb42c3b75dc25111aedf0ed0849e14f1d367732993"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1945",
    "kind": "arxiv",
    "version": 3
  }
}