Pith Number

pith:WO437GXU

pith:2014:WO437GXUSEC4P24WTPMUCPZO66

not attested not anchored not stored refs pending

Explicit Gross-Zagier and Waldspurger Formulae

Jie Shu, Li Cai, Ye Tian

arxiv:1408.1733 v2 · 2014-08-07 · 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{WO437GXUSEC4P24WTPMUCPZO66}

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	2026-05-18T01:22:21.904557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3b9bf9af49105c7eb969bd9413f2ef79bb97703139aee0d812627977bd08549

Aliases

arxiv: 1408.1733 · arxiv_version: 1408.1733v2 · doi: 10.48550/arxiv.1408.1733 · pith_short_12: WO437GXUSEC4 · pith_short_16: WO437GXUSEC4P24W · pith_short_8: WO437GXU

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/WO437GXUSEC4P24WTPMUCPZO66 \
  | 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: b3b9bf9af49105c7eb969bd9413f2ef79bb97703139aee0d812627977bd08549

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c6f521518762235cf5f7ea7ffafea2732021f083de40b729dd11efe60480876",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-08-07T23:30:31Z",
    "title_canon_sha256": "830763b67a30a15ab74ade4b8346c8500f580cc639a6a47c8721523b0bccb8fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1733",
    "kind": "arxiv",
    "version": 2
  }
}