Pith Number

pith:TJTUHFY3

pith:2011:TJTUHFY3FJYHRSLJF5AJ6N5A6O

not attested not anchored not stored refs pending

A Gross-Zagier formula for quaternion algebras over totally real fields

Eyal Z. Goren, Kristin E. Lauter

arxiv:1112.2009 v1 · 2011-12-09 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TJTUHFY3FJYHRSLJF5AJ6N5A6O}

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	2026-05-18T04:06:44.395520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a6743971b2a7078c9692f409f37a0f3aad4af614627394756de4c3047da11c4

Aliases

arxiv: 1112.2009 · arxiv_version: 1112.2009v1 · doi: 10.48550/arxiv.1112.2009 · pith_short_12: TJTUHFY3FJYH · pith_short_16: TJTUHFY3FJYHRSLJ · pith_short_8: TJTUHFY3

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/TJTUHFY3FJYHRSLJF5AJ6N5A6O \
  | 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: 9a6743971b2a7078c9692f409f37a0f3aad4af614627394756de4c3047da11c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e32d63b19977e9056bbae80732eae1fdd73ada3c76348521b3c0d4253f13ded",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-09T03:00:51Z",
    "title_canon_sha256": "f2345a2fd90cf80688e9408d54fd81748bc26d96f258383b81ec4d9893d5e033"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2009",
    "kind": "arxiv",
    "version": 1
  }
}