Pith Number

pith:O2H3EFQH

pith:2012:O2H3EFQHD5EJDJA3PYW55PYMH5

not attested not anchored not stored refs pending

Arithmetic invariant theory

Benedict H. Gross, Manjul Bhargava

arxiv:1206.4774 v2 · 2012-06-21 · math.NT · math.AG · 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{O2H3EFQHD5EJDJA3PYW55PYMH5}

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	2026-05-18T03:49:21.664221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

768fb216071f4891a41b7e2ddebf0c3f452f9b0605e35b905308f7cb9e16392f

Aliases

arxiv: 1206.4774 · arxiv_version: 1206.4774v2 · doi: 10.48550/arxiv.1206.4774 · pith_short_12: O2H3EFQHD5EJ · pith_short_16: O2H3EFQHD5EJDJA3 · pith_short_8: O2H3EFQH

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/O2H3EFQHD5EJDJA3PYW55PYMH5 \
  | 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: 768fb216071f4891a41b7e2ddebf0c3f452f9b0605e35b905308f7cb9e16392f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b96386985807f7100c685221a52d2c0ff96814b6922ea220cacedcebe22a37e5",
    "cross_cats_sorted": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-21T04:53:06Z",
    "title_canon_sha256": "e8b7c983c1d1cbb2ab45e4b4fc3365ada1b6f69e83ac9062f8423b9c987b9404"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4774",
    "kind": "arxiv",
    "version": 2
  }
}