Pith Number

pith:UNTCT4ZM

pith:2004:UNTCT4ZM6XI4G22YSJL44TV6CW

not attested not anchored not stored refs pending

Prime Number Races

Andrew Granville, Greg Martin

arxiv:math/0408319 v1 · 2004-08-24 · 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{UNTCT4ZM6XI4G22YSJL44TV6CW}

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	2026-07-04T14:39:00.992840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a36629f32cf5d1c36b589257ce4ebe15b6396b16482be6b93b57517886aeb1aa

Aliases

arxiv: math/0408319 · arxiv_version: math/0408319v1 · doi: 10.48550/arxiv.math/0408319 · pith_short_12: UNTCT4ZM6XI4 · pith_short_16: UNTCT4ZM6XI4G22Y · pith_short_8: UNTCT4ZM

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/UNTCT4ZM6XI4G22YSJL44TV6CW \
  | 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: a36629f32cf5d1c36b589257ce4ebe15b6396b16482be6b93b57517886aeb1aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d98eb6cdc7651e201cd01de03dd457a143de0992d502a44b3e0f0c0fc93328c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-08-24T00:03:21Z",
    "title_canon_sha256": "2d9d7fb1af7d2a878dbc76cdfa6b7e8c71f6897fd3d6813502a92b3c729c2f62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408319",
    "kind": "arxiv",
    "version": 1
  }
}