Pith Number

pith:2EXKUG2Y

pith:2015:2EXKUG2Y6BNJYL7YYT3X47XRDH

not attested not anchored not stored refs pending

What is the probability that a random integral quadratic form in $n$ variables has an integral zero?

J. E. Cremona, J. P. Keating, M. Bhargava, N. G. Jones, T. A. Fisher

arxiv:1502.05992 v1 · 2015-02-20 · 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{2EXKUG2Y6BNJYL7YYT3X47XRDH}

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	2026-05-18T02:26:39.834887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d12eaa1b58f05a9c2ff8c4f77e7ef119c507dce33fe32f51c521a000c753e7e1

Aliases

arxiv: 1502.05992 · arxiv_version: 1502.05992v1 · doi: 10.48550/arxiv.1502.05992 · pith_short_12: 2EXKUG2Y6BNJ · pith_short_16: 2EXKUG2Y6BNJYL7Y · pith_short_8: 2EXKUG2Y

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/2EXKUG2Y6BNJYL7YYT3X47XRDH \
  | 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: d12eaa1b58f05a9c2ff8c4f77e7ef119c507dce33fe32f51c521a000c753e7e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d82c3b0a967ee6428635e2f3647837ab5838d174fafd75e17ad1f14babc85774",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-02-20T20:53:44Z",
    "title_canon_sha256": "faffff8f0891b424e7f74d7a023f6aada899b292049861001cd4cc90942a3e6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.05992",
    "kind": "arxiv",
    "version": 1
  }
}