Pith Number

pith:TGXIWMZG

pith:2013:TGXIWMZGDH4MRKUCKA6FXTALWM

not attested not anchored not stored refs pending

What is the probability that a random integral quadratic form in $n$ variables is isotropic?

John Cremona, Manjul Bhargava, Tom Fisher

arxiv:1311.5543 v2 · 2013-11-21 · 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{TGXIWMZGDH4MRKUCKA6FXTALWM}

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	2026-05-18T02:26:45.603587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99ae8b332619f8c8aa82503c5bcc0bb32862b90833ff9c0c1627d104ca24c09a

Aliases

arxiv: 1311.5543 · arxiv_version: 1311.5543v2 · doi: 10.48550/arxiv.1311.5543 · pith_short_12: TGXIWMZGDH4M · pith_short_16: TGXIWMZGDH4MRKUC · pith_short_8: TGXIWMZG

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/TGXIWMZGDH4MRKUCKA6FXTALWM \
  | 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: 99ae8b332619f8c8aa82503c5bcc0bb32862b90833ff9c0c1627d104ca24c09a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20f69b43cf8dc0b7e2d45794ca1630794d278e840edd8fb9d5e2f5fb84f50530",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-21T20:31:12Z",
    "title_canon_sha256": "537377897929baa8c71d39ef6c103c920fe0383c3c41b608c35f8c1f11ae3626"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5543",
    "kind": "arxiv",
    "version": 2
  }
}