Pith Number

pith:U3M7GZDK

pith:2011:U3M7GZDKA6SE4PH6UYUPCZTPW6

not attested not anchored not stored refs pending

Quadratic polynomials represented by norm forms

D. R. Heath-Brown, T. D. Browning

arxiv:1109.0232 v1 · 2011-09-01 · 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{U3M7GZDKA6SE4PH6UYUPCZTPW6}

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	2026-05-18T04:14:17.022870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6d9f3646a07a44e3cfea628f1666fb7b6512876d3e9f76f202589db3285704e

Aliases

arxiv: 1109.0232 · arxiv_version: 1109.0232v1 · doi: 10.48550/arxiv.1109.0232 · pith_short_12: U3M7GZDKA6SE · pith_short_16: U3M7GZDKA6SE4PH6 · pith_short_8: U3M7GZDK

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/U3M7GZDKA6SE4PH6UYUPCZTPW6 \
  | 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: a6d9f3646a07a44e3cfea628f1666fb7b6512876d3e9f76f202589db3285704e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "538a1da9758da30300b89d26f08c4ee2276923b0bc669e099bd8b0f5fec015d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-09-01T16:44:02Z",
    "title_canon_sha256": "be8b2d08e1990dd8f38acb4d04b7dd97613ad6be334089e9d8e662928cc0a9d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0232",
    "kind": "arxiv",
    "version": 1
  }
}