Pith Number

pith:PLIPAKZK

pith:2011:PLIPAKZKFHFSJILO4NFP5TYSHO

not attested not anchored not stored refs pending

On representation of an integer as the sum of three squares and the ternary quadratic forms with the discriminants p^2, 16p^2

Alexander Berkovich, Will Jagy

arxiv:1101.2951 v2 · 2011-01-15 · math.NT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLIPAKZKFHFSJILO4NFP5TYSHO}

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	2026-05-18T04:30:25.245878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ad0f02b2a29cb24a16ee34afecf123b96125d4c16d240c2bb7615c68ef99c4c

Aliases

arxiv: 1101.2951 · arxiv_version: 1101.2951v2 · doi: 10.48550/arxiv.1101.2951 · pith_short_12: PLIPAKZKFHFS · pith_short_16: PLIPAKZKFHFSJILO · pith_short_8: PLIPAKZK

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/PLIPAKZKFHFSJILO4NFP5TYSHO \
  | 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: 7ad0f02b2a29cb24a16ee34afecf123b96125d4c16d240c2bb7615c68ef99c4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "632ab40410aadad736ae7d0c5e60bd5651074473a47ea333392ca649a75659a8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-15T08:32:26Z",
    "title_canon_sha256": "af294f434a04dda165e8c32d9ba710358542911e9ba04fdd60266513f58d57b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2951",
    "kind": "arxiv",
    "version": 2
  }
}