Pith Number

pith:KYS5JK22

pith:2006:KYS5JK22VRYRFYC4L4LDB54LZO

not attested not anchored not stored refs pending

Product set estimates for non-commutative groups

Terence Tao

arxiv:math/0601431 v3 · 2006-01-18 · 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{KYS5JK22VRYRFYC4L4LDB54LZO}

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	2026-05-18T04:10:10.935678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5625d4ab5aac7112e05c5f1630f78bcb802870eb42a4ab4416d9de49dfbda4b5

Aliases

arxiv: math/0601431 · arxiv_version: math/0601431v3 · doi: 10.48550/arxiv.math/0601431 · pith_short_12: KYS5JK22VRYR · pith_short_16: KYS5JK22VRYRFYC4 · pith_short_8: KYS5JK22

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/KYS5JK22VRYRFYC4L4LDB54LZO \
  | 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: 5625d4ab5aac7112e05c5f1630f78bcb802870eb42a4ab4416d9de49dfbda4b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d2ffe882bdd0d74dbaf437184ae76cbc67c6bffb5d925fef8b906d22e26854d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2006-01-18T09:35:50Z",
    "title_canon_sha256": "4c6c228af3bc11e656c02899c7f88db00e54e158c71e8a508afffae6ee31b717"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601431",
    "kind": "arxiv",
    "version": 3
  }
}