Pith Number

pith:T2BPFDHK

pith:2011:T2BPFDHK2MY6OVN3FYP2F75ZKM

not attested not anchored not stored refs pending

Noncommutative sets of small doubling

Terence Tao

arxiv:1106.2267 v2 · 2011-06-11 · 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{T2BPFDHK2MY6OVN3FYP2F75ZKM}

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	2026-05-18T03:58:48.735063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e82f28cead331e755bb2e1fa2ffb9530c6ceb842037b95dc00d7c4935f0281b

Aliases

arxiv: 1106.2267 · arxiv_version: 1106.2267v2 · doi: 10.48550/arxiv.1106.2267 · pith_short_12: T2BPFDHK2MY6 · pith_short_16: T2BPFDHK2MY6OVN3 · pith_short_8: T2BPFDHK

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/T2BPFDHK2MY6OVN3FYP2F75ZKM \
  | 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: 9e82f28cead331e755bb2e1fa2ffb9530c6ceb842037b95dc00d7c4935f0281b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96897bfb5cc0c9ff043744314f156fae3198d65fdbc60119aca504358d07e0c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-11T23:24:03Z",
    "title_canon_sha256": "a83e367d5a77aa66bea6a5030aa4205c63c90de3f08eda52185970d19cd88959"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2267",
    "kind": "arxiv",
    "version": 2
  }
}