Pith Number

pith:CE3N4TT3

pith:2011:CE3N4TT3DKIOEL3QL3RHCZ2S6W

not attested not anchored not stored refs pending

Contractions and expansion

Ben Green, Emmanuel Breuillard

arxiv:1112.3468 v1 · 2011-12-15 · math.CO · 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{CE3N4TT3DKIOEL3QL3RHCZ2S6W}

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	2026-05-18T04:06:18.515731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1136de4e7b1a90e22f705ee2716752f5a56597d6870c7155e2aa3c4e34af9eed

Aliases

arxiv: 1112.3468 · arxiv_version: 1112.3468v1 · doi: 10.48550/arxiv.1112.3468 · pith_short_12: CE3N4TT3DKIO · pith_short_16: CE3N4TT3DKIOEL3Q · pith_short_8: CE3N4TT3

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/CE3N4TT3DKIOEL3QL3RHCZ2S6W \
  | 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: 1136de4e7b1a90e22f705ee2716752f5a56597d6870c7155e2aa3c4e34af9eed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b2ddbe93da74a36658066d6dfb190a971befc5c96d2f3517aa08efc0feb6698",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-15T10:17:53Z",
    "title_canon_sha256": "512bea8410e542059ebde42f41e7795887314670b9b2c0abd03364eb79413097"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3468",
    "kind": "arxiv",
    "version": 1
  }
}