Pith Number

pith:XYJOUJOD

pith:2015:XYJOUJOD55T4PQ3A4DKIKIRTQH

not attested not anchored not stored refs pending

Nilprogressions and groups with moderate growth

Emmanuel Breuillard, Matthew Tointon

arxiv:1506.00886 v3 · 2015-06-02 · math.GR · math.CO · math.MG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYJOUJOD55T4PQ3A4DKIKIRTQH}

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	2026-05-18T01:09:07.043390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be12ea25c3ef67c7c360e0d485223381dad9444498b68ddee5afa1ee5e83f511

Aliases

arxiv: 1506.00886 · arxiv_version: 1506.00886v3 · doi: 10.48550/arxiv.1506.00886 · pith_short_12: XYJOUJOD55T4 · pith_short_16: XYJOUJOD55T4PQ3A · pith_short_8: XYJOUJOD

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/XYJOUJOD55T4PQ3A4DKIKIRTQH \
  | 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: be12ea25c3ef67c7c360e0d485223381dad9444498b68ddee5afa1ee5e83f511

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ad6b339cd2080f1f82e711f14af59e3c9957da1983a347fb7418cc42fe649a8",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-02T13:54:54Z",
    "title_canon_sha256": "8ba021f50346ad713bb9366107c27f0556b6213e0d4ce930cbd46f69c2df861a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00886",
    "kind": "arxiv",
    "version": 3
  }
}