Pith Number

pith:YI2UNTTW

pith:2013:YI2UNTTWUM3M3QI5O2LF22FQ5E

not attested not anchored not stored refs pending

Diophantine properties of nilpotent Lie groups

Emmanuel Breuillard, Lior Rosenzweig, Menny Aka, Nicolas de Saxc\'e

arxiv:1307.1489 v2 · 2013-07-04 · math.GR · 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{YI2UNTTWUM3M3QI5O2LF22FQ5E}

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	2026-05-18T01:41:00.293856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c23546ce76a336cdc11d76965d68b0e903f68dc99377c14abc1985bb837f0ee9

Aliases

arxiv: 1307.1489 · arxiv_version: 1307.1489v2 · doi: 10.48550/arxiv.1307.1489 · pith_short_12: YI2UNTTWUM3M · pith_short_16: YI2UNTTWUM3M3QI5 · pith_short_8: YI2UNTTW

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/YI2UNTTWUM3M3QI5O2LF22FQ5E \
  | 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: c23546ce76a336cdc11d76965d68b0e903f68dc99377c14abc1985bb837f0ee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13777a2593b5244b3ea399d03f5e2eed5c0dfa20c618707e5e85ca9fcebe3ce4",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-07-04T21:04:47Z",
    "title_canon_sha256": "e147b55198cf70654386e9e48b33d176f684888e12c12e15b6dade9c7f82c653"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1489",
    "kind": "arxiv",
    "version": 2
  }
}