Pith Number

pith:4VQFE6NR

pith:2016:4VQFE6NRC4X6ZQCQOMNY47V7A4

not attested not anchored not stored refs pending

Indicable groups and $p_c<1$

Aran Raoufi, Ariel Yadin

arxiv:1606.06139 v2 · 2016-06-20 · 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{4VQFE6NRC4X6ZQCQOMNY47V7A4}

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	2026-05-18T01:11:40.829178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5605279b1172fecc050731b8e7ebf07234fdf27a53f1958b619965077440280

Aliases

arxiv: 1606.06139 · arxiv_version: 1606.06139v2 · doi: 10.48550/arxiv.1606.06139 · pith_short_12: 4VQFE6NRC4X6 · pith_short_16: 4VQFE6NRC4X6ZQCQ · pith_short_8: 4VQFE6NR

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/4VQFE6NRC4X6ZQCQOMNY47V7A4 \
  | 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: e5605279b1172fecc050731b8e7ebf07234fdf27a53f1958b619965077440280

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72251d0874e9636cd352345fe1a7696f345488716cfdbbd69dd56151d87e70fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-20T14:31:04Z",
    "title_canon_sha256": "8e39ffba296bc05b674a19323f415f62b1e1457ebb0efa1b257ab2eb373fcffe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06139",
    "kind": "arxiv",
    "version": 2
  }
}