Pith Number

pith:EU5U23PY

pith:2014:EU5U23PYBD3RPNOIYF6DGR2Q2L

not attested not anchored not stored refs pending

A sharp threshold for collapse of the random triangular group

Ehud Friedgut, Sylwia Antoniuk, Tomasz {\L}uczak

arxiv:1403.3516 v2 · 2014-03-14 · math.GR · 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{EU5U23PYBD3RPNOIYF6DGR2Q2L}

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	2026-05-18T00:57:44.546412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

253b4d6df808f717b5c8c17c334750d2ea3e03b73584132ac1c047c1a9cdedbb

Aliases

arxiv: 1403.3516 · arxiv_version: 1403.3516v2 · doi: 10.48550/arxiv.1403.3516 · pith_short_12: EU5U23PYBD3R · pith_short_16: EU5U23PYBD3RPNOI · pith_short_8: EU5U23PY

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/EU5U23PYBD3RPNOIYF6DGR2Q2L \
  | 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: 253b4d6df808f717b5c8c17c334750d2ea3e03b73584132ac1c047c1a9cdedbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf066623efe964092ecc361ccf074bfa653f8cf5dc3b08d7fcd6c24c023ba439",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-03-14T09:47:56Z",
    "title_canon_sha256": "63edbb49dcb7728c73db95190b617f854bd01d64ed144bae950905549e44404b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.3516",
    "kind": "arxiv",
    "version": 2
  }
}