Pith Number

pith:EGC54OOO

pith:2014:EGC54OOOOPZQBRCXFJVFK7ZT42

not attested not anchored not stored refs pending

A sharper threshold for random groups at density one-half

Andrew P. S\'anchez, John M. Mackay, Kasia Jankiewicz, Moon Duchin, Samuel Leli\`evre, Shelby C. Kilmer

arxiv:1412.8741 v1 · 2014-12-30 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EGC54OOOOPZQBRCXFJVFK7ZT42}

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	2026-05-18T02:30:16.635693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2185de39ce73f300c4572a6a557f33e6ab0d6d08d8651ed6efdfaf6fd40d9511

Aliases

arxiv: 1412.8741 · arxiv_version: 1412.8741v1 · doi: 10.48550/arxiv.1412.8741 · pith_short_12: EGC54OOOOPZQ · pith_short_16: EGC54OOOOPZQBRCX · pith_short_8: EGC54OOO

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/EGC54OOOOPZQBRCXFJVFK7ZT42 \
  | 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: 2185de39ce73f300c4572a6a557f33e6ab0d6d08d8651ed6efdfaf6fd40d9511

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f0b55a61c55575c26c1740eff4ae43fc5d57ace3455316a7111485d0b89c0e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-12-30T19:27:42Z",
    "title_canon_sha256": "b7daeef634ab79665719b5bac1565add1ad705d16abdfaeb88d8c374d30a2c78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8741",
    "kind": "arxiv",
    "version": 1
  }
}