Pith Number

pith:2GQKBQLK

pith:2015:2GQKBQLKXBSG3MLJGFLKR3YTFC

not attested not anchored not stored refs pending

A geometric entropy detecting the Erd\"os-R\'enyi phase transition

Domenico Felice, Marco Pettini, Roberto Franzosi, Stefano Mancini

arxiv:1507.08409 v1 · 2015-07-30 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GQKBQLKXBSG3MLJGFLKR3YTFC}

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	2026-05-18T01:30:50.748740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1a0a0c16ab8646db1693156a8ef1328adee352ede2bee4941d25e57e829e6fd

Aliases

arxiv: 1507.08409 · arxiv_version: 1507.08409v1 · doi: 10.48550/arxiv.1507.08409 · pith_short_12: 2GQKBQLKXBSG · pith_short_16: 2GQKBQLKXBSG3MLJ · pith_short_8: 2GQKBQLK

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/2GQKBQLKXBSG3MLJGFLKR3YTFC \
  | 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: d1a0a0c16ab8646db1693156a8ef1328adee352ede2bee4941d25e57e829e6fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ee38faeae79fd335c81bb7a6dc08fd0cff08088d814a8fa112a8e9e507a5a52",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-07-30T07:56:32Z",
    "title_canon_sha256": "2fe1b98c0e31b7790842572877a9861491e04a610330bc418703bfe294749ae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08409",
    "kind": "arxiv",
    "version": 1
  }
}