Pith Number

pith:QPBKZEX6

pith:2013:QPBKZEX6J7JWHW7YRXQ6GACN34

not attested not anchored not stored refs pending

Phase Transition of Random Non-Uniform Hypergraphs

Elie de Panafieu

arxiv:1304.5932 v5 · 2013-04-22 · 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{QPBKZEX6J7JWHW7YRXQ6GACN34}

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	2026-05-18T02:25:34.359391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83c2ac92fe4fd363dbf88de1e3004ddf0cc91a0d8e390ae412f9fd7ad4a68179

Aliases

arxiv: 1304.5932 · arxiv_version: 1304.5932v5 · doi: 10.48550/arxiv.1304.5932 · pith_short_12: QPBKZEX6J7JW · pith_short_16: QPBKZEX6J7JWHW7Y · pith_short_8: QPBKZEX6

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/QPBKZEX6J7JWHW7YRXQ6GACN34 \
  | 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: 83c2ac92fe4fd363dbf88de1e3004ddf0cc91a0d8e390ae412f9fd7ad4a68179

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db296358624d72f0b16a4183abe048235420e3123d95ca5a5e358c65d0bb0e81",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-22T12:45:15Z",
    "title_canon_sha256": "dcff3fcedf5d93e5285c49e62cd4f2f483264d71e87f702ad547a1533b72d3fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5932",
    "kind": "arxiv",
    "version": 5
  }
}