Pith Number

pith:FCTBFGZJ

pith:2013:FCTBFGZJYAFWXEJ6UACBLDHOKN

not attested not anchored not stored refs pending

Spectra of large diluted but bushy random graphs

Laurent Menard (MODAL'X), Modal'x), Nathanael Enriquez (LPMA

arxiv:1310.8216 v2 · 2013-10-30 · 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{FCTBFGZJYAFWXEJ6UACBLDHOKN}

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	2026-05-18T00:53:24.865291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28a6129b29c00b6b913ea004158cee537f8b5d3a0a0cd763c658a58582dd9ddd

Aliases

arxiv: 1310.8216 · arxiv_version: 1310.8216v2 · doi: 10.48550/arxiv.1310.8216 · pith_short_12: FCTBFGZJYAFW · pith_short_16: FCTBFGZJYAFWXEJ6 · pith_short_8: FCTBFGZJ

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/FCTBFGZJYAFWXEJ6UACBLDHOKN \
  | 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: 28a6129b29c00b6b913ea004158cee537f8b5d3a0a0cd763c658a58582dd9ddd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f12cb21bd49b1fbf533b882f69ec058e4f787795c85e6eba5609089aac74928",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-30T16:19:48Z",
    "title_canon_sha256": "4b2263faf3712443e01a33336cb9f7ed69a72673e05a0c25a7121fc67f7c1f2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8216",
    "kind": "arxiv",
    "version": 2
  }
}