Pith Number

pith:2AH32Z33

pith:2026:2AH32Z333YWBF6KOMPTRCF5UGV

not attested not anchored not stored refs pending

Critical Erd{\H o}s-R\'enyi digraph: all eigenvectors away from zero are delocalized

Johannes Alt, Sarah Timhadjelt

arxiv:2606.24887 v1 · 2026-06-23 · 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{2AH32Z333YWBF6KOMPTRCF5UGV}

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.

Cited by

1 paper in Pith

Spectrum of Directed Inhomogeneous Random Graphs

Receipt and verification

First computed	2026-06-24T01:15:45.492707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d00fbd677bde2c12f94e63e71117b43545a85792ce08aa06ab1ef5ed4d722925

Aliases

arxiv: 2606.24887 · arxiv_version: 2606.24887v1 · doi: 10.48550/arxiv.2606.24887 · pith_short_12: 2AH32Z333YWB · pith_short_16: 2AH32Z333YWBF6KO · pith_short_8: 2AH32Z33

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/2AH32Z333YWBF6KOMPTRCF5UGV \
  | 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: d00fbd677bde2c12f94e63e71117b43545a85792ce08aa06ab1ef5ed4d722925

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "debc2a22c5ba0705eac4adb1d1ffe83ea1d42b73bf51d0af75e5812dddc5451e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-23T17:59:29Z",
    "title_canon_sha256": "fadbb51f9aa25089aa91d2c26c63faff3583e6d4336ebf8729f7b431c6cba901"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24887",
    "kind": "arxiv",
    "version": 1
  }
}