Pith Number

pith:URXZO3XD

pith:2023:URXZO3XD7K6INIE2IYTSNA7M2N

not attested not anchored not stored refs pending

Edge universality of sparse Erd\H{o}s-R\'enyi digraphs

Yukun He

arxiv:2304.04723 v5 · 2023-04-10 · math.PR · 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{URXZO3XD7K6INIE2IYTSNA7M2N}

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

2 papers in Pith

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

Local laws and spectral properties of deformed sparse random matrices

Receipt and verification

First computed	2026-07-05T12:11:11.238470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a46f976ee3fabc86a09a46272683ecd366f77d31d912d8e7533a4d0c8f8df84a

Aliases

arxiv: 2304.04723 · arxiv_version: 2304.04723v5 · doi: 10.48550/arxiv.2304.04723 · pith_short_12: URXZO3XD7K6I · pith_short_16: URXZO3XD7K6INIE2 · pith_short_8: URXZO3XD

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/URXZO3XD7K6INIE2IYTSNA7M2N \
  | 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: a46f976ee3fabc86a09a46272683ecd366f77d31d912d8e7533a4d0c8f8df84a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5bba41ba535e9e4d363e1300bebd4ffbdc8931f0e24c5c1189f2c4b3d29c10f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-04-10T17:35:06Z",
    "title_canon_sha256": "6ccd8d9a5a7c166408080c8b26e084da8cf777cd785d83ffe444bc49afb6cdd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.04723",
    "kind": "arxiv",
    "version": 5
  }
}