Pith Number

pith:NF7EK7RP

pith:2024:NF7EK7RPYSMGARHMQL7TTV33FB

not attested not anchored not stored refs pending

Ramanujan Property and Edge Universality of Random Regular Graphs

Horng-Tzer Yau, Jiaoyang Huang, Theo McKenzie

arxiv:2412.20263 v2 · 2024-12-28 · math.PR · math-ph · math.CO · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NF7EK7RPYSMGARHMQL7TTV33FB}

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

8 papers in Pith

Loop Equations Characterize Random Matrix Statistics

Bass notes of random hyperbolic surfaces of large genus

Discrete Mixed Quantization

Spectral Theory of Isogeny Graphs

Deconfinement For $\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling

Receipt and verification

First computed	2026-07-05T10:08:26.897831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

697e457e2fc4986044ec82ff39d77b287d75def941f8a837de24d59f17bebcd9

Aliases

arxiv: 2412.20263 · arxiv_version: 2412.20263v2 · doi: 10.48550/arxiv.2412.20263 · pith_short_12: NF7EK7RPYSMG · pith_short_16: NF7EK7RPYSMGARHM · pith_short_8: NF7EK7RP

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/NF7EK7RPYSMGARHMQL7TTV33FB \
  | 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: 697e457e2fc4986044ec82ff39d77b287d75def941f8a837de24d59f17bebcd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f036df27aabb748ac241e01613284fd55b60f510ed33ffe08bbc3043b26677f0",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-28T20:34:12Z",
    "title_canon_sha256": "29cbbc051915b87240cb78b5f76c3e3c3d0f2fb94f6038d6e107f7280d782f5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.20263",
    "kind": "arxiv",
    "version": 2
  }
}