Pith Number

pith:VIPB7EXZ

pith:2017:VIPB7EXZQZDGVUGG5VMFFKK5YZ

not attested not anchored not stored refs pending

Quantum Chaos on random Cayley graphs of ${\rm SL}_2[\mathbb{Z}/p\mathbb{Z}]$

Igor Rivin, Naser T. Sardari

arxiv:1705.02993 v1 · 2017-05-08 · math.NT · math-ph · math.CO · 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{VIPB7EXZQZDGVUGG5VMFFKK5YZ}

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	2026-05-18T00:44:53.155970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa1e1f92f986466ad0c6ed5852a95dc6719ef2d4c203414eb29d0b3833503f6f

Aliases

arxiv: 1705.02993 · arxiv_version: 1705.02993v1 · doi: 10.48550/arxiv.1705.02993 · pith_short_12: VIPB7EXZQZDG · pith_short_16: VIPB7EXZQZDGVUGG · pith_short_8: VIPB7EXZ

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/VIPB7EXZQZDGVUGG5VMFFKK5YZ \
  | 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: aa1e1f92f986466ad0c6ed5852a95dc6719ef2d4c203414eb29d0b3833503f6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9704117e31576b5707109f1750f9eee4e44e254e9e73d7be071509dcd44ff38",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-05-08T17:51:29Z",
    "title_canon_sha256": "cd6868a6740989bad96b5c40aadd0846f2ef85b3beb09a9aa29e91c86217a9a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.02993",
    "kind": "arxiv",
    "version": 1
  }
}