Pith Number

pith:PDDSWM2P

pith:2018:PDDSWM2PUSV3MM65EIZWB75MIB

not attested not anchored not stored refs pending

Kesten-McKay law for the Markoff surface mod p

Matthew de Courcy-Ireland, Michael Magee

arxiv:1811.00113 v1 · 2018-10-31 · math.NT · math.GR · 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{PDDSWM2PUSV3MM65EIZWB75MIB}

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	2026-05-18T00:01:48.230846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78c72b334fa4abb633dd223360ffac4070d4a2529d0d463fedb2d82f89d0a3d0

Aliases

arxiv: 1811.00113 · arxiv_version: 1811.00113v1 · doi: 10.48550/arxiv.1811.00113 · pith_short_12: PDDSWM2PUSV3 · pith_short_16: PDDSWM2PUSV3MM65 · pith_short_8: PDDSWM2P

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/PDDSWM2PUSV3MM65EIZWB75MIB \
  | 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: 78c72b334fa4abb633dd223360ffac4070d4a2529d0d463fedb2d82f89d0a3d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d7df28d760c0d9e0273a5a915562f582bb92b424966f20d4980ec57b7df2e40",
    "cross_cats_sorted": [
      "math.GR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-31T20:54:40Z",
    "title_canon_sha256": "c7bc1fb8aef2313cbe23a2403d8f6bd085299c906d9a456b8099d4f69b0b5431"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.00113",
    "kind": "arxiv",
    "version": 1
  }
}