Pith Number

pith:C42RHJDZ

pith:2026:C42RHJDZW24NUCIOFLGPQVZHQJ

not attested not anchored not stored refs pending

Sharp vertex connectivity of the Markoff graphs modulo $p$

Jie Ma, Mengxi Yang, Zichen Yang

arxiv:2608.07880 v1 · 2026-08-08 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C42RHJDZW24NUCIOFLGPQVZHQJ}

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	2026-08-11T01:18:49.256505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

173513a479b6b8da090e2accf857278261092669d3e24b3e5826121736b6ad1a

Aliases

arxiv: 2608.07880 · arxiv_version: 2608.07880v1 · doi: 10.48550/arxiv.2608.07880 · pith_short_12: C42RHJDZW24N · pith_short_16: C42RHJDZW24NUCIO · pith_short_8: C42RHJDZ

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/C42RHJDZW24NUCIOFLGPQVZHQJ \
  | 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: 173513a479b6b8da090e2accf857278261092669d3e24b3e5826121736b6ad1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a39099c79132542df86093408c1d27fefca30687d2cf28d8e46ce12f3aa4fd3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-08-08T03:14:17Z",
    "title_canon_sha256": "f8ade0368a2e1d1e223b7c465b01239ac0e72c3c0bcf7515d5401b2dddc9b224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07880",
    "kind": "arxiv",
    "version": 1
  }
}