Pith Number

pith:R4JU3DYN

pith:2016:R4JU3DYNHMQDBV3Q5BS7UT7SHB

not attested not anchored not stored refs pending

Markoff Surfaces and Strong Approximation: 1

Alexander Gamburd, Jean Bourgain, Peter Sarnak

arxiv:1607.01530 v1 · 2016-07-06 · math.NT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R4JU3DYNHMQDBV3Q5BS7UT7SHB}

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

1 paper in Pith

Strong Approximation for the Character Variety of the Four-Times Punctured Sphere

Receipt and verification

First computed	2026-05-18T01:11:26.212344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f134d8f0d3b2030d770e865fa4ff23862b5acf0a53e39400d9a99b4beaa7f4c

Aliases

arxiv: 1607.01530 · arxiv_version: 1607.01530v1 · doi: 10.48550/arxiv.1607.01530 · pith_short_12: R4JU3DYNHMQD · pith_short_16: R4JU3DYNHMQDBV3Q · pith_short_8: R4JU3DYN

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/R4JU3DYNHMQDBV3Q5BS7UT7SHB \
  | 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: 8f134d8f0d3b2030d770e865fa4ff23862b5acf0a53e39400d9a99b4beaa7f4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "292d1152cc13f76b1108a3a2ba7402e8f42497a3b736db39a815f80904d9354a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-07-06T09:20:15Z",
    "title_canon_sha256": "6c6dc2bbf0f1212a59bd9f1e1d255cc8a6105efd0909b7e142246837e5ed6696"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01530",
    "kind": "arxiv",
    "version": 1
  }
}