Pith Number

pith:BG2HNFAG

pith:2018:BG2HNFAGQOPIGK3KILDPET3RBW

not attested not anchored not stored refs pending

Probability laws for the distribution of geometric lengths when sampling by a random walk in a Fuchsian fundamental group

Peter S. Park

arxiv:1807.03775 v3 · 2018-07-10 · math.GT · math.DS · math.GR · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BG2HNFAGQOPIGK3KILDPET3RBW}

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	2026-05-17T23:54:28.239910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09b4769406839e832b6a42c6f24f710d84ba2b72512d0cb7dda7c5e9e11c22cf

Aliases

arxiv: 1807.03775 · arxiv_version: 1807.03775v3 · doi: 10.48550/arxiv.1807.03775 · pith_short_12: BG2HNFAGQOPI · pith_short_16: BG2HNFAGQOPIGK3K · pith_short_8: BG2HNFAG

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/BG2HNFAGQOPIGK3KILDPET3RBW \
  | 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: 09b4769406839e832b6a42c6f24f710d84ba2b72512d0cb7dda7c5e9e11c22cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65585c1e847026d12c6f202f6b16834f5814098be4d161bc83a5cd2d75bf1303",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-07-10T17:54:03Z",
    "title_canon_sha256": "9ff2f104beb932cfcbfddd2c2b9bf84b81b9714db0836d4f03b9a4a37cd1b997"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03775",
    "kind": "arxiv",
    "version": 3
  }
}