Pith Number

pith:XS3QI4FD

pith:2017:XS3QI4FDSFCKMX6UNT537QTJWJ

not attested not anchored not stored refs pending

Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order

Ken Yamamoto

arxiv:1701.03213 v1 · 2017-01-12 · math.PR · 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{XS3QI4FDSFCKMX6UNT537QTJWJ}

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	2026-05-18T00:28:16.273689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736

Aliases

arxiv: 1701.03213 · arxiv_version: 1701.03213v1 · doi: 10.48550/arxiv.1701.03213 · pith_short_12: XS3QI4FDSFCK · pith_short_16: XS3QI4FDSFCKMX6U · pith_short_8: XS3QI4FD

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/XS3QI4FDSFCKMX6UNT537QTJWJ \
  | 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: bcb70470a39144a65fd46cfbbfc269b264e4ffc352cf087c2df7fa5dc8514736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7566a412097d92deaf792a856b095b1a33acede7f3c9355f7fff711c523af186",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-01-12T02:24:31Z",
    "title_canon_sha256": "eb7ffc644bd32f04a8f189eff42e38840fe1fc26faf8e026b2759fc05588df2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.03213",
    "kind": "arxiv",
    "version": 1
  }
}