Pith Number

pith:AFLS57KD

pith:2017:AFLS57KDW6OKMT2VOO2S65VUA7

not attested not anchored not stored refs pending

The heavy path approach to Galton-Watson trees with an application to Apollonian networks

Cecilia Holmgren, Henning Sulzbach, Luc Devroye

arxiv:1701.02527 v1 · 2017-01-10 · math.PR · cs.DM · 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{AFLS57KDW6OKMT2VOO2S65VUA7}

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	2026-05-18T00:53:04.060832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01572efd43b79ca64f5573b52f76b407d8b0a7135f7601936c094fedb2d71d7b

Aliases

arxiv: 1701.02527 · arxiv_version: 1701.02527v1 · doi: 10.48550/arxiv.1701.02527 · pith_short_12: AFLS57KDW6OK · pith_short_16: AFLS57KDW6OKMT2V · pith_short_8: AFLS57KD

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/AFLS57KDW6OKMT2VOO2S65VUA7 \
  | 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: 01572efd43b79ca64f5573b52f76b407d8b0a7135f7601936c094fedb2d71d7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bfa0c2aeb2199cd795c274971f7f70eb0d961c9196ca1c1727f15c873ab124e",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-01-10T11:46:38Z",
    "title_canon_sha256": "845989bd5b5666606fc4d4d37e04ccb060fd4a4060d1b65346eabbc714fd6f60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02527",
    "kind": "arxiv",
    "version": 1
  }
}