Pith Number

pith:CIUXHGVL

pith:2013:CIUXHGVL2BN7U67A7LB4GALHBK

not attested not anchored not stored refs pending

A strong law of large numbers for branching processes: almost sure spine events

Matthew I. Roberts, Simon C. Harris

arxiv:1302.7199 v1 · 2013-02-28 · 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{CIUXHGVL2BN7U67A7LB4GALHBK}

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	2026-05-18T03:32:16.443280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1229739aabd05bfa7be0fac3c301670ab7eb043fd094c1a2ece6d59e8e6dd4d2

Aliases

arxiv: 1302.7199 · arxiv_version: 1302.7199v1 · doi: 10.48550/arxiv.1302.7199 · pith_short_12: CIUXHGVL2BN7 · pith_short_16: CIUXHGVL2BN7U67A · pith_short_8: CIUXHGVL

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/CIUXHGVL2BN7U67A7LB4GALHBK \
  | 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: 1229739aabd05bfa7be0fac3c301670ab7eb043fd094c1a2ece6d59e8e6dd4d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abd6c94c4bbcabd6fbea7573dda51b34788d433e271bb24f88b5f9636f1eb30a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-28T14:08:45Z",
    "title_canon_sha256": "84190bb7b7eb0c8fa9e233377ec5cf7cf8ca94ecfc0daf99e4ac2b1396360b02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.7199",
    "kind": "arxiv",
    "version": 1
  }
}