Pith Number

pith:QHAHOVBQ

pith:2017:QHAHOVBQRV7YRPMYWHHDK6AWS5

not attested not anchored not stored refs pending

An elementary proof of the total progeny size of a birth-death process, with application to network component sizes

Joel C. Miller

arxiv:1710.06009 v2 · 2017-10-16 · q-bio.QM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QHAHOVBQRV7YRPMYWHHDK6AWS5}

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	2026-05-18T00:31:59.464396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81c07754308d7f88bd98b1ce357816976442947d206309d9beb8208783fd3e22

Aliases

arxiv: 1710.06009 · arxiv_version: 1710.06009v2 · doi: 10.48550/arxiv.1710.06009 · pith_short_12: QHAHOVBQRV7Y · pith_short_16: QHAHOVBQRV7YRPMY · pith_short_8: QHAHOVBQ

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/QHAHOVBQRV7YRPMYWHHDK6AWS5 \
  | 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: 81c07754308d7f88bd98b1ce357816976442947d206309d9beb8208783fd3e22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4785e56a20250ee1ae6578f6fe4c0cbb7a7d02a4bd068cf1afe5f8f6ab2fb4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.QM",
    "submitted_at": "2017-10-16T22:11:19Z",
    "title_canon_sha256": "429097127f96485b5aa172d77de1572c50c0c91f25f2d316fdffa704b28905b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.06009",
    "kind": "arxiv",
    "version": 2
  }
}