Pith Number

pith:UPXTKYYY

pith:2023:UPXTKYYYKRHCKDRGTXZH2R3SAY

not attested not anchored not stored refs pending

Critical exponential tiltings for size-conditioned multitype Bienaym\'e--Galton--Watson trees

Paul Th\'evenin

arxiv:2310.12897 v1 · 2023-10-19 · 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{UPXTKYYYKRHCKDRGTXZH2R3SAY}

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	2026-07-05T07:02:44.100395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3ef356318544e250e269df27d4772061b727cfbefc7a27dacd82ff6050aabdd

Aliases

arxiv: 2310.12897 · arxiv_version: 2310.12897v1 · doi: 10.48550/arxiv.2310.12897 · pith_short_12: UPXTKYYYKRHC · pith_short_16: UPXTKYYYKRHCKDRG · pith_short_8: UPXTKYYY

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/UPXTKYYYKRHCKDRGTXZH2R3SAY \
  | 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: a3ef356318544e250e269df27d4772061b727cfbefc7a27dacd82ff6050aabdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a7a683847a4003cb6b02d3ce99e836d3e2ca448e0a8533d6139435f7a2372b0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-10-19T16:48:15Z",
    "title_canon_sha256": "846ba2f4d4d1f0d93fde31d689ca33cd45371be5cad3be8226be3348b127df30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.12897",
    "kind": "arxiv",
    "version": 1
  }
}