Pith Number

pith:6AW3OAMX

pith:2024:6AW3OAMXREJO4263X7B7REIN6S

not attested not anchored not stored refs pending

An extension of the cogrowth formula to arbitrary subsets of the tree

Doron Puder

arxiv:2405.18169 v2 · 2024-05-28 · math.PR · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6AW3OAMXREJO4263X7B7REIN6S}

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	2026-07-05T09:54:27.040555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f02db701978912ee6bdbbfc3f8910df48ce94d46250372ab9355966460d59149

Aliases

arxiv: 2405.18169 · arxiv_version: 2405.18169v2 · doi: 10.48550/arxiv.2405.18169 · pith_short_12: 6AW3OAMXREJO · pith_short_16: 6AW3OAMXREJO4263 · pith_short_8: 6AW3OAMX

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/6AW3OAMXREJO4263X7B7REIN6S \
  | 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: f02db701978912ee6bdbbfc3f8910df48ce94d46250372ab9355966460d59149

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da066df7b73fcb17d0ad3366b043a3f51b08558c2e795714cb6fe906d855f19a",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-05-28T13:30:06Z",
    "title_canon_sha256": "9eae7c72e0986001a2887943a68be18bdabc7c594b7ba1c76a5314ee218f539e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.18169",
    "kind": "arxiv",
    "version": 2
  }
}