Pith Number

pith:CGPJZ3T4

pith:1999:CGPJZ3T4BZBV2LDCUDTB4TMRDX

not attested not anchored not stored refs pending

Cesaro mean distribution of group automata starting from measures with summable decay

Alejandro Maass, Pablo A. Ferrari, Peter Ney, Servet Martinez

arxiv:math/9912135 v1 · 1999-12-16 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CGPJZ3T4BZBV2LDCUDTB4TMRDX}

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	2026-05-18T04:08:35.461067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

119e9cee7c0e435d2c62a0e61e4d911dffdc6077af31614bce4c0695449f3654

Aliases

arxiv: math/9912135 · arxiv_version: math/9912135v1 · doi: 10.48550/arxiv.math/9912135 · pith_short_12: CGPJZ3T4BZBV · pith_short_16: CGPJZ3T4BZBV2LDC · pith_short_8: CGPJZ3T4

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/CGPJZ3T4BZBV2LDCUDTB4TMRDX \
  | 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: 119e9cee7c0e435d2c62a0e61e4d911dffdc6077af31614bce4c0695449f3654

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75a40374dc2ff5ec5c1c8fc1ab564437d25ce71932d53a441a21bf45b21d662b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-12-16T21:58:11Z",
    "title_canon_sha256": "f8b9acd298c62eab195c069c15acb0854c9a140821accd2c959ac1263d43fd3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912135",
    "kind": "arxiv",
    "version": 1
  }
}