Pith Number

pith:4DQEITOZ

pith:2010:4DQEITOZAAITRUIYHADCX3QVIU

not attested not anchored not stored refs pending

Bernoulli measure on strings, and Thompson-Higman monoids

Jean-Camille Birget

arxiv:1004.5589 v1 · 2010-04-30 · 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{4DQEITOZAAITRUIYHADCX3QVIU}

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	2026-05-18T02:24:09.749986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0e0444dd9001138d11838062bee1545112ed2b32cc4c9d3f3ec3d478a3c73fa

Aliases

arxiv: 1004.5589 · arxiv_version: 1004.5589v1 · doi: 10.48550/arxiv.1004.5589 · pith_short_12: 4DQEITOZAAIT · pith_short_16: 4DQEITOZAAITRUIY · pith_short_8: 4DQEITOZ

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/4DQEITOZAAITRUIYHADCX3QVIU \
  | 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: e0e0444dd9001138d11838062bee1545112ed2b32cc4c9d3f3ec3d478a3c73fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5eeb3fffed4de43fd05dc6625c254d15a6d824de94f4acf1d4249321da299c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-30T18:53:18Z",
    "title_canon_sha256": "74db557c08bb12f552fe5710ead06d6147d740184d97bb06aa8cbf9e68fe8b5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5589",
    "kind": "arxiv",
    "version": 1
  }
}