Pith Number

pith:XHRFO4OZ

pith:2010:XHRFO4OZRJHM6PWNKHYZBDUCLO

not attested not anchored not stored refs pending

A constructive version of Birkhoff's ergodic theorem for Martin-L\"of random points

Adam Day, Alexander Shen, Ilya Mezhirov, Laurent Bienvenu, Mathieu Hoyrup

arxiv:1007.5249 v2 · 2010-07-29 · math.DS · cs.LO · 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{XHRFO4OZRJHM6PWNKHYZBDUCLO}

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	2026-05-18T04:16:12.166356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9e25771d98a4ecf3ecd51f1908e825badb00c063fb75839d513188db13f0b78

Aliases

arxiv: 1007.5249 · arxiv_version: 1007.5249v2 · doi: 10.48550/arxiv.1007.5249 · pith_short_12: XHRFO4OZRJHM · pith_short_16: XHRFO4OZRJHM6PWN · pith_short_8: XHRFO4OZ

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/XHRFO4OZRJHM6PWNKHYZBDUCLO \
  | 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: b9e25771d98a4ecf3ecd51f1908e825badb00c063fb75839d513188db13f0b78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e51d8a1a5756b6b5a323373d2918c0afc427cb4935c168f8613b1748b7396e44",
    "cross_cats_sorted": [
      "cs.LO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-07-29T15:32:54Z",
    "title_canon_sha256": "452759d5e6c911177876fa0c291d6edea5da0c997441745a0934328d6f6ee5ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.5249",
    "kind": "arxiv",
    "version": 2
  }
}