Pith Number

pith:4J4ANK35

pith:2015:4J4ANK35BNHPR6YYXUUAHLW7RQ

not attested not anchored not stored refs pending

Ergodic Theory of Kusuoka Measures

Anders Johansson, Anders \"Oberg, Mark Pollicott

arxiv:1506.03037 v3 · 2015-06-09 · 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{4J4ANK35BNHPR6YYXUUAHLW7RQ}

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	2026-05-18T00:43:09.689403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e27806ab7d0b4ef8fb18bd2803aedf8c152b9749862c9e7d8b0b3bf63f25de18

Aliases

arxiv: 1506.03037 · arxiv_version: 1506.03037v3 · doi: 10.48550/arxiv.1506.03037 · pith_short_12: 4J4ANK35BNHP · pith_short_16: 4J4ANK35BNHPR6YY · pith_short_8: 4J4ANK35

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/4J4ANK35BNHPR6YYXUUAHLW7RQ \
  | 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: e27806ab7d0b4ef8fb18bd2803aedf8c152b9749862c9e7d8b0b3bf63f25de18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07a08aacce19c3b149a0e7a16be1e84e7c97de34dbc7dca3221ce4ec23e1ce92",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-06-09T18:43:48Z",
    "title_canon_sha256": "5f6899aae3c7cbd8e0be7bd15e590723080626bea0404761be7b6a06d8cdfa63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03037",
    "kind": "arxiv",
    "version": 3
  }
}