Pith Number

pith:MUUJJZAS

pith:2012:MUUJJZASQYXVIGWODD25C2WODB

not attested not anchored not stored refs pending

Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems

Ai-Hua Fan (LAMFA), Lingmin Liao (LAMA), Meng Wu

arxiv:1208.1755 v2 · 2012-08-08 · 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{MUUJJZASQYXVIGWODD25C2WODB}

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	2026-05-18T01:21:40.954967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

652894e412862f541ace18f5d16ace18730498a90ae54ad43ba9b235bb98809a

Aliases

arxiv: 1208.1755 · arxiv_version: 1208.1755v2 · doi: 10.48550/arxiv.1208.1755 · pith_short_12: MUUJJZASQYXV · pith_short_16: MUUJJZASQYXVIGWO · pith_short_8: MUUJJZAS

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/MUUJJZASQYXVIGWODD25C2WODB \
  | 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: 652894e412862f541ace18f5d16ace18730498a90ae54ad43ba9b235bb98809a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "981fb83e235cd977b39512badf685959fae4ac3681e2c83df89f449ef33ed538",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-08T19:54:23Z",
    "title_canon_sha256": "e115b437642de24894d9213746914e39dc8d5aa43cb1538b5e8482858b7ec89e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1755",
    "kind": "arxiv",
    "version": 2
  }
}