Pith Number

pith:MELFVQGE

pith:2012:MELFVQGEJADPDLJIVOVXM4KWJ4

not attested not anchored not stored refs pending

Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents

Lingmin Liao (LAMA), Michal Rams (PAN)

arxiv:1206.1397 v2 · 2012-06-07 · 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{MELFVQGEJADPDLJIVOVXM4KWJ4}

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	2026-05-18T03:52:54.437947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61165ac0c44806f1ad28abab7671564f0b9604f899c9c6c79b1167bc0f023d62

Aliases

arxiv: 1206.1397 · arxiv_version: 1206.1397v2 · doi: 10.48550/arxiv.1206.1397 · pith_short_12: MELFVQGEJADP · pith_short_16: MELFVQGEJADPDLJI · pith_short_8: MELFVQGE

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/MELFVQGEJADPDLJIVOVXM4KWJ4 \
  | 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: 61165ac0c44806f1ad28abab7671564f0b9604f899c9c6c79b1167bc0f023d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3721ed72f6f32649cc1f530c0266bd301e70c61a4dd336353b41d0ec64627712",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-06-07T04:34:37Z",
    "title_canon_sha256": "e7355cb1244cf776ff62f788d94b3be521fdb9e2a24251ed3c49ad4d07c48f53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1397",
    "kind": "arxiv",
    "version": 2
  }
}