Pith Number

pith:K5X6ZVPO

pith:2011:K5X6ZVPO4PW2YZETGHD2AFJ2J6

not attested not anchored not stored refs pending

Probabilistic Universality in two-dimensional Dynamics

Marco Martens, Mikhail Lyubich

arxiv:1106.5067 v1 · 2011-06-24 · 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{K5X6ZVPO4PW2YZETGHD2AFJ2J6}

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	2026-05-18T04:19:21.429319Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

576fecd5eee3edac649331c7a0153a4faea1322193b43e2fd540fb55ff489803

Aliases

arxiv: 1106.5067 · arxiv_version: 1106.5067v1 · doi: 10.48550/arxiv.1106.5067 · pith_short_12: K5X6ZVPO4PW2 · pith_short_16: K5X6ZVPO4PW2YZET · pith_short_8: K5X6ZVPO

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/K5X6ZVPO4PW2YZETGHD2AFJ2J6 \
  | 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: 576fecd5eee3edac649331c7a0153a4faea1322193b43e2fd540fb55ff489803

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa4831206558261166cd1b56a216bcb5caa0d091d24db145f32b006391fd7f81",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-06-24T20:50:57Z",
    "title_canon_sha256": "947e16b16a1121049808d5e18b96da5f4a3fab68b3baf5a2f0e6acbfc0efff37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5067",
    "kind": "arxiv",
    "version": 1
  }
}