Pith Number

pith:XNIXX4DJ

pith:2016:XNIXX4DJYJWTVA467CQJUUR7TH

not attested not anchored not stored refs pending

Almost sure invariance principle for random piecewise expanding maps

C. Gonz\'alez-Tokman, D. Dragicevic, G. Froyland, S. Vaienti

arxiv:1611.04003 v3 · 2016-11-12 · 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{XNIXX4DJYJWTVA467CQJUUR7TH}

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	2026-05-17T23:59:10.360745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb517bf069c26d3a839ef8a09a523f99e63e2ebf8629994716d3d49da2b1b7e4

Aliases

arxiv: 1611.04003 · arxiv_version: 1611.04003v3 · doi: 10.48550/arxiv.1611.04003 · pith_short_12: XNIXX4DJYJWT · pith_short_16: XNIXX4DJYJWTVA46 · pith_short_8: XNIXX4DJ

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/XNIXX4DJYJWTVA467CQJUUR7TH \
  | 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: bb517bf069c26d3a839ef8a09a523f99e63e2ebf8629994716d3d49da2b1b7e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "439f9e6549b16f21d56f46cdadf65928f0de1eac6bf2e05c2ef3f035c14f9a9f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-11-12T14:23:55Z",
    "title_canon_sha256": "6c7bbc8dcc0046ee4f1738b8b10fd247ef1b6dce4201f7daead88483a1f61ae3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04003",
    "kind": "arxiv",
    "version": 3
  }
}