Pith Number

pith:NDBTB52G

pith:2000:NDBTB52G2D4T6G6QTKSHPZJ53G

not attested not anchored not stored refs pending

Statistical stability for robust classes of maps with non-uniform expansion

Jose F. Alves, Marcelo Viana

arxiv:math/0011183 v1 · 2000-11-22 · 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{NDBTB52G2D4T6G6QTKSHPZJ53G}

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	2026-07-04T14:34:56.370571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68c330f746d0f93f1bd09aa477e53dd9a1386732dfaaef7f43a33ebb8df5aa6c

Aliases

arxiv: math/0011183 · arxiv_version: math/0011183v1 · doi: 10.48550/arxiv.math/0011183 · pith_short_12: NDBTB52G2D4T · pith_short_16: NDBTB52G2D4T6G6Q · pith_short_8: NDBTB52G

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/NDBTB52G2D4T6G6QTKSHPZJ53G \
  | 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: 68c330f746d0f93f1bd09aa477e53dd9a1386732dfaaef7f43a33ebb8df5aa6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1126ef389925b4629acf83ed231369b7e4489232a0bfbf7056c746e97839d55",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2000-11-22T18:40:48Z",
    "title_canon_sha256": "664a8feef350f61a707feecacac47c0a0ec204f7394b3307d076a06db028c992"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0011183",
    "kind": "arxiv",
    "version": 1
  }
}