Pith Number

pith:AY4CCEB7

pith:2013:AY4CCEB73UNH6KMDTX7F7RYMVC

not attested not anchored not stored refs pending

Shadowing property, weak mixing and regular recurrence

Jian Li, Piotr Oprocha

arxiv:1311.0451 v2 · 2013-11-03 · 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{AY4CCEB73UNH6KMDTX7F7RYMVC}

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	2026-05-18T03:05:27.768669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

063821103fdd1a7f29839dfe5fc70ca8894b775acb81d5a50802755e90ce9a76

Aliases

arxiv: 1311.0451 · arxiv_version: 1311.0451v2 · doi: 10.48550/arxiv.1311.0451 · pith_short_12: AY4CCEB73UNH · pith_short_16: AY4CCEB73UNH6KMD · pith_short_8: AY4CCEB7

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/AY4CCEB73UNH6KMDTX7F7RYMVC \
  | 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: 063821103fdd1a7f29839dfe5fc70ca8894b775acb81d5a50802755e90ce9a76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c9af577c48f1b6f28773f8c38a98dc0f8f561d8f41ee659badf6ff11d9b90f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-11-03T10:17:55Z",
    "title_canon_sha256": "4d0ba2ee62edf943963ece00a1fe888e8e573d5d017afca3936aeea1864d36e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0451",
    "kind": "arxiv",
    "version": 2
  }
}