Pith Number

pith:O3RZYUYI

pith:2016:O3RZYUYIJMLUX42F3LNEOEUSPB

not attested not anchored not stored refs pending

Entropy, topological transitivity, and dimensional properties of unique $q$-expansions

Derong Kong, Rafael Alcaraz Barrera, Simon Baker

arxiv:1609.02122 v3 · 2016-09-07 · math.DS · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O3RZYUYIJMLUX42F3LNEOEUSPB}

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	2026-05-18T00:37:48.304464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76e39c53084b174bf345dada471292786e26b4f041aef80af094ec2f4de4eff0

Aliases

arxiv: 1609.02122 · arxiv_version: 1609.02122v3 · doi: 10.48550/arxiv.1609.02122 · pith_short_12: O3RZYUYIJMLU · pith_short_16: O3RZYUYIJMLUX42F · pith_short_8: O3RZYUYI

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/O3RZYUYIJMLUX42F3LNEOEUSPB \
  | 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: 76e39c53084b174bf345dada471292786e26b4f041aef80af094ec2f4de4eff0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b6ca2f5cdb849eb10586aabe2c3cd66896b1837b3851bab392742b1e81213cf",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-09-07T19:20:56Z",
    "title_canon_sha256": "d5a65ceb8b7778d1a0f464f78c6eec43a5fc9c5340147c2b18abeed1b3c85a19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02122",
    "kind": "arxiv",
    "version": 3
  }
}