Pith Number

pith:ZQBOZBBS

pith:2015:ZQBOZBBSHWQYMDG6WQOMZKRVYA

not attested not anchored not stored refs pending

On the escape rate of unique beta-expansions

Bing Li, Chih-Hung Chang, Jung-Chao Ban

arxiv:1510.01117 v2 · 2015-10-05 · 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{ZQBOZBBSHWQYMDG6WQOMZKRVYA}

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	2026-05-18T00:57:38.211782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc02ec84323da1860cdeb41cccaa35c020891878d799598991e48032cfcc9d9d

Aliases

arxiv: 1510.01117 · arxiv_version: 1510.01117v2 · doi: 10.48550/arxiv.1510.01117 · pith_short_12: ZQBOZBBSHWQY · pith_short_16: ZQBOZBBSHWQYMDG6 · pith_short_8: ZQBOZBBS

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/ZQBOZBBSHWQYMDG6WQOMZKRVYA \
  | 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: cc02ec84323da1860cdeb41cccaa35c020891878d799598991e48032cfcc9d9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6d2a47b0c54076fe8da69ff7e3b7f42f5a421a799534e458ee5f605a626ba4b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-05T12:09:06Z",
    "title_canon_sha256": "0046669e13177bf73a05b154cd46b23b97a335a84d777cdea5bd6a58710ceaa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01117",
    "kind": "arxiv",
    "version": 2
  }
}