Pith Number

pith:7LIIBZBS

pith:2015:7LIIBZBS4TRNBJLOR6GBMOSJE5

not attested not anchored not stored refs pending

Multiple expansions of real numbers with digits set $\{0,1,q\}$

Derong Kong, Kan Jiang, Karma Dajani, Wenxia Li

arxiv:1508.06138 v2 · 2015-08-25 · math.NT · 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{7LIIBZBS4TRNBJLOR6GBMOSJE5}

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	2026-05-18T00:10:19.757968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fad080e432e4e2d0a56e8f8c163a49275c1b3038d41d821771d0abce56790b1e

Aliases

arxiv: 1508.06138 · arxiv_version: 1508.06138v2 · doi: 10.48550/arxiv.1508.06138 · pith_short_12: 7LIIBZBS4TRN · pith_short_16: 7LIIBZBS4TRNBJLO · pith_short_8: 7LIIBZBS

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/7LIIBZBS4TRNBJLOR6GBMOSJE5 \
  | 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: fad080e432e4e2d0a56e8f8c163a49275c1b3038d41d821771d0abce56790b1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "912f45f8a6aec9332f4a38d3a311c2dc6399681865a17cc22be5854a4a9f8262",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-08-25T13:13:58Z",
    "title_canon_sha256": "e3737c040382d99d02233568b7d445a2e8c337c46f02d7fbfda97b182b655a2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.06138",
    "kind": "arxiv",
    "version": 2
  }
}