Pith Number

pith:UZYX7DBF

pith:2018:UZYX7DBF5IC2YTD7MKGVBC6VPA

not attested not anchored not stored refs pending

Circular critical exponents for Thue-Morse factors

Jeffrey Shallit, Ramin Zarifi

arxiv:1808.02529 v1 · 2018-08-07 · cs.FL · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UZYX7DBF5IC2YTD7MKGVBC6VPA}

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	2026-05-18T00:08:35.128944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6717f8c25ea05ac4c7f628d508bd5783135626548cfe19d8a9a60d61c99b6af

Aliases

arxiv: 1808.02529 · arxiv_version: 1808.02529v1 · doi: 10.48550/arxiv.1808.02529 · pith_short_12: UZYX7DBF5IC2 · pith_short_16: UZYX7DBF5IC2YTD7 · pith_short_8: UZYX7DBF

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/UZYX7DBF5IC2YTD7MKGVBC6VPA \
  | 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: a6717f8c25ea05ac4c7f628d508bd5783135626548cfe19d8a9a60d61c99b6af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b8490ee92c0e087a3ef3f258b0c15e78762385256288effc7d354b2e306b958",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2018-08-07T19:25:35Z",
    "title_canon_sha256": "e1cc63994f57a21221fbcd53251cb49214412384b44ac59fd4abfb294ae925e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.02529",
    "kind": "arxiv",
    "version": 1
  }
}