Pith Number

pith:6QOT3W5P

pith:2011:6QOT3W5PYL4PT5B3TCMI46EWYN

not attested not anchored not stored refs pending

Factor frequencies in generalized Thue-Morse words

Lubomira Balkova

arxiv:1107.5033 v1 · 2011-07-25 · 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{6QOT3W5PYL4PT5B3TCMI46EWYN}

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	2026-05-18T03:34:46.378605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f41d3ddbafc2f8f9f43b98988e7896c34c2a99eab9b006a3610b8001e4ebc2df

Aliases

arxiv: 1107.5033 · arxiv_version: 1107.5033v1 · doi: 10.48550/arxiv.1107.5033 · pith_short_12: 6QOT3W5PYL4P · pith_short_16: 6QOT3W5PYL4PT5B3 · pith_short_8: 6QOT3W5P

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/6QOT3W5PYL4PT5B3TCMI46EWYN \
  | 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: f41d3ddbafc2f8f9f43b98988e7896c34c2a99eab9b006a3610b8001e4ebc2df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fde9ddc7775a6901165ff3534e94e10e23c2d408bc10f55671e9582a88b85764",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-25T19:52:50Z",
    "title_canon_sha256": "163f7750d75fbc2c39559bab3128f9c32f1772aef67040692a65f97e6c19123f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5033",
    "kind": "arxiv",
    "version": 1
  }
}