Pith Number

pith:ZC6Y4MLQ

pith:2011:ZC6Y4MLQ4JGFA63DBUPSX6Q5QS

not attested not anchored not stored refs pending

On the distribution of the cardinalities of level sets of the Takagi function

Pieter C. Allaart

arxiv:1107.0712 v2 · 2011-07-04 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZC6Y4MLQ4JGFA63DBUPSX6Q5QS}

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	2026-05-18T03:59:47.766985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8bd8e3170e24c507b630d1f2bfa1d84b7b5cf1ce65d2774d49c6b347dd7a38f

Aliases

arxiv: 1107.0712 · arxiv_version: 1107.0712v2 · doi: 10.48550/arxiv.1107.0712 · pith_short_12: ZC6Y4MLQ4JGF · pith_short_16: ZC6Y4MLQ4JGFA63D · pith_short_8: ZC6Y4MLQ

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/ZC6Y4MLQ4JGFA63DBUPSX6Q5QS \
  | 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: c8bd8e3170e24c507b630d1f2bfa1d84b7b5cf1ce65d2774d49c6b347dd7a38f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6758746c630cb0dd166b11acb837a16f217d559fc329893f4d8bc4a4c912b2c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-07-04T19:51:44Z",
    "title_canon_sha256": "b0eb6fd69b553b0ba77b5738423fb286c8d7802660b29c6c6cd7f222cb5494dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0712",
    "kind": "arxiv",
    "version": 2
  }
}