Pith Number

pith:KKBZGMRV

pith:2013:KKBZGMRVXAR5PTYC2BH2OILM55

not attested not anchored not stored refs pending

Correction and strengthening of "How large are the level sets of the Takagi function?"

Pieter C. Allaart

arxiv:1306.0167 v2 · 2013-06-02 · 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{KKBZGMRVXAR5PTYC2BH2OILM55}

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	2026-05-18T02:30:32.616036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5283933235b823d7cf02d04fa7216cef679fc35b3afeeea368ce6d6eb4c99f4a

Aliases

arxiv: 1306.0167 · arxiv_version: 1306.0167v2 · doi: 10.48550/arxiv.1306.0167 · pith_short_12: KKBZGMRVXAR5 · pith_short_16: KKBZGMRVXAR5PTYC · pith_short_8: KKBZGMRV

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/KKBZGMRVXAR5PTYC2BH2OILM55 \
  | 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: 5283933235b823d7cf02d04fa7216cef679fc35b3afeeea368ce6d6eb4c99f4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b8b18dc24824d9d9e2282b170e462e64bc67d030440797ff189db16901eff5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-06-02T02:35:08Z",
    "title_canon_sha256": "2b82c8a3867e15e638eea48b86f069e9471dfaec1696b39d7af21ebd06cf1e77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0167",
    "kind": "arxiv",
    "version": 2
  }
}