Pith Number

pith:B3JXQT3I

pith:2026:B3JXQT3IU2RANTSFDQHFXGOZE2

not attested not anchored not stored refs pending

An almost sure invariance principle for the Takagi-van der Waerden class functions

Yuzaburo Nakano

arxiv:2605.23461 v1 · 2026-05-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B3JXQT3IU2RANTSFDQHFXGOZE2}

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	2026-05-25T02:01:55.313161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ed3784f68a6a206ce451c0e5b99d92694fad04b79a5550d8a1f4d9371a52f34

Aliases

arxiv: 2605.23461 · arxiv_version: 2605.23461v1 · doi: 10.48550/arxiv.2605.23461 · pith_short_12: B3JXQT3IU2RA · pith_short_16: B3JXQT3IU2RANTSF · pith_short_8: B3JXQT3I

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/B3JXQT3IU2RANTSFDQHFXGOZE2 \
  | 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: 0ed3784f68a6a206ce451c0e5b99d92694fad04b79a5550d8a1f4d9371a52f34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffe5fb3b9f1380eba93f3b29ed4969606d59d503fffbd11edc1315c564f0d949",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-22T10:22:34Z",
    "title_canon_sha256": "301c07172a3e6f0ba9828520a700edaed58ab72bb297908870a8fb2c002acaf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23461",
    "kind": "arxiv",
    "version": 1
  }
}