Pith Number

pith:ZQLF3JVG

pith:2026:ZQLF3JVG32CVAADONKCO6SAKGG

not attested not anchored not stored refs pending

Canonical Mandelbrot Cascades on Curves Are Rajchman

Chengbo Xiao, Guozheng Cheng, Hongdou Qu, Menghan Li, Xiang Fang, Yin Cai

arxiv:2607.15966 v1 · 2026-07-17 · math.PR · 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{ZQLF3JVG32CVAADONKCO6SAKGG}

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	2026-07-20T02:19:23.066549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc165da6a6de8550006e6a84ef480a3182c92befcf805bd9187aba1fbbe40595

Aliases

arxiv: 2607.15966 · arxiv_version: 2607.15966v1 · doi: 10.48550/arxiv.2607.15966 · pith_short_12: ZQLF3JVG32CV · pith_short_16: ZQLF3JVG32CVAADO · pith_short_8: ZQLF3JVG

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/ZQLF3JVG32CVAADONKCO6SAKGG \
  | 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: cc165da6a6de8550006e6a84ef480a3182c92befcf805bd9187aba1fbbe40595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9592b38e7a18f8c3c69f4b9a57c91fb61df04ff4fe61c786c94d9f62a6068f7e",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-17T13:53:14Z",
    "title_canon_sha256": "77c26ea6be9d1775b9587a65b86071f81ba6f4470df1f4d85f6b51412f8955e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15966",
    "kind": "arxiv",
    "version": 1
  }
}