Pith Number

pith:BXQXZO7W

pith:2026:BXQXZO7WLPTRA4IKTLUPB253HY

not attested not anchored not stored refs pending

Ptolemy's Equant Equates to a Universal Dynamical Clock via Machine Learning

Celso Grebogi, Jingdong Zhang, Luan Yang, Murilo S. Baptista, Qunxi Zhu, Wei Lin, Zefeng Zhang

arxiv:2607.15472 v1 · 2026-07-16 · math.DS · cs.LG · physics.bio-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BXQXZO7WLPTRA4IKTLUPB253HY}

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	2026-07-20T00:18:35.812780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0de17cbbf65be710710a9ae8f0ebbb3e13c45bc4ef3de0f744a81d80f8caa192

Aliases

arxiv: 2607.15472 · arxiv_version: 2607.15472v1 · doi: 10.48550/arxiv.2607.15472 · pith_short_12: BXQXZO7WLPTR · pith_short_16: BXQXZO7WLPTRA4IK · pith_short_8: BXQXZO7W

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/BXQXZO7WLPTRA4IKTLUPB253HY \
  | 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: 0de17cbbf65be710710a9ae8f0ebbb3e13c45bc4ef3de0f744a81d80f8caa192

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c66cf6f671972963b7dbdd89afcc6d551a73a6e6bc7eb1c6ac6a68c10554ef5a",
    "cross_cats_sorted": [
      "cs.LG",
      "physics.bio-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-07-16T21:42:33Z",
    "title_canon_sha256": "9037aff1644981dfff02908473001bf475064b24456e44ead6e60059ba205000"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15472",
    "kind": "arxiv",
    "version": 1
  }
}