Pith Number

pith:GCUIJPWQ

pith:2026:GCUIJPWQY5QX2BAQPE5X4R2MAW

not attested not anchored not stored refs pending

From Quantum-Plane Hamiltonians to Jackson Dynamics: Dilation Representations, Normal Symbols, and Euclidean Limits

Xiaomei Yang, Zhiliang Deng

arxiv:2607.26454 v1 · 2026-07-29 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCUIJPWQY5QX2BAQPE5X4R2MAW}

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	2026-07-30T01:20:33.027058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

30a884bed0c7617d0410793b7e474c05bd2b4349782240a14317253ae2f59a80

Aliases

arxiv: 2607.26454 · arxiv_version: 2607.26454v1 · doi: 10.48550/arxiv.2607.26454 · pith_short_12: GCUIJPWQY5QX · pith_short_16: GCUIJPWQY5QX2BAQ · pith_short_8: GCUIJPWQ

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/GCUIJPWQY5QX2BAQPE5X4R2MAW \
  | 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: 30a884bed0c7617d0410793b7e474c05bd2b4349782240a14317253ae2f59a80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "762014751861944da43738c60ab9d5ac9ecd68d82aa256d2f59865030091ea9d",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-29T04:09:45Z",
    "title_canon_sha256": "50f4b2b277e62bcb168a80f3924c45b434e8a37ee6025917d17428e6baa62a43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26454",
    "kind": "arxiv",
    "version": 1
  }
}