Pith Number

pith:AZCCZI2W

pith:2025:AZCCZI2WFRATOUU3OFYA5KENJF

not attested not anchored not stored refs pending

Exact Solutions to the Klein--Gordon Equation via Reduction Algebras

Dwight Anderson Williams II, Jonas T. Hartwig, Lillian Ryan Uhl

arxiv:2507.04572 v1 · 2025-07-06 · math.RT · 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{AZCCZI2WFRATOUU3OFYA5KENJF}

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	2026-07-05T11:32:49.964247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06442ca3562c4137529b71700ea88d4959ed77e7ba4152a06ec29994883270c7

Aliases

arxiv: 2507.04572 · arxiv_version: 2507.04572v1 · doi: 10.48550/arxiv.2507.04572 · pith_short_12: AZCCZI2WFRAT · pith_short_16: AZCCZI2WFRATOUU3 · pith_short_8: AZCCZI2W

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/AZCCZI2WFRATOUU3OFYA5KENJF \
  | 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: 06442ca3562c4137529b71700ea88d4959ed77e7ba4152a06ec29994883270c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "560f543f42c7e20b33d9a2afdf855e63aae23789ce8331c682b2f04744592cd8",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2025-07-06T23:10:13Z",
    "title_canon_sha256": "03faa1626db632de4e86ff0cdb2e67672daafcec36ed5b635143493e32870063"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04572",
    "kind": "arxiv",
    "version": 1
  }
}