Pith Number

pith:QOQONLGZ

pith:2026:QOQONLGZOD72WCTZ7FRYCLGBU7

not attested not anchored not stored refs pending

Gauge invariant generalizations of the Proca equation and the Yang-Mills-Proca equation

Nikolay Marchuk

arxiv:2606.20828 v1 · 2026-06-18 · 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{QOQONLGZOD72WCTZ7FRYCLGBU7}

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	2026-06-23T00:12:00.016879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83a0e6acd970ffab0a79f963812cc1a7dae8e69952773f2dbb35c02ecf24604a

Aliases

arxiv: 2606.20828 · arxiv_version: 2606.20828v1 · doi: 10.48550/arxiv.2606.20828 · pith_short_12: QOQONLGZOD72 · pith_short_16: QOQONLGZOD72WCTZ · pith_short_8: QOQONLGZ

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/QOQONLGZOD72WCTZ7FRYCLGBU7 \
  | 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: 83a0e6acd970ffab0a79f963812cc1a7dae8e69952773f2dbb35c02ecf24604a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b909d758e2f01ef83b2c487c7f8ccd1ef5c29766ea5b39663e0db9df09b4f5",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-18T18:12:39Z",
    "title_canon_sha256": "a136d37e5fd2a4c305d5741ded5ba7da4f99f9b481469224dbf661b88667d0ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20828",
    "kind": "arxiv",
    "version": 1
  }
}