Pith Number

pith:UWNPDWCU

pith:2026:UWNPDWCUICFPBLTBFAKUNL2OBO

not attested not anchored not stored refs pending

On the possibility of differential-algebraic elimination of the spinor field from the Maxwell--Dirac electrodynamics

Andrey Akhmeteli

Spinor components are uniquely fixed by the electromagnetic field and its derivatives in the Maxwell-Dirac system.

arxiv:2602.15907 v3 · 2026-02-16 · quant-ph

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Claims

C1strongest claim

Our results indicate that, generically, the spinor components are uniquely determined by the electromagnetic field and its derivatives. Furthermore, the fourth-order time derivatives of the components of the electromagnetic four-potential are uniquely determined by derivatives of the lower order with respect to time. These findings strongly suggest that the spinor field can be differential-algebraically eliminated.

C2weakest assumption

The truncated power-series solution is assumed to be sufficiently generic that the matrix-rank conclusions apply to physically relevant solutions; the analysis may fail for special or singular cases not captured by the truncation.

C3one line summary

Generically the spinor components are uniquely determined by the electromagnetic field and derivatives, allowing fourth-order time derivatives of the EM four-potential to be fixed by lower-order ones and enabling a Cauchy problem in EM variables alone.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T02:07:21.570075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a59af1d854408af0ae61281546af4e0b898dfe15256cb4c8d5acd06754fc4813

Aliases

arxiv: 2602.15907 · arxiv_version: 2602.15907v3 · doi: 10.48550/arxiv.2602.15907 · pith_short_12: UWNPDWCUICFP · pith_short_16: UWNPDWCUICFPBLTB · pith_short_8: UWNPDWCU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UWNPDWCUICFPBLTBFAKUNL2OBO \
  | 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: a59af1d854408af0ae61281546af4e0b898dfe15256cb4c8d5acd06754fc4813

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba0c0401738c05dbc0d708f9b35fd08071af8ec0c0bd1b3a6a38884bd1f9aded",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-02-16T10:58:28Z",
    "title_canon_sha256": "c8806273b48989ca19efcb767e61f29ba2bcb10285aed16bbe33118cba6ddc28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.15907",
    "kind": "arxiv",
    "version": 3
  }
}