Pith Number

pith:WDWT37MA

pith:2026:WDWT37MAKLYORLSHKY5EGPQI73

not attested not anchored not stored refs resolved

Countable basis for free electromagnetic fields

Ivan Fernandez-Corbaton

Free Maxwell fields admit a countable basis of polychromatic single-photon waves that lie inside the Hilbert space.

arxiv:2601.12911 v1 · 2026-01-19 · math-ph · math.MP · physics.optics

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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.

Claims

C1strongest claim

The basis set is countable, and the Hilbert space is separable and isomorphic to ℓ². Each basis vector represents a polychromatic single-photon wave with quantized energy and a wavelet-like temporal dependence.

C2weakest assumption

That four commuting operators exist whose simultaneous eigenstates with integer eigenvalues form a complete basis for the Hilbert space of free Maxwell fields.

C3one line summary

A countable basis of polychromatic single-photon waves for free Maxwell fields is constructed as simultaneous eigenstates of four commuting operators with integer eigenvalues, making the space isomorphic to ℓ².

References

47 extracted · 47 resolved · 1 Pith anchors

[1] The second row, which contains Eq

[2] J. S. Lomont and H. E. Moses, The representations of the inhomogeneous lorentz group in terms of an angular momentum basis, Journal of Mathematical Physics5, 294 (1964) 1964

[3] H. A. Kastrup, Conformal group and its connection with an indefinite metric in hilbert space, Phys. Rev.140, B183 (1965) 1965

[4] H. E. Moses, Transformation from a linear momentum to an angular momentum basis for particles of zero mass and finite spin, Journal of Mathematical Physics6, 928 (1965) 1965

[5] H. E. Moses, Transformation from a linear momentum to an angular momentum basis for relativistic particles of nonzero mass and any spin, Journal of Mathematical Physics6, 1244 (1965) 1965

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:45:06.066090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0ed3dfd8052f0e8ae47563a433e08fef644980b716e77a9954824b1cf321acb

Aliases

arxiv: 2601.12911 · arxiv_version: 2601.12911v1 · doi: 10.48550/arxiv.2601.12911 · pith_short_12: WDWT37MAKLYO · pith_short_16: WDWT37MAKLYORLSH · pith_short_8: WDWT37MA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WDWT37MAKLYORLSHKY5EGPQI73 \
  | 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: b0ed3dfd8052f0e8ae47563a433e08fef644980b716e77a9954824b1cf321acb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "226f722d01823a68592febf2cfba1d02a366e19b0cb05bbf9a33e66751b1987d",
    "cross_cats_sorted": [
      "math.MP",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-01-19T10:05:08Z",
    "title_canon_sha256": "847ac6d8a53413f564d1afb12046d10e8c5227454a0ef5f941633a0a8210fc21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.12911",
    "kind": "arxiv",
    "version": 1
  }
}