axiomdefinitionalappendix
PS--C4 (Ray invariance)
axiom:appC_psc4
Exact LaTeX body
\begin{axiom}[PS--C4 (Ray invariance)]
\label{axiom:appC_psc4}
$\mathcal{C}_{\Obs}(e^{i\theta} \tilde\psi_{\Obs}, \Pi)
= \mathcal{C}_{\Obs}(\tilde\psi_{\Obs}, \Pi)$ \quad (cf.~\ref{definition:appC_coherence_functional}).
The corresponding complex homogeneity is phase-faithful: amplitudes scale through
$\overline a a=|a|^2$, not through the real shadow $a^2$.
\end{axiom}Reference roles
| Target | Role | Logical support |
|---|---|---|
definition:appC_coherence_functional | cf_near_match | yes |
Complete structured record
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"definition:appC_coherence_functional"
],
"file": "appendix_dual_horizon.tex",
"id": "axiom:appC_psc4",
"label": "axiom:appC_psc4",
"latex_body": "\\begin{axiom}[PS--C4 (Ray invariance)]\n\\label{axiom:appC_psc4}\n$\\mathcal{C}_{\\Obs}(e^{i\\theta} \\tilde\\psi_{\\Obs}, \\Pi)\n= \\mathcal{C}_{\\Obs}(\\tilde\\psi_{\\Obs}, \\Pi)$ \\quad (cf.~\\ref{definition:appC_coherence_functional}).\nThe corresponding complex homogeneity is phase-faithful: amplitudes scale through\n$\\overline a a=|a|^2$, not through the real shadow $a^2$.\n\\end{axiom}",
"lean_alignment": {
"conditions": [
"Gleason-type uniqueness (axioms force the Born form in d>=3) and PS-C5 stay open; only the forward direction Born => axioms is certified",
"continuum charge/action integrals stay open; the discrete conservation mechanism is certified"
],
"countermodels": [],
"full_record": "bib/principia_lean_alignment.json",
"kernel_certified": true,
"notes": [
"The Born form is phase-invariant (ray invariance).",
"The exact kernel supports the phase-faithful correction without certifying the PS axiom as derived."
],
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"statuses": [
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"witnesses": [
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"Book7QuantumGleason.vectorExpectation_globalPhase",
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"Born.psc4_ray_invariance"
]
},
"line": 612,
"macros_used": [
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],
"matter_region": "appendix",
"matter_role": "appendix_expansion",
"name": "PS--C4 (Ray invariance)",
"proof_status": "definitional",
"ref_roles": [
{
"context": "_psc4} $\\mathcal{C}_{\\Obs}(e^{i\\theta} \\tilde\\psi_{\\Obs}, \\Pi) = \\mathcal{C}_{\\Obs}(\\tilde\\psi_{\\Obs}, \\Pi)$ \\quad (cf.~\\ref{definition:appC_coherence_functional}). The corresponding complex homogeneity is phase-faithful: amplitudes scale through $\\overline a a=|a|^2$, not through",
"label": "definition:appC_coherence_functional",
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