Black Holes as Horizon-Mediated Transformers of Realised Physical Distinguishability in Compact S³ Geometry

What if the black-hole information problem begins with the wrong primitive? Rather than treating information as a substance that must be stored, hidden, destroyed, or recovered, this research reframes the problem around Realised Physical Distinguishability (RPD): the physically actual capacity to discriminate between alternative states by operations performed with finite energy, finite time, finite resolution, and access to a specified algebra of observables. Two states belong to the same operational class when no admissible measurement can distinguish them above a fixed threshold. The resulting structure is RPD (M): = 𝒮 (M) / ~, while information appears only as the derived quantity I (M): = log₂ |RPD (M) |. From this perspective, a black hole is not primarily a container of inaccessible bits. It is a horizon-mediated transformer of distinguishability classes. The event horizon changes which operations remain available to an exterior observer. Because the exterior algebra 𝒜ₑxt is only a restricted part of the global algebra, states that remain globally distinct may become operationally indistinguishable from outside. This produces the observer-dependent quotient RPD_𝒜 (M): = 𝒮 (M) / ~_𝒜 and motivates a time-dependent transformation of the form TH (t): RPD_𝒜₁ (M, t₁) ⇝ RPD_𝒜₂ (M, t₂). Horizon crossing therefore need not mean the destruction of physical distinctions; it may instead mean their removal from one accessible channel and their redistribution into others. The paper identifies three candidate channels: null-wave delocalisation, in which causal structure and redshift carry distinctions beyond ordinary localisation; gravitational-geometric re-expression, in which mass, angular momentum, multipole structure, gravitational waves, and memory preserve aspects of the preceding configuration; and quantum-radiative redistribution, in which correlations among Hawking radiation, residual geometry, and possible topological sectors may progressively restore exterior-accessible distinctions. Unitarity is consequently interpreted not as the miraculous reconstruction of a former macroscopic object, but as the possible lawful continuity of distinguishability through changing physical forms. The framework is developed on a compact or effectively compact S³ carrier, while Schwarzschild-, Kerr-, or de Sitter-type horizons remain local models of operational inaccessibility. A quantitative selector branch compares the causal-spectral capacity of S³ with explicitly declared external ceilings such as Bekenstein or holographic bounds. Its central filter is Σgrav^ (P) = min (1, Bceil / (bP ΓR (T) NP (ε) ) ), where ΓR (T) describes the causally accessible fraction of the compact carrier and NP (ε) counts distinguishable spectral modes at resolution ε. In the local regime, a notable cancellation gives Bcausal^ (P) ~ (2bP CP / 3π) (cT/ε) ³, removing the carrier radius R from the leading term and producing the threshold relation (ε_*^ (P) ) ³ = (2bP CP ln 2 / 3π²) cTℓP². This selector is not proposed as a force law or a complete microscopic theory; it is a disciplined diagnostic of how causal access, spectral resolution, and gravitational ceilings constrain physically realisable distinctions. The work further introduces topological horizon capacity as an open research object and explores whether holonomy, Berry phases, the Hopf fibration S¹ → S³ → S², and sectors labelled by QH ∈ ℤ could protect or transform distinguishability during collapse and evaporation. No final solution of the black-hole information paradox is claimed. The research contribution is a sharper foundational question: not “Where are the bits? ”, but “Which physical differences remain realisable, for whom, through which channels, and under what geometric and topological limits? ”