The Stoney–Planck Construction: Interaction Units, Screen Capacity, Quantum Geometry, Microscopic Reconstruction, and Infrared Gravitational Response (Seven-Paper Corpus)

This record presents seven linked preprints forming a unified Stoney–Planck construction, progressing from interaction-defined natural scales through quantum phase-space geometry, finite screen-carrier statistics, microscopic dimensional reconstruction, infrared gravitational response, and unitary information release. The construction is organized around a positive inverse-radius interaction load λ, with universal scale map mλ = √λ mₚ, ℓλ = √λ ℓₚ, Aλ = λℏ, and, for the Schwarzschild screen realization developed in the corpus, bit-equivalent capacity coordinate Nλ = 4πλ / ln 2. Once this normalization is fixed, the seven papers establish the exact composition, transport, reconstruction, reciprocity, dimensional-selection, fluctuation, response, and rigidity structures carried by the Stoney–Planck framework. The central original contribution of the corpus is a theorem-linked architecture connecting interaction load, action, screen capacity, symplectic geometry, finite carrier statistics, primitive dimensional data, effective gravitational coefficients, and horizon information transfer. Classical results—including the Stoney–Planck relation, Bekenstein–Hawking entropy, quantum uncertainty theory, Lovelock tensor classification, Landauer’s principle, and black-hole area quantization—serve as established interfaces. The novel contribution is the exact mathematical structure built across those interfaces: the universal normalization, positive interaction-load composition calculus, action–capacity reciprocity, finite-mode tomography, dimensional reconstruction and curvature selection, infrared gravitational coefficient hierarchy, and unitary support-transfer rigidity. Paper 1 — Stoney–Planck Interaction Units and the Action–Screen Capacity Map.Paper 1 generalizes the Stoney balance from the electromagnetic value α to an arbitrary fixed positive inverse-radius interaction load λ. It proves the resulting √λ mass and length family together with the action coordinate Aλ = λℏ, establishes the unequal-mass balance manifold m₁m₂ = λmₚ², identifies its equal-mass extremizer, and derives reciprocal-load scale identities. For the Schwarzschild screen realization used in the paper, Nλ = 4πλ / ln 2, which yields the exact action–capacity conversion Aλ = (ℏ ln 2 / 4π) Nλ. This establishes the fundamental map linking interaction strength, mechanical action, and screen capacity. Paper 2 — Gauge–Channel Stoney–Planck Units and Positive Interaction–Load Composition.Paper 2 develops the mathematical and physical interface that carries realistic gauge interactions into the universal Stoney–Planck scale map. It distinguishes signed gauge-channel coefficients from positive interaction loads, proves resolution monotonicity and a stochastic data-processing inequality for retained load, derives exact split-Casimir cancellation and root-mean-square load identities, and constructs a typed positive composition calculus incorporating orthogonal sectors, coherent Gram geometry, Schur/parallel reduction, calibration maps, and renormalization-group invariants. A Kubo–Mori susceptibility supplies a concrete positive response geometry for the common-carrier construction. The result is a systematic composition theory for converting multi-channel gauge structure into the positive load variable required by the Stoney–Planck map. Paper 3 — Stoney–Planck Quantum Geometry: Uncertainty, Symplectic Capacity, and Response Coordinates.Paper 3 identifies the conformally symplectic phase-space geometry generated by load-scaled Stoney–Planck coordinates. It derives exact covariance-volume compensation and common-load symplectic-capacity reciprocity. Its central invariant eliminates the interaction load: Aλ cₛₚ(Eλ) = 2πℏνₘᵢₙ ≥ πℏ, with equality at the minimum quantum edge. This identity converts the load-dependent Stoney–Planck scaling into a load-independent action–symplectic-capacity invariant. The paper also separates renormalization-group evolution of the interaction load from physical squeezing of the quantum state and transports the normalization into metrological, thermodynamic, and gravitational source–response coordinates. Paper 4 — Finite-Mode Stoney–Planck Screen Tomography and Capacity–Response Geometry.Paper 4 realizes real-valued screen capacity as the expectation value of a finite integer-valued carrier count. It proves sharp universal and independent-carrier variance bands, including the discrete lower edge f(1 − f). For independent carriers, the first two count moments determine the exact quadratic participation number Kₑff = N² / [N − Var(Ň)], where Ň is the integer-valued carrier count and N = E(Ň). The full unresolved count law reconstructs the complete active occupation-probability multiset through the probability-generating polynomial or, equivalently, through factorial cumulants. The paper transports this finite-mode tomography to area fluctuations and general response observables. Combined with Paper 5, the results produce the capacity–curvature fluctuation ceiling and identify the exact saturation criterion that realizes its scaling exponent. Paper 5 — Microscopic Screen Primitives, Fundamental Constants, and Capacity–Curvature Dimensionality.Paper 5 identifies three positive microscopic dimensional primitives: an action increment per calibrated capacity unit, an infrared signal speed, and a normalized capacity–curvature product. It proves that these quantities form a complete multiplicative basis for mechanical dimensions. Their determination reconstructs ℏ, c, ℓₚ, and G. The paper proves the reporting-base-invariant combination c³/G, develops an affine unimodular logarithmic reconstruction with exact covariance transport and determinant conservation, and establishes that a nontrivial dimensionless coupling such as α enters through an independent dimensionless datum. Its generalized capacity–curvature theorem produces the dimensional selector dₕ = 2s + q − η_N − η_s, which, in the canonical three-dimensional, codimension-one, non-anomalous case, selects first-order curvature. This creates the dimensional bridge from microscopic screen primitives to the curvature order governing the infrared geometric response. Paper 6 — Screen Effective Action and the Einstein Infrared Response.Paper 6 constructs a regulated closed-time-path screen effective action that separates selected stress, causal response, stochastic noise, and Ward closure. Using the primitive-basis theorem of Paper 5, every local geometric coefficient of derivative order s factors into a dimensionless invariant and a universal dimensional basis: Cₛ,ⱼ = q̄ₛ,ⱼ Π_G v∗ ℓₚ^[2(s − 1)]. This factorization establishes an exact infrared suppression hierarchy for higher-curvature sectors. The capacity–curvature selector, the infrared hierarchy, and the four-dimensional Lovelock classification jointly select the Einstein sector within the paper’s defined hypothesis class. The remaining Einstein amplitude is reduced to a single dimensionless closure number q_E. The value q_E = 1/(8π) is the exact Stoney–Planck closure target, giving a precise microscopic normalization condition for the Einstein response. The paper also establishes an invertible reconstruction from gravitational-noise cumulants to finite-screen carrier cumulants whenever the retained response map is injective, creating a direct mathematical bridge from effective gravitational fluctuations back to microscopic carrier statistics. Paper 7 — Screen Capacity, Unitary Carrier Transfer, Physical Information Processing, and Horizon Release.Paper 7 develops the information-processing consequences of the screen-capacity coordinate for specified carriers and physical protocols. It combines information ceilings, cut and Dirichlet load bounds, operation-rate estimates, Landauer–Smarr relations, and the horizon action Aₕ = GM²/c. Its central unitary theorem proves that any isometry preserving the full initial horizon code space requires newly emitted support capacity satisfying N_B ≥ K_H,i − K_H,f. When the horizon saturates its geometric capacity and the outgoing support is supplied entirely by the lost horizon capacity, this becomes the exact rigidity relation N_B = ΔN_H. Exact finite-support saturation then determines the corresponding support-compatible Schwarzschild spectrum. The resulting release laws connect Hilbert-space dimension, horizon-action loss, emitted energy, and information. Combined with Papers 4–6, these results yield action-loss tomography of microscopic transfer probabilities and an Einstein–Landauer reset-power identity. Taken together, the seven papers form a single theorem-linked progression from interaction physics to a capacity-normalized screen description. The construction connects interaction load to natural units, action, gauge composition, quantum phase-space geometry, finite carrier statistics, microscopic dimensional primitives, curvature selection, effective gravitational response, and unitary information transfer while maintaining the exact mathematical typing of each layer. This Zenodo deposit provides a single persistent citation for the complete Stoney–Planck construction and preserves its cross-paper definitions, theorem dependencies, reconstruction maps, and principal novel results as one integrated research object.