Enter, En04-B-v4, 2026, pp. 1-61
En04-B Finite Carriers on Prescribed Enter Spacetimes: Geometric Blindness, the Shredder Cut, and Host-Fibre Certificates
Author unset
October 25, 2026 (version 4; versions 1–3: October 25, 2026)
Abstract
We study finite quantum carriers placed on prescribed Enter spacetime hosts, in which the metric is an input and never an output, and ask when a declared finite probe register shows a code-dependent response. The main findings, and why each matters, are the following. (1) Leakage equals the probe radius. For a controlled probe the complete-complement leakage equals the trace-distance radius of the supplied probe states; a quantity defined by an optimization over channels becomes an explicit invariant of the coupling. (2) Optimal response equals the diameter. The largest normalized response of any probe observable is the trace-distance diameter of the probe states, attained by a Helstrom observable, so 1/2D ≤ leak ≤ D and γ ≤ 2 leak; every finite geometric witness is bounded by distinguishability that the coupling itself supplies. (3) Fixed-field sampling. A finite compression of a fixed continuum scalar (current, Wick square, curvature) has zero witness for every code pair exactly when the compressed matrix is scalar; a nonzero witness is a sampling response, not a field or metric update, and a constant field is blind under every coupling. (4) Coupling-slot nonidentifiability. Data that do not depend on the carrier-to-probe coupling, including named host readings and independent phase data, cannot determine leakage or a witness: every rule has two-point error at least half the target separation, which locates the missing declaration exactly. (5) Robust spectator envelope. Within distance ε of a spectator coupling every normalized witness is at most b(ε) = 2ε√(1 − ε^2) (ε ≤ 1/√(2)); the bound is attained for every ε by the declared holonomy observable whenever sin μ ≠ 0, and by a probe Helstrom observable for every μ, so small implementation errors cannot imitate large response. (6) Correlation-hidden response. If the probe marginal stays within δ of a pure state, the complete complement is within the sharp distance φ(δ) = 1/2(δ + √(4δ − 3δ^2)) of a product, replacing the earlier 2√(δ); with both marginals constant and pure outputs, hidden response is at most √(1 − max {0, 2λ_max − 1}^2), attained, while an exact rational certificate shows that this bound fails for mixed outputs. Marginal tests alone cannot certify blindness. (7) Curvature sampling on a curved host. On the settled Host-B neck, with 𝓡_B = −2b^2/(a_{∞}^2(ℓ^2 + b^2)^2), finite neck modes give a nonzero sampling witness while the metric and curvature are unchanged; on the constant-curvature host DSS_H every curvature compression is blind. Curvature can be sampled by a probe without being moved by it. (8) Parameter estimation versus quantum recovery. Echo-only reports, however informative about the deficit, give entanglement fidelity exactly 1/d^2, below the shredder value 1/d; host diagnosis is not logical recovery. The echo reading is monotone in the deficit only locally, on compact parameter windows and short gates. (9) Side-register floor. If the complete output is a classical record together with a k-dimensional quantum register that is the only retained quantum system, and the decoder is any record-dependent quantum operation with fresh ancillas, then F_e ≤ k/d and the error is at least 1 − k/d, attained by a cyclic-window channel; with a pre-shared entangled resource the bound fails (teleportation gives F_e = 1 at k = 1), so the floor measures retained quantum access exactly. (10) Conditional cosmological extrapolations. Six proposed extrapolations towards open-system models of primordial perturbations become conditional theorems on declared finite data. If a model supplies a carrier with declared sectors, every joint witness obeys γ ≤ 2 leak, attained by a family in which every marginal on fewer than all sectors is fixed and only an all-sector correlator responds; retained coherence and leakage obey c^2 + 4 leak^2 ≤ 1 for every carrier, with equality v^2 + 4 leak^2 = 1 for pure controlled probes; the curvature sampler reads Δx · ∇𝓡 with an explicit cubic remainder, vanishes for constant curvature of any size, and is exact on the Host-B neck; a normalized response γ excludes every implementation within ε < sin (1/2arcsin γ) of a spectator, sharply; more precise data of an admitted type never identify the coupling, while one coupling-sensitive datum estimates leakage at rate 1/(2√(n)); and classical-looking records with input-independent marginals can still allow full recovery, while all retained quantum dimension, pre-shared systems included, bounds F_e ≤ kd_B/d. A finite model meets four declared programme criteria at once. This layer matters because it states exactly which finite data a cosmological model must supply before any of these constraints applies, and it corrects the proposed statements where they were loose; none of its results is a cosmological prediction. Several ingredients are standard finite-dimensional facts (diameter bounds, two-point minimax, measure-and-prepare floors); the contribution lies in their integration into a typed host–carrier interface and in the sharp constants. No metric derivation, selected matter law, quantum coefficient, Page curve, or gravitational endpoint is constructed. Standing ledger. No quantum coefficient. The coefficient slot stays unfilled. No Einstein dynamics, derived metric, spacetime emergence, de Sitter state, Page curve, or gravitational endpoint. Host A and Host B stay separate. Host C is not created. O.1 stays NOT_CLOSED. Gate 0 and ST4b stay NOT_SUPPLIED. XV-B is not opened. XVI-N is not discharged. H2, I3, J2, T3 stay unresolved. U6-sel is not moved. Magic is not leakage. Residual response is not geometric response. Readout-and-drop is not physical deletion. A finite probe witness is not an identification with a field or metric degree of freedom. Cited sheets, including OpenAI catalogue entries and Big05-A, are source records and are not premises. Parents are not revised. En05–En09 are not rewritten. No quantum coefficient is admitted. No numerical κ is supplied. Citations identify source records only; no proof transfer. Every newly cited sheet is a source record; not a premise. En04-B is not registered in the companion (its manuscript API route returned 404 on October 25, 2026), and no browse link is claimed for it.
Bibliographic record
- Title
- En04-B Finite Carriers on Prescribed Enter Spacetimes: Geometric Blindness, the Shredder Cut, and Host-Fibre Certificates
- Publication date
- 2026
- Institution
- Enter
- Report number
- En04-B-v4
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 61
- Language
- en