Enter, Big04-A-v6, 2026, pp. 1-58
Big04-A: External Radiation Labels and Causal-Access Certificates on Prescribed Comparison Geometries
Ngo Cheung
24 October 2026
Abstract
We separate coefficient identifiability, causal accessibility, and finite-channel recovery on a prescribed spatially flat comparison geometry. A radiation-type prefix carries external labels Tᵣ ∝ U^{1/4}κ^{3/4}/a and Sᵣ ∝ (U/κ)^{3/4}. We give their calibration inverses, exact absolute and relative minimax risks, and randomized-decision lower certificates. For a relative coefficient window of width δ, the radiation relative risk is tanh (3/4artanh δ), not δ; equal endpoint weights certify absolute loss, whereas relative loss requires unequal weights.
Under an explicitly stated located-circuit contract, a source with no causal path to the complete receiver interface induces a joint replacement channel, even for correlated receiver outputs. Its optimized half-diamond recovery error is 1 − d⁻². We prove the robust envelope, quantify partially dark mixtures, and distinguish joint replacement certificates from products of marginal certificates. At a fixed external temperature label, identity, energy-basis dephasing, and Gibbs replacement are thermal operations with different recovery errors.
For smooth futures obeying a declared bound on d/(dt)(1/H), we prove the exact open interval of early-junction horizon radii and its minimax consequences. General-w label dictionaries, late-label supply cases, two-prefix comparison, and spectator-resource qualifications are included. The contribution is a self-contained collection of separation and certification results. No physical dark-radiation species, host Hilbert-space dimension, temperature, entropy, Einstein dynamics, or Page curve is derived.
Version 5 adds, by insertion only, the sharp relative risk tanh (C_Kδ/(κ₀(1 − δ²))), C_K = πc⁵/(GK²), of the late dimension label at a supplied terminal rate K; a local re-proof of the two-label reduction of the hybrid-cut closed forms; and documentary separations from the energy-constrained replacement floor, the vacuum term, four-label closed sectors, and a rate-family energy minimax.
Version 6 adds, by insertion only, seven groups of results on the same prescribed host. (i) The radiation labels depend on (κ, α) only through z = κ³/α and on no declared ordinary/dark/vacuum split; the fibre of the split-blind data together with both labels is exactly the product of the split fibre and the coefficient orbit, so a calibrated coefficient selects no split and a declared split selects no point of the orbit. (ii) A finite adaptive protocol whose initial law, selection kernels and complete accessible process are coefficient-blind has one law for every κ; it cannot calibrate either label, and on a supplied window it cannot beat the risks 1/2(u − ℓ) and tanh (3/4artanh δ). (iii) For general w, ∂ln T_w/∂ln κ = 3w/(1 + w) and S_w is constant in time on every supplied scale factor; the two-prefix comparison is the equal-exponent case of a cross-ratio certificate, and a declared change of w breaks its common-rescaling invariance. (iv) On the prefix the apparent radius Bz² is fixed by early data while the event radius is not; under the rate bound the event radius strictly exceeds it, and a sharp modulus bounds horizon differences. (v) The absolute and relative risks are instances of one fibre principle. (vi) The floor 1 − d⁻² differs from the Shredder floor 1 − 1/d by (d − 1)/d² and is neither a magic-fibre response nor a Page curve. (vii) A constant volume term preserves every label and selects no point of the orbit. Further inserted results, re-proved from the author's draft of version-6 additions, give the general-w quotient and epoch-change ratios, two-point bounds under approximate blindness, calibration with a supplied normalization window, the finite-settling horizon functional, the fact that a fixed terminal rate alone leaves every positive radius R₀ ∈ (0, ∞), and an exact clock-feedback factorization test. These results matter because they replace isolated calculations by checkable separations: none of them selects a split, a future, or a vacuum term, and κ is calibrated only by an added supply such as an exact label at fixed supplied normalization. Printed radii and risks are calculations, not measurements. A separate conditional prediction layer states six theorems under supplied closures, which are optional hypotheses outside the ledger: a radiation consistency relation with redshift drift −H₀z(1 + z) on the prefix interval; the relation 2s_H − s_T = 3, which is equivalent to a supplied general-w closure; exact finite-time reception envelopes under the rate bound, with their attainment cases; a drift envelope; logarithmic tails with and without an event horizon; and an information-isolation threshold. It makes no observational claim and uses no measured number.
Standing ledger (verbatim from Section): Host A and Host B stay separate. Host C is not created. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N is not discharged. N-Ins.4 stays unresolved. U6-sel is not moved. Gate 0 stays NOT_SUPPLIED. ST4b stays NOT_SUPPLIED. No quantum coefficient is admitted. No quantum coefficient is derived. No Einstein dynamics, derived metric, spacetime emergence, Page curve, island, vacuum-energy computation, or quantized relational time without an external clock is claimed. A source record is not a premise. The OpenAI catalogue is not a premise. noindentCitations identify source records only; no proof transfer.
Bibliographic record
- Title
- Big04-A: External Radiation Labels and Causal-Access Certificates on Prescribed Comparison Geometries
- Author
- Cheung, Ngo
- Publication date
- 2026/10/24
- Institution
- Enter
- Report number
- Big04-A-v6
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 58
- Language
- en