IIIbis. Breakdown, Profile, and Class of Intervention: Numerical Signature and the Encounter with the Fourth Turn

The extended exposition of the Third Turn takes three steps with the instrument introduced in the third article — steps that were either impossible or premature within the third article itself. The first step is a numerical operationalisation of the four dimensions of the epistemic deficit profile on a physical substrate. On a minimal model of a bistable collective of cells coupled through gap junctions, two scenarios are computed — formation of an anomalous focus under blocked connectivity and its subsequent normalisation upon restoration of connectivity (a Cx43 intervention). All four dimensions of the profile — distribution of representation, coherence, observability of the boundaries, and capacity for revision — admit numerical estimation and take qualitatively different values across these scenarios. A quantitative expression is obtained for a fundamental property described qualitatively in the third article: the destruction of an established anomalous state requires substantially greater connectivity than its prevention. This hysteresis is the numerical signature of the fourth dimension of the profile; for the model parameters on a lattice N=128 it amounts to 1.45× (the ratio of g₂ ≈ 0.799 to g₁ ≈ 0.553 under the rate-based criterion, t_max = 4000). Parallel computations on N=50 and N=256 give a monotonically increasing dependence g₁(N): 0.10 (N=50) → 0.553 (N=128) → ≈ 2.0 (N=256). A preliminary estimate from a previous iteration, in which N=256 yielded an anomalously low g₁ ≈ 0.096, turned out to be an artefact of the average-based convergence criterion at insufficient integration horizon; recomputation with the rate-based criterion at t_max = 4000 reclassified that value and removed the apparent non-monotonicity. The detailed discussion of this revision is presented in §3.6 as a methodological self-check result. All numerical values of g₁, g₂, and the hysteresis ratio refer to the lattice N=128 and do not claim to estimate the thermodynamic limit. The second step is a numerical operationalisation of the third dimension on an immunological substrate. On a separate ODE system with four variables (tumour, effector T-cells, immunosuppressive pool, antigenic signal) four scenarios are computed: prophylaxis at an early stage, mono-vaccination on an established cold focus, and two forms of vaccination within the combined protocol (EBRT — External Beam Radiotherapy; ADT — Androgen Deprivation Therapy) — within the ADT vulnerability window and after the full ADT course. It is shown that mono-vaccination on an established cold focus is not achievable within the surveyed range of TCR coverage (D₂ > 25, not reached within D ∈ [0.5; 25]), whereas the EBRT + ADT preparation reduces the required coverage by more than two orders of magnitude. A sensitivity analysis along three clinically meaningful axes (patient age, mutational load × vaccine target breadth, lymph-node damage from EBRT) yields a robust picture of the window-vaccination advantage over the post-ADT variant, especially in elderly patients and at low mutational load. The third step is a deployment of the class of interventions to which the profile methodologically points and which exists in research form. The class is defined structurally: interventions that act not on the substrate and not on individual cells, but on the collective's distributed representation of its own state. Levin's bioelectric corpus offers an operational route to numerical estimation of the second dimension (coherence). CRISPR editing of connexin and ion-channel expression is an example of the class in which a digital sequence directly reorganises a biological state. Personalised mRNA vaccines with neoantigens within the EBRT + ADT combined protocol exemplify intervention on the third dimension through construction of an immune metarepresentation of the focus's specificity; the numerical computation provides a quantitative characterisation of this intervention. The extended exposition inherits all limitations of the third article and adds new ones: the numerical models of Sections 3 and 5.3.1 are minimal reductions, their results are structural rather than quantitatively transferable to specific tissues. This leaves open the question of clinically relevant parameter values — a task that requires calibration on tissue for the instrument in each dimension.

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