Plant/sensor/controller/surveillance

### PDF page 54 hepatocytes, and other tissues. Under this framework, exercise-induced and dietary- restriction-induced adaptations require mitochondrial ROS production at intermediate levels; antioxidant supplementation quenches the signal and blocks the adaptation. The four-component framework agrees with the explanandum but offers a structurally different account. Mitohormesis posits a positive role for mitochondrial ROS at intermediate levels — a U-shaped dose-response from a single mechanism. The four-component framework reads the same data as a Mode 2-then-Mode 1 trajectory: at low β, Φ* < Φ_surv (Mode 2 toe, no adaptation); at intermediate β, Φ* enters Σ’s dose-proportional band (adaptive zone — what mitohormesis calls “the optimal mitochondrial ROS”); at high β, β > β_c (Mode 1 collapse). The framework does not require ROS to be a positive signal in itself; the U-shape comes from the geometry of the (V, β) plane. Discriminating prediction. Mitohormesis predicts that compartment-specific mitochondrial- ROS interventions (mito-targeted antioxidants vs. cytosolic antioxidants) should differentially affect adaptive responses. The four-component framework predicts that any intervention reducing β (regardless of compartment) blocks adaptation if it drops Φ* into Σ’s toe — and Mode 3 (compartmental isolation) is when the two predictions diverge. In ageing tissue with high SASP burden and Mode 3 already active, mito-specific antioxidants may fail to block adaptation while cytosolic antioxidants may block adaptation. This is testable in single-cell flow studies. 13.2 Two-Hit Hypothesis for NRF2 in cancer The two-hit framework [13] proposes that NRF2 activation in normal tissue is protective (first hit prevents transformation), while subsequent KEAP1 mutation (second hit) constitutively activates NRF2 in established tumours conferring chemoresistance. The four-component framework recovers this as Corollary 5 with a structural reading: the first regime is Mode 1 prevention (V_ctrl healthy, V responsive to chronic Φ, β kept below β_c); the second regime is Mode 4b → Mode 2 cascade (KEAP1 LoF locks V_set at V_max, V is pinned, Φ* drops into Σ’s toe, DDR-mediated apoptosis fires below threshold under chemotherapy, tumour resists). The two hits are reframed as two state transitions of the controller: from healthy V_ctrl to Mode 4b-high. 14. Discussion 14.1 What the framework offers The framework’s contribution is structural unification through a single architectural template — plant + sensor + slow adaptive controller + parallel surveillance readout — that admits four threshold-typed failure modes, role-typed by which architectural component supplies the violated threshold. Within the redox/NRF2 instantiation, all four modes are derivable in closed form, three are empirically anchored in published clinical and experimental data, and one (Mode 4c) is a forward structural prediction conditional on cohort regressions described in §6.2.3. Page 53 of 213 Dose Response ### PDF page 55 14.2 The four-mode partition is sharp at the architectural level The partition is sharp at the architectural level: each mode is typed by which role’s threshold is violated, not by the threshold value. This is what makes Proposition 5’s role- typed disjointness operationally consequential: the modes are not on a continuum, and continuous deformation cannot connect them without crossing the role boundary. The diagnostic and intervention implications follow: Mode 4 → 3 → 2 → 1 intervention ordering, Mode 3 vs Mode 4c discrimination via P17, and the cascade-corrected fragility index. 14.3 What the framework does not offer The framework does not predict individual cell fate from individual cell parameters; it makes population-scale and cohort-scale claims under A5. It does not specify which molecular pathway implements Σ for a given tissue and readout — that is empirical input. It does not address sub-cellular signalling spatial dynamics within a single cell (concentration gradients), which would require an extension of 𝒞_full from a vector projection to a function-valued projection. It does not address coupled-cell dynamics in tissue except through the SASP-style fidelity-loss mechanism of §5.2.1; richer tissue-scale couplings (gap-junction-mediated redox sharing, paracrine NRF2 signalling) are extensions worth pursuing — these would add a tissue-scale fifth component to the architecture if structurally distinct from the cellular ℳ_fast / 𝒞 / Σ / V_ctrl. 14.4 Scope and limitations The framework does not claim every biological phenomenon is a four-component failure. It claims that within the class of bounded adaptive systems with a closed feedback loop satisfying A1–A4 and A2b, failures partition structurally into the four threshold-types of Proposition 5. Phenomena outside this class — developmental bifurcations without flux- coupled surveillance, immune memory failures without graded readout, structural-protein aggregation diseases not coupled to a slow controller — are not claimed to fit the classification. Noise and stochasticity. The dynamics (1)–(3a) are deterministic ODEs, but real biological systems are stochastic at the single-cell level: protein numbers fluctuate, sensor signals are noisy, surveillance thresholds are not crisp. Crisp threshold-crossing language (β > β_c, Φ < Φ_surv) should be read as the deterministic limit of stochastic crossings whose probabilities depend on noise amplitude. We expect the qualitative four-mode classification to survive stochastic extensions — each mode corresponds to a distinct mean-field fixed- point structure that noise probabilistically samples — but the sharpness of the classification depends on signal-to-noise ratios that are tissue- and readout-specific. A full stochastic treatment is a worthwhile extension that would yield event-rate predictions rather than crisp threshold criteria. The framework as presented should be understood as the deterministic skeleton; stochastic flesh remains to be added. Mode 4c provisional status. As flagged in §6.2.3 and §11 P17, Mode 4c remains a structural prediction without empirical validation. Its operational deployment via P17 Page 54 of 213 Dose Response ### PDF page 56 depends on cohort regressions that have not yet been performed. The framework’s claim is that Mode 4c is in-principle measurable and structurally distinct from Mode 3 effects on closed-loop behaviour; whether the predicted V-Φ-misalignment-tracks-fitness pattern obtains in real cohorts is the empirical question that future work must answer. 14.5 Future directions Five directions look productive. (i) Empirical anchoring of A4 for non-DDR readouts. Single-cell flow dose-responses for UPR, PGC-1α, and HIF-1α readouts would either firm up Corollaries 3, 4, 6 quantitatively or expose A4-violations that would refine the framework. (ii) Quantitative Mode 3 + senolytic-rescue diagnostics. Compartment-resolved redox probes joint with V_ctrl-bandwidth measurements and senolytic-stratified V-Φ trajectories should distinguish Mode 3 phenotypes (resolved by senolytic) from genuine Mode 4c phenotypes (controller-internal calibration drift, persistent post-senolytic) in ageing populations — operationalising P17. (iii) Quantitative δ for Mode 4c. Population-scale studies of V_set,actual versus environmental V_set,fitness in tissues with diverse exposure histories would calibrate the calibration tolerance δ. (iv) Mode 4a controller-bandwidth pharmacology. Constitutive low-grade NRF2 induction (sulforaphane, low-dose bardoxolone methyl, dimethyl fumarate co-administration during disturbance-rich exposures) is the framework’s suggested intervention path for Mode 4a; pre-clinical models would test it. (v) Closed-form thresholds in non-redox instantiations. The calcium-handling sketch in §15.1 maps R1–R4 onto well-characterised cardiomyocyte components and demonstrates the Mode 4b → Mode 2 cascade parallel, but does not deliver closed-form analogues of β_c or Φ_surv for the calcium system. Calibrated derivation of these thresholds — analogous to the redox companion paper [16] for the GSH/NRF2 system — is the natural next step, with calcineurin–NFAT kinetic parameters from [38,39] supplying the empirical anchors. Beyond calcium, the candidate systems sketched in §15.2 (immune tolerance, bone remodelling, ER proteostasis, neural firing-rate homeostasis) await similar empirical mapping. 14.6 Closing remark The structural insight, stated as the Architectural Grammar Statement in §2.7, is that biology builds robust adaptive systems by coupling a fast plant to a slow internal-model controller, then bolting on an independent surveillance layer that shares the same input signal. Because the four functional roles are architecturally distinct and their normative thresholds are supplied by parameters in disjoint role blocks (Proposition 5, with the threshold Jacobian block-diagonal under role-preserving reparameterizations), every system instantiating this four-role template under the actuator-folding convention of §2.7 exhibits four threshold-typed failure modes. These modes cannot be deformed into one another because they are typed by which role’s threshold is violated, not by what the threshold value is — and orthogonal interventions on one role block leave the other three thresholds invariant, as the Jacobian-block-diagonality argument shows. The U-shaped curves, paradoxical reversals, and baseline-stratified harms recurring across toxicology, nutrition, oncology, and ageing are surface projections of this same deep architectural structure. Page 55 of 213 Dose Response

stress cardiomyopathy, exercise-adaptation blocking, NRF2 duality, senescence- decoupling). A second instantiation in cardiomyocyte calcium handling demonstrates portability: the framework’s distinctive Mode 4b cascade-topology prediction has a direct empirical parallel (constitutive calcineurin activation produces dilated cardiomyopathy rescued by calcineurin/NFAT inhibition). Numerical simulations verify each mode’s defining condition. Conclusions. The framework’s contribution is partly classificatory (a unifying language for previously-separated phenomena) and partly predictive. The four modes are asymmetrically anchored: Mode 1 is calibrated against independent biochemistry; Mode 2 is empirically scaffolded; Mode 3 is structural with piecemeal anchors; Mode 4c is flagged as forward research pending cohort-based fitness regressions. Four genuinely novel forward predictions await test: P11 (timescale-stratified hormesis), P13 (controller- bandwidth pharmacology rescues Mode 4a more effectively than β-reduction in matched dose), P14 (V-distribution as Mode 4b diagnostic in chronic Mode 2 populations), and P17 (intervention-orthogonality stratification of V–Φ dissociation). The framework is falsified by finding an in-class system with a clinically-relevant homeostatic-failure phenotype that cannot be located in any of {Mode 1, Mode 4, surveillance-toe regime, sensor-fidelity regime}. Keywords: bounded adaptive systems; architectural grammar; plant-sensor-controller-

controller; and DDR / UPR / PGC-1α as parallel surveillance readouts. The redox instantiation is rich enough to derive each of the four modes in closed form, to make 17 falsifiable predictions, and to numerically verify the four-mode partition in simulation. To convert the architectural-grammar claim from a one-instantiation conjecture to a partially- demonstrated structural result, §15.1 develops a second worked instantiation in cardiomyocyte calcium handling — at the level of detail necessary to map R1–R4 onto well- characterised independent literature, predict the four mode-types, and demonstrate that the framework’s most distinctive structural prediction (Mode 4b → Mode 2 cascade with controller-unpinning rescue) has a direct empirical parallel. The calcium instantiation does not develop closed-form thresholds; that is forward work parallel to the redox companion paper [16]. Other candidate systems (immune tolerance, bone remodelling, ER proteostasis, neural firing-rate homeostasis) are sketched as forward research in §15.2. Falsifiability of the architecture. The four-mode partition is sharp at the architectural level. Identifying a fifth threshold-typed failure phenotype in any system within the class would force either a fifth role (a genuine extension of the architecture) or a refinement of an existing role (a sub-mode within the existing partition). Both are progressive refinements rather than refutations. What would falsify the framework is finding a system within the class that exhibits fewer than four threshold-types, or a phenotype within an in- class system that cannot be located in any of the four roles by any threshold-type analysis. The framework’s primary risk is therefore that its scope of applicability is narrower than claimed; we discuss this in §14.4.

accommodate the relevant phenotypes). Section 7 establishes Proposition 5 (Role-Typed Structural Disjointness, applied tightest to the two component-failure parameter blocks) and the architecture’s falsifiability conditions. Section 8 defines the healthy operating region and the four-term fragility index. Section 9 enumerates the 2⁴ = 16 combined-mode taxonomy. Section 10 walks through six redox-instantiation corollaries. Section 11 lists falsifiable predictions. Section 12 reports numerical verification, with §12.5 anchoring the framework’s closed-form predictions in published literature data. Section 13 compares the framework with alternative accounts. Section 14 discusses scope, limitations, and the framework’s relation to control-theory canon. Section 15 develops a second worked instantiation (calcium handling in cardiomyocytes, §15.1) and sketches further candidate systems as forward research (§15.2).

(Dose-Response, in peer review). Closed-form derivation of the dose-axis projection (the present paper’s Corollary 1) using Aczél’s representation theorem and metabolic control analysis. Predicts peak amplitudes and zone widths (5–50× threshold separation). Note that the canonical Calabrese characterisation reports peak amplitudes typically 30–60% above control across the broad hormesis database; the higher amplitude range (130– 160%) derived in [20] applies to a specific subclass of strongly-bounded adaptive systems where the geometric necessity argument is sharpest. The present paper does not commit to failure modes in any system satisfying A1–A4 with controller A2b, the typing of each mode by which component supplies its normative threshold (Proposition 5), and the directional predictions of all six corollaries — follow from the axioms and the canonical four- component decomposition stated herein and require no input from companion work. Empirical magnitudes that do require companion input are confined to: (i) the calibrated values κ ≈ 0.05, G_max ≈ 2000 μM, K_M ≈ 100 μM, γ_V ≈ 1/8 h imported from [16] (a minimal self-contained sketch is presented in §3.2 below); (ii) any specific quantitative hormetic peak amplitudes derived in [20], which are not relied upon in the present paper’s standalone qualitative claim of biphasic shape (Corollary 1); and (iii) the stated Phase II analysis-specification thresholds for Corollary 5/P5 in [16, §5.4]. Where these values appear in the present paper, they are flagged as imported. Reframings of known biology vs. genuinely novel predictions. The framework’s contribution divides into two categories. Reframings of known biology — valuable for unification but not novel as predictions — include: Mode 1 in G6PD-deficient erythrocytes; Mode 4b → Mode 2 in KEAP1-mutant NSCLC chemoresistance; NRF2-transgenic Page 6 of 213 Dose Response

cardiomyopathy rescued by NRF2 deficiency; antioxidant blockade of exercise adaptation; baseline-stratified divergence in antioxidant prevention trials. Genuinely novel predictions — not part of the prior literature and currently awaiting test — include: P11 (timescale- stratified hormesis: acute vs chronic peak attenuation), P13 (controller-bandwidth pharmacology rescues Mode 4a more than β-reduction), P14 (V-distribution as Mode 4b diagnostic in chronic Mode 2 populations), and P17 (senolytic-rescue stratification of V–Φ dissociation). The classificatory contribution gives a common language to previously- separated phenomena; the predictive contribution is the four novel forward predictions above. Readers should weight the two contributions accordingly. 2. The Architectural Grammar and Axiomatic Foundation 2.1 The system class: bounded adaptive biological systems with surveillance We define a bounded adaptive biological system with surveillance (BAS-S) as a dynamical Multiplicity of R4: the canonical-readout convention. Many BAS-S systems contain multiple cell-fate-engaging readouts reading the same flux Φ — for the redox/NRF2 instantiation, DDR via p53/ATM, UPR via XBP1/ATF4, and PGC-1α/AMPK metabolic adaptation are each parallel branches off Φ without closing the feedback loop, each with potentially distinct Σ- Page 7 of 213 Dose Response

interventions; pathways with surveillance-dominant coupling should respond to engagement-threshold interventions. Pathways exhibiting comparable response to both are dual-coupled, and the framework predicts (i) that they generate hybrid Mode 4 / Mode 2 phenotypes when perturbed, and (ii) that the four-mode partition still holds at the threshold-violation level even though the parameter-block disjointness of Proposition 5 is weakened. Specifically, dual-coupled pathways place some parameters jointly in the controller-block p_4 and the surveillance-readout parameters that define Φ_surv, so the

an internal reference. This is control-theory canon and contributes R1, R2, R3 without ambiguity. The fourth role is added by the biological fact that cell-fate machinery (DDR via p53/ATM; UPR via XBP1/ATF4; PGC-1α/AMPK metabolic adaptation; the calcineurin/NFAT and CaMKII branches discussed in §15.1) reads the same flux signal Φ as the controller but does not close the feedback loop. This is R4. The fourth role is not chosen from a menu — it is the unique additional topology available off a feedback loop’s sensor output: a downstream branch either feeds back to the plant (in which case it merges with

defined by their respective roles (Proposition 5); no continuous transformation that preserves the role-decomposition can map one threshold-type onto another. The grammar is empirically falsifiable in two ways: (i) finding a BAS-S with fewer than four threshold- types collapses the partition; (ii) finding a phenotype within a BAS-S that cannot be located in any of the four roles forces either a fifth role or an exit from the class. 2.2 Axiomatic foundation, tiered by epistemic status The axioms split into three tiers reflecting their epistemic role.

that depend on these readouts are conditional on A4 holding for the specific readout invoked. Tier III — Sampling assumption (used in cohort-scale predictions) A5 (Population heterogeneity in baseline V and θ). Clinical populations, animal cohorts, and cell populations are not at a common operating point: baseline V varies across individuals by an order of magnitude or more; the parameters θ of all four roles similarly vary. A5 is a sampling assumption used in deriving population-scale predictions (Corollary 2 and the related cross-trial pattern); it does not enter the existence proofs of the failure modes. Table 1. Axiom classification by epistemic status, with system-class reframing. Axiom Statement Tier Role in framework R4 A5 Population heterogeneity III (Sampling) Used in cohort-scale predictions Treating A4 as a system-class membership condition rather than as an axiom-with- empirical-content dissolves a recurring tension. A4 is part of the class definition: a system that lacks parallel surveillance with a low-signal-to-output threshold (Φ_surv) is not a BAS- S in the sense relevant to Mode 2. For systems where A4 is empirically established (DDR

readout in single-cell measurements [23,24]), the system is in-class with respect to that readout; for systems where A4 is conditional, in-class status is itself a forward prediction. We note also that A4 admits two complementary readings of varying strictness. The strict reading (toe-band-saturation Hill geometry, as established for the DDR readout) is the form used in the formal proofs and the Σ(Φ) curves of Figure 5. A relaxed reading suffices for the existence of Mode 2: any monotone threshold function with a low-output region below

controller dynamics. Each mode inherits a different kind of empirical scaffolding, and we resist framing them as symmetric. Mode 4c specifically is the framework’s most operationally provisional mode; the senolytic-rescue diagnostic P17 (§6.4, §11) is consequently a forward hypothesis rather than a deployable diagnostic, and we flag this throughout. Figure 1 visualises the claims hierarchy at a glance. Page 13 of 213 Dose Response

verified; empirically scaffolded). Columns are the four failure modes. Each cell’s colour encodes status: green = established (closed-form derivation or matched data); amber = scaffolded (literature anchor or partial); pink = forward prediction awaiting empirical test; grey = not applicable to this mode. Reading down each column shows what kind of evidence supports that mode; the asymmetry across columns is the framework’s honest epistemic posture rather than a uniform claim. 2.3 Instantiation in redox / NRF2 biology (the worked example)

effect on closed-loop behaviour, not a controller-internal failure (the controller is performing correctly given its input). We make this distinction sharply in §6.4 and use it to derive a diagnostic test (P17). Third, ℳ_fast and V_ctrl are architecturally distinct. ℳ_fast has fast (minutes-to-hours) timescales for (e, G); V_ctrl has slow (~8h) timescale for V. Their parameter sets are disjoint. Failures of one do not imply failures of the other; their thresholds are independent.

smears the boundaries between mode-active and mode-inactive operating points but cannot move a parameter from one block to another. What changes under stochasticity is the sharpness of clinical event prediction at any given operating point, not the typing of failures. Observed clinical event rates therefore correspond to the integrated probability of threshold crossing over the observation window, with the mode classification supplying the which-block answer and the noise model supplying the how-often answer. Stochastic refinement of the framework — Langevin extensions of (1)–(2), state-dependent noise on V_ctrl, population-level distributions over the parameter blocks — is forward work that adjusts event-rate predictions but does not redraw the mode partition. 2.6 Notation summary Conventions on V, β, and Hill exponents across instantiations. Three symbols carry instantiation-specific content and shift in character between the redox worked example and the calcium instantiation of §15.1; readers tracking the cross-domain claim should note instantiation [16]; m setting Σ’s toe-band-saturation geometry, with the strict reading of A4 fixing m via the bounded-observable analysis of [21]) are imported from companion work where they enter quantitative predictions. Page 17 of 213 Dose Response

(departure from the viable region X_viable) implies violation of at least one of the four roles’ thresholds, and these violations are mutually irreducible. The number of threshold-typed failure modes equals the number of architecturally distinct functional roles. Falsification: identifying a phenotype within 𝒮 that violates homeostasis but cannot be located in any of R1–R4 forces either an exit from the class or the introduction of a fifth role. Proof structure. The four claims are proved or constructed as follows. Claim (C1) is

shape arms are typed by Mode 1 (high-β arm) and Mode 2 (low-β arm) of the redox instantiation. Claim (C4) — exhaustiveness — follows from Proposition 5 combined with the empirical hypothesis P7 (§11) that the four-role decomposition exhausts the architectural roles of any in-class system; the count of threshold-types equals the count of architectural roles, with both the count itself (which depends on the actuator-folding convention; see “Why the count is four” below) and the role count of any candidate system being empirical claims about how that system is wired. four-role count of the present framework is therefore substantively justified for biological controllers in the γ_V ≈ 1/8 h regime that includes NRF2, calcineurin–NFAT, and the other slow transcriptional controllers we discuss, and is itself a falsifiable structural prediction: identifying an actuator-internal failure surface in a candidate BAS-S system would force a five-role refinement. The architectural-grammar claim is therefore that the four-role decomposition is the minimal architecture under the substantively-justified actuator- folding regime; alternative decompositions with three roles (collapsing surveillance into

Axiom A4 posits that the parallel surveillance readout Σ has toe-band-saturation geometry — a low-output toe below Φ_surv, a roughly proportional band above it, and saturation at high Φ. We have flagged A4 as empirically established for DDR (p53/ATM via Loewer/Sakai single-cell measurements [23,24]) and conditional for other biological readouts. The cross-domain claim of §15 is conditional on A4 holding for the relevant non- DDR readout in each candidate system. The bounded-observable framework developed in [21] provides a structural reason to the deviation is itself a diagnostic signal about the regulatory regime. We do not claim A4 as a default prior across all biological surveillance — only as a structurally-motivated hypothesis whose empirical scope is co-extensive with the bounded-observable conditions of [21], and whose primary independent verification (DDR via Loewer/Sakai) leaves non- DDR readouts as forward-research tests. Page 21 of 213 Dose Response

consequence, and Mode 3’s effect on closed-loop behaviour looks like a sensor-side fault rather than a downstream-of-sensor failure. Both observations are correct, and they are exactly what the 2 + 2 structure predicts: regime conditions are reached because of component failures (or environmental conditions, or class-membership absence). They are Page 22 of 213 Dose Response

condition threshold geometries (Φ_surv from Σ; rank/fidelity from 𝒞) are well-defined functions of the component states but do not constitute independent parameter blocks at the same level. (ii) The Mode 4b → Mode 2 cascade is not an empirical hypothesis about whether two modes co-occur; it is a structural prediction that any Mode 4b component failure projects into the Mode 2 regime, with the cross-domain calcium parallel (constitutive calcineurin → dilated cardiomyopathy rescued by calcineurin/NFAT inhibition) being the realisation of the same structural prediction in a non-redox substrate. (iii) Intervention ordering (Mode 4 → Mode 3 → Mode 2 → Mode 1) becomes more natural to read: address component failures (Mode 4 first, then sensor-projection restoration as a state-space regime correction, then surveillance-engagement region) before addressing the plant-boundary state if it has already been crossed. The ordering is not arbitrary; it tracks the causal chain from component fault to regime to plant collapse. (iv) Falsification at the architectural level is sharpened: a system in the BAS-S class with a clinically-relevant homeostatic-failure phenotype that cannot be located in any of {Mode 1, Mode 4, surveillance-toe regime, sensor-fidelity regime} would force either an exit from the class or a fifth role.

4.2 Empirical anchor Mode 2 is calibrated in [16] against the KEAP1-mutant NSCLC × NAC × platinum chemotherapy setting [Sayin et al. 2014; Wiel et al. 2019]. The framework predicts that NAC supplementation in NRF2-active NSCLC suppresses Φ* via two mechanisms — direct G_max elevation and KEAP1-NRF2-pinned V_set,actual at high V — driving Φ* into Σ’s toe and reducing platinum-induced apoptosis triggering. The companion paper [16, §5] presents a stated analysis specification for any future Phase II of this design, with stated threshold-like dose-response, and an 8-oxo-dG within-trial mechanistic biomarker. The framework’s claim is the analysis-specification thresholds; the author has no role in trial conduct or execution, and the prediction is offered as a structural commitment that any properly-stratified Phase II of this design would test. The Mode 2 threshold is supplied by surveillance-readout geometry alone; in principle a system with intact ℳ_fast and intact V_ctrl can still violate Mode 2 if it operates at Φ* < Φ_surv. In practice, chronic Mode 2 in nucleated cells almost always involves a Mode 4b

target). This operational definition does not require direct measurement of V_set,fitness — which is empirically inaccessible in the absence of cohort regressions — only the response signature under three orthogonal intervention classes. The Mode 4c hypothesis is falsified the moment a putative Mode 4c phenotype responds equally to a bandwidth intervention or to a pinning-release intervention: in that case the phenotype was Mode 4a or Mode 4b all along, and the framework reclassifies accordingly. This makes Mode 4c structurally testable now, independent of the longer-term cohort regressions required to define from F₄’s dependence on δ), but the construction relies on cohort-based fitness regressions that have not yet been performed for any biological system. Until such cohort regressions are conducted and analysed, Mode 4c remains a structural prediction without empirical validation. The independent operational definition below establishes that Mode 4c is in- principle measurable; whether the predicted V-Φ-misalignment-tracks-fitness pattern actually obtains in real cohorts is the empirical question that future work must answer. The senolytic-rescue diagnostic P17 (§6.4, §11) is consequently a forward hypothesis, not a deployable diagnostic. Independent definition of V_set,fitness. To avoid circularity in the calibration tolerance δ that defines Mode 4c, we define V_set,fitness independently of the fragility index F (which itself depends on δ via F₄). V_set,fitness(Φ) is the setpoint function that maximises long- cause mortality, mortality-adjusted reproductive success, healthspan, or disease-specific incidence), V_set,fitness is the V(Φ) function that, when used as the regressor for individual V deviations, maximally predicts variance in the fitness outcome. δ is then the empirical tolerance at which |V_set,actual − V_set,fitness| begins to predict adverse outcomes in cross-population studies. Neither V_set,fitness nor δ references F, F₄, F₁, or F₂; the chain is acyclic. Proof (existence-by-construction). With V_set,fitness defined independently as above, V_set,actual is the controller’s implemented setpoint function — encoded by the genome

chemical exposure with shift-work patterns; intermittent ischemia-reperfusion in transplant medicine; rapidly cycling chemotherapy regimens; β-adrenergic stress in cardiomyocytes during arrhythmia. The framework predicts that speeding up γ_V (e.g., constitutive partial-induction by low-dose sulforaphane co-administration, or eliminating KEAP1 negative feedback) should rescue these phenotypes more effectively than reducing time-averaged β. Mode 4b-high — V-pinning at V_max. KEAP1 LoF in NSCLC (the canonical

regulation. The clinical fingerprint of Mode 4c is dissociation between cytosolic V and outcome that persists after correcting Φ corruption — distinguishing it operationally from Mode 3 effects on the same biomarker (§6.4 P17). The Mode 3 → controller-action cascade (corrupted Φ leading to inappropriate V via correct V_set) is not Mode 4c; it is the consequence of Mode 3 on closed-loop behaviour, sharply distinguished in §6.4. We emphasise that empirical validation of Mode 4c — and consequently of P17 — awaits the cohort-based fitness regressions described above. 6.4 Mode 3 effect on closed-loop behaviour: a Mode 3 phenomenon, not a Mode 4 sub-mode A subtle architectural distinction must be drawn at this point: the case where V_ctrl Restoring 𝒞 fidelity does not restore V trajectory — V remains misaligned because V_set,actual is itself misaligned. The senolytic-rescue diagnostic (P17, §11) operationalises this distinction: in any cohort presenting with V-Φ dissociation, post-senolytic restoration of the V-Φ relationship to its V_set,actual-prescribed slope identifies the structural fault as Mode 3 (sensor); persistent V-Φ dissociation post-senolytic identifies the fault as genuine Mode 4c (controller-internal Page 33 of 213

calibration drift). P17 is presented as a forward hypothesis whose validation requires both (i) the cohort regressions establishing V_set,fitness and δ for the relevant tissue, and (ii) empirical demonstration of the predicted bimodal stratification under senolytic intervention. Until both are in place, P17 is a structural prediction, not a clinical decision aid. 7. Proposition 5: Role-Typed Structural Disjointness Proposition 5 (Role-Typed Structural Disjointness). Under the BAS-S architecture of §2.1 with all four roles (R1 plant, R2 sensor, R3 controller, R4 surveillance) functionally distinct,

shape. Bandwidth-acceleration of NRF2 transcriptional response (a p_4 perturbation narrowly affecting γ_V) does not change β_c, Φ_surv, or 𝒞 rank. The orthogonal- perturbation predictions are testable in cell-line and tissue experiments where each block Page 35 of 213 Dose Response

shift the V_set,actual mapping in p_4 if chronic NADPH limitation alters NRF2-target transcriptional dynamics. The block-diagonality argument applies on the role-preserving manifold; it predicts what would be observed under role-preserving perturbations, while empirical interventions may project onto multiple role blocks simultaneously and produce apparent cross-coupling. Cross-coupling observed in such cases — where an intervention nominally targeting one block also moves another threshold — would localise a hidden parameter shared between two role blocks and constitute a structurally-informative refinement of the role decomposition (a falsifiable, progressive consequence of Proposition 5). The framework’s commitment is to the orthogonal-perturbation prediction conditional on the perturbation factoring through a single role block; demonstrating which biological interventions actually do so is empirical work to be undertaken alongside the framework’s deployment. The classification is exhaustive over the four roles: any failure of homeostatic regulation supplied by R1, R2, R3, or R4. This is the four-mode partition. The architectural exhaustiveness — that the four roles are themselves the complete decomposition — is the empirical hypothesis P7 (§11), falsifiable by finding a phenotype within an in-class system that cannot be located in any of R1–R4. ∎ The proposition’s role is structural, not a deep mathematical theorem. It establishes that the four threshold-types are typed by their parameter set, not by their threshold value, and that the typing is the framework’s classification primitive. Two phenotypes with the same

(p_2, p_3) regime conditions are entered as consequences of (p_1, p_4) component faults rather than as independent threshold violations. Each role’s contribution to F is essential: a system with F_i = 0 in any one role is at threshold and homeostasis fails. F predicts which mode is closest to violation and therefore which intervention is most urgent. 8.3 Cascade-corrected fragility When mode interactions produce cascades (e.g., Mode 4b → Mode 2; Mode 3 → Mode 4- effect), the simple min-of-four can over- or under-estimate fragility. The cascade-corrected

— most apparent Mode 1 risk arises from threshold-migration via Mode 4-or-3 cascades; correct those first. This ordering is the framework’s clinically-actionable structural prediction: for any combined-mode patient, intervention should target Mode 4 first, Mode 3 second, Mode 2 third, Mode 1 last. 10. Six Biological Corollaries We now walk through six biological domains and locate each within the four-component decomposition. For each corollary we state the relevant ℳ_fast, 𝒞, Σ, and V_ctrl; identify the failure mode invoked (including any Mode 4 cascade); derive a forward prediction; and indicate the empirical status (calibrated / framework-derived / committed-with- thresholds). 10.1 Corollary 1 — Hormesis as a dose-axis projection ℳ_fast: the generic bounded adaptive cell of (1)–(2). 𝒞: Φ = (rG + β)e. Σ: any of the toe–

Mode 4a (γ_V·τ_β ≪ 1) collapses the adaptive zone — the controller cannot adapt fast enough, so the trajectory in (V, β) space is more like a direct β-sweep at fixed V, no hormetic peak. This generates P11 (timescale-stratified hormesis): the Calabrese database’s hormetic peaks should be largest for acute exposures (V quasi-static) and attenuated for chronic exposures (V_ctrl active, peak smoothed). 10.2 Corollary 2 — The antioxidant prevention-trial paradox ℳ_fast: epithelial and stromal cells in cancer-prevention populations. 𝒞: Φ as DSB-rate- correlate. Σ: DDR (p53/ATM-pathway) firing, by A4 (Loewer/Sakai). V_ctrl: heterogeneous across baseline-V strata under A5; Mode 4b-high pinning common in chronically- supplemented stratum. Mode invoked: baseline-V scan; Mode 1 in deficient strata, Mode 4b → Mode 2 cascade in chronically-adapted strata. Antioxidant supplementation trials (β-carotene in CARET [3], vitamin E in SELECT [4], pinning, locking V at V_max and pushing Φ* deeper into Σ’s toe. The trial average integrates over the heterogeneity and reads null or weakly harmful — but the stratum-specific effects are opposite-signed, exactly as the framework predicts. The U-shape between baseline biomarker and outcome (e.g. selenium and cancer risk [6]) is a direct readout of this stratum-specific divergence. Status: framework-derived qualitative direction and stratification; empirically established U-shape. 10.3 Corollary 3 — Reductive stress cardiomyopathy (Mode 4b → Mode 2

engagement. The decisive genetic test is that NRF2-deficiency rescues the cardiomyopathy [9] — the four-component framework predicts this exactly: removing the Mode 4b-high pinning (NRF2-deficiency restores dV_set/dΦ > 0) re-enables V_ctrl to relax V toward a fitness- aligned setpoint, the operating point exits Σ’s toe, and surveillance firing is restored. The intervention target is V_ctrl unpinning, not direct manipulation of β or V_max. Status: framework-derived qualitative direction; empirically established with genetic-

falls into Σ’s toe (Mode 2 cascade); DDR-mediated apoptosis fires below threshold; the tumour resists therapy. The molecular identity of the player (NRF2) is the same; what has changed structurally is that V_ctrl has gone into Mode 4b. The framework predicts that Mode 4b unpinning (e.g., by NRF2 inhibitor co-administration) should restore chemotherapy efficacy. Status: framework-derived structural unification; stated analysis specification for any future Phase II of this design in [16, §5.4]. 10.6 Corollary 6 — Senescence-associated and pseudohypoxic decoupling (Mode state to a global Φ. Σ: any of the readouts of A4. V_ctrl: receives corrupted Φ from Mode 3 𝒞, producing apparent Mode 4c-like effect (but structurally Mode 3, distinguishable by P17). Mode invoked: Mode 3 — coupling failure via fidelity loss (SASP) or rank reduction (compartmental aggregation, pseudohypoxia) — with cascading downstream effect on V trajectory. Three phenotypes that have been described piecemeal in the literature receive a unified structural account: chemokine, and matrix-remodelling factor mix into the local milieu. Within tissue, this corrupts the Φ-signal that downstream surveillance integrates: individual-cell Φ becomes a worse predictor of tissue-level Σ-input. The result is age-related tissue dysfunction with apparently-healthy individual-cell ℳ_fast. The framework predicts that senolytic intervention should restore not just cell number but the fidelity of 𝒞 — and through 𝒞, the calibration of V_ctrl on the true ℳ_fast-state. (b) Pseudohypoxia [15,31]. Tumour cells stabilise HIF-1α under normoxic conditions, decoupling HIF-readout from actual oxygen state. This is rank reduction in 𝒞 — two distinct ℳ_fast-states (true hypoxia; pseudohypoxic normoxia) collapse to the same Σ-input. The framework predicts that interventions targeting HIF-1α stability should be selectively active in pseudohypoxic versus genuinely hypoxic cells, distinguishable by orthogonal coupling readouts (mitochondrial metabolic flux, lactate dehydrogenase isoform balance). (c) Compartmental isolation. Mitochondrial GSH dynamics decouple from cytosolic GSH dynamics in age-related mitochondrial dysfunction [32] and in selenium deficiency via selenoprotein-P [33]. The global Φ averaged over compartments hides the failing one. The framework predicts that compartment-resolved redox biomarkers (mito-roGFP, MitoSOX-validated kinetics) should show divergence in clinical Page 42 of 213 Dose Response

specific content. The phenomena it unifies have not previously been read as instances of a single sensor-level failure with structural consequences for the closed-loop controller. The senolytic-rescue diagnostic (P17) is proposed as a forward hypothesis to discriminate this Mode 3 cascade from genuine Mode 4c (V_set,actual itself altered) — same surface phenotype, different structural fault, different intervention target. Empirical validation of P17 awaits both cohort regressions establishing V_set,fitness and direct test of the predicted bimodal response stratification under senolytic intervention. Status: framework-derived structural unification; predictions are forward and falsifiable. Conditional on A4 holding for the relevant downstream readouts (HIF-1α, DDR, compartment-specific); A4 is empirically strongest for DDR and remains conditional for HIF-1α and compartment-resolved redox readouts. 11. Forward Predictions Each corollary supplies one or more falsifiable predictions. We list the headline prediction for each, indicate the discriminating observation, and state the conditions under which the framework would be falsified. Two epistemic classes. The seventeen predictions below fall into two epistemic classes that should be weighted differently when assessing the framework’s predictive record. Structural reframings (P1–P10, P12, P15, P16): these locate established empirical phenomena (hormesis, the antioxidant-paradox, KEAP1- mutant NSCLC chemoresistance, NRF2-transgenic cardiomyopathy, compartment-resolved redox divergence) at specific roles in the architecture. Their value is unification — supplying a common language for previously-separated phenomena — rather than novel prediction. They are falsifiable in the sense that an alternative architectural location would refute the role-typing claim, but the empirical phenomena themselves are already established. Forward predictions awaiting empirical test (P11, P13, P14, P17): these are novel and not part of the prior literature. P11 (timescale-stratified hormesis: peak attenuation under chronic versus acute dosing), P13 (controller-bandwidth pharmacology rescues Mode 4a more effectively than β-reduction in matched dose), P14 (V-distribution as Mode 4b diagnostic in chronic Mode 2 populations), and P17 (intervention- orthogonality stratification of V–Φ dissociation) are the framework’s genuine forward commitments. Readers should weight the two classes accordingly: the classificatory contribution is the thirteen reframings; the predictive contribution is the four forward predictions. P13–P17 are new predictions specific to Mode 4 and Mode 3-vs-4c discrimination. P1 (Corollary 1, Hormesis). Bounded adaptive systems should display biphasic dose- responses (inverted-U) with arms of distinct architectural type — Mode 1 on the high-β arm and Mode 2 on the low-β arm — derivable in closed form from A1–A4. The qualitative claim is that the U-shape exists and its arms map structurally onto different failure modes. The canonical Calabrese database reports peak stimulation typically 30–60% above control

with zone widths of 5–50× threshold separation [1,2]; specific quantitative amplitudes for strongly-bounded adaptive subclasses are derived in [20]. Falsification of the qualitative claim: a substantial class of bounded adaptive systems showing monotonic rather than biphasic dose-responses without an identifiable confound, or biphasic curves whose arms do not segregate by Mode 1 / Mode 2 typing. P2 (Corollary 2, Antioxidant paradox). Baseline-V stratification of antioxidant cancer- prevention RCTs should show opposite-signed effects in deficient versus chronically- supplemented strata, with the strata-difference exceeding the population-average effect in absolute magnitude. Falsification: a well-powered baseline-stratified meta-analysis showing concordant signs across strata, or a stratum-difference smaller than the average effect. P3 (Corollary 3, Reductive cardiomyopathy as Mode 4b → Mode 2). In any tissue with chronically-elevated V from a Mode 4b-high mechanism (genetic, exposure, or pharmacological origin producing dV_set/dΦ ≈ 0 at the operating Φ), proteostatic surveillance should fire below dose-proportional baseline, and unpinning V_ctrl (not merely lowering V by other means) should rescue. Falsification: a high-V tissue with intact proteostatic surveillance firing at dose-proportional rate, or a tissue in which V-lowering rescues damage even when V_ctrl pinning is left intact. P4 (Corollary 4, Exercise blockade). High-dose antioxidant supplementation should block adaptive readouts of any low-amplitude bounded stress (not just exercise — e.g. mild hypoxia training, intermittent fasting, cold exposure). Falsification: a bounded-stress training intervention in which equivalently-dosed antioxidant supplementation does not blunt the adaptive readout. P5 (Corollary 5, NRF2 in KEAP1-mutant NSCLC + NAC). Stated analysis specification for any future Phase II of this design, presented in [16, §5.4]: in a Phase II RCT of NAC + platinum chemotherapy in NSCLC, the NRF2-active stratum (KEAP1-mutant or NRF2-IHC- high) should show progression HR 1.20–2.00 versus control, the NRF2-low stratum HR < 1.20, and a selectivity ratio ≥ 1.30. Plasma 8-oxo-dG should fall in the NRF2-active arm without rising in the NRF2-low arm. Falsification: any of the four conditions failing. The framework’s commitment is to the analysis-specification thresholds; the author has no role in trial execution, sponsorship, or registration. The framework predicts what the analysis would show in any properly-stratified Phase II of this design. P6 (Corollary 6, Mode 3 with downstream controller-action consequence). Compartment-resolved redox biomarkers should diverge from cytosolic-pool biomarkers in (a) ageing tissue with high SASP burden, (b) pseudohypoxic tumours with stable HIF-1α under normoxic O₂, (c) selenium-deficient populations with normal cytosolic GSH. Falsification: any of the three populations showing concordant compartmental and cytosolic biomarkers. Joint with P17: the V-Φ relation in these populations should normalise on senolytic / 𝒞-fidelity-restoration intervention without requiring V_set,actual change — confirming Mode 3 as the structural fault. Persistent V-Φ dissociation after such intervention would re-locate the fault as genuine Mode 4c. Page 44 of 213

P7 (Structural — sharpened). Any bounded adaptive system satisfying A1–A4 with the canonical four-component decomposition (ℳ_fast, 𝒞, Σ, V_ctrl) should admit at most four threshold-typed failure modes corresponding to its four components. Falsification: a candidate failure mode that produces a biomarker signature distinguishable from all of Mode 1, Mode 2, Mode 3, and Mode 4 (4a/4b/4c) by every combination of the framework’s diagnostic assays — a phenotype which simultaneously (a) shows no β_c crossing, (b) operates with Φ* in Σ’s dose-proportional band, (c) shows no compartment-resolved or with adequate γ_V·τ_β. Such a phenotype would force the addition of a fifth threshold-type, indicating a finer architectural decomposition. P8 (Optimal V). Activator pharmacology that drives V toward V_max should produce U- shaped dose-response curves for chronic-prevention outcomes, with a tissue-specific optimum V* strictly less than V_max. Falsification: a population-scale, tissue-specific dose- response showing monotonic improvement in chronic outcomes with increasing activator dose up to and including V_max-saturating doses, in a tissue with measurable Σ-toe geometry consistent with A4. P9 (V-lowering paradox in Mode 2). In a population identified as occupying the Mode 4b → Mode 2 region (KEAP1-mutant or NRF2-IHC-high tumours not yet receiving cytotoxic therapy; high-V chronic-supplement-replete cohorts), interventions that reduce V or modestly raise β should improve surveillance-mediated outcomes. Falsification: a randomised trial of antioxidant restriction or controlled mild pro-oxidant intervention in a verified Mode 4b stratum showing no improvement or harm. P10 (Mode 3 precedes and conceals Mode 1 in compartmentally-isolated tissue). When 𝒞_full is rank-degraded, failing compartments can reach the Mode 1 boundary while standard cytosolic biomarkers remain normal. The framework predicts a temporal sequence: compartment-resolved redox biomarkers diverge (Mode 3 onset) months to years before catastrophic events register on standard panels (Mode 1 onset in the hidden compartment). Falsification: sequential compartment-resolved imaging showing concurrent (rather than temporally-ordered) divergence. P11 (Timescale-stratified hormesis as Mode 4a effect). The hormetic peak amplitudes of [20] assume acute β-sweeps with γ_V·t_exposure ≪ 1. For chronic dosing at equivalent total β, V_ctrl is in its responsive bandwidth regime (γ_V·τ_β ≫ 1), tracks V_set, and re- centres the operating point near the middle of Σ’s dose-proportional band, attenuating the hormetic peak. The Calabrese database mixes acute and chronic exposures; disaggregating by exposure timescale should reveal robust hormetic peaks for acute exposures and substantially attenuated peaks for chronic exposures of equivalent cumulative dose. Falsification: timescale-disaggregated meta-analysis showing identical peaks across timescale. P12 (Four-term fragility index as ageing biomarker). The fragility index F(V, β, Φ, V_ctrl-state; θ) of equation (10) — minimum across Mode 1, 2, 3, 4 distance terms — should track ageing-related risk of redox-coupled clinical events more accurately than any single-compartment biomarker. In paired-cohort studies, individuals matched on standard Page 45 of 213

biomarkers but differing in F should show divergent event rates. Falsification: matched cohorts with the same F-component scores but divergent total F showing no event-rate divergence over the relevant follow-up window. P13 (Controller bandwidth restoration in Mode 4a). In tissue or cell-line systems exhibiting kinetic-mismatch failure (Mode 4a, transient β_c crossings during pulse-train stress with γ_V·τ_β < 1), pharmacological or genetic acceleration of γ_V (e.g., constitutive low-grade KEAP1 inhibition, accelerator agents on NRF2-target enhancer chromatin) should rescue clinical outcomes more effectively than equivalent reductions in time- averaged β. Falsification: a Mode 4a phenotype where γ_V acceleration provides no rescue or where β-reduction alone gives equivalent rescue. This is the Mode 4a-specific intervention prediction; it differs from any prediction the three-component framing would generate, since the three-component framing folds Mode 4a into Mode 1 and proposes only β-reduction. P14 (V-set decoupling diagnostics for Mode 4b). In any population of “chronic Mode 2”- presenting individuals, the diagnostic signature distinguishing genuine Σ-failure from Mode 4b → Mode 2 cascade is the V-Φ joint distribution: Mode 4b cases have V locked at V_max regardless of Φ-perturbation (constant V despite varying Φ across individuals or time), while genuine Σ-failure cases have V tracking Φ via V_set with normal slope. The framework predicts that population-scale Mode 2 phenotypes are predominantly Mode 4b cascades, with V essentially constant across individuals in the affected stratum. Falsification: a population stratified into chronic Mode 2 in which V varies normally with Φ, indicating no Mode 4b component. P15 (Calibration tolerance δ in Mode 4c — provisional). The calibration tolerance δ that defines Mode 4c is in principle measurable: for any tissue with enough fitness-relevant outcome data, V_set,fitness can be inferred from the V that maximises long-term outcome, and V_set,actual can be measured by mapping V vs. Φ in non-Mode-4b individuals. The framework predicts that across populations with diverse environmental histories (e.g., different chronic dietary β-distributions), δ-violations correlate with chronic outcome divergence. Falsification: a population scan showing no correlation between V_set,actual– V_set,fitness mismatch and chronic outcome divergence after controlling for V_max and other confounders. This prediction is conditional on the cohort regressions described in §6.2.3 actually being conducted; until then, P15 is a structural prediction without empirical validation. P16 (Mode 3 effect on closed-loop behaviour). The structurally distinctive signature of the Mode 3 effect on closed-loop behaviour (corrupted Φ propagating through V_ctrl) is dissociation between cytosolic V level (appears appropriate for measured cytosolic Φ) and clinical outcome (events occur despite normal biomarker panels), with the dissociation magnitude proportional to the magnitude of compartmental Φ-mismatch (mitochondrial Φ ≠ cytosolic Φ as measured by orthogonal compartment-resolved probes). The framework predicts that interventions on Mode 3 (senolytics, compartmental fidelity restoration) should, in the same individuals, normalise the V-Φ relation across compartments without changing V_set,actual. The structural fault is in 𝒞, not in V_ctrl; the controller is innocent. Page 46 of 213 Dose Response

Falsification: senolytic-rescued individuals showing persistent V-Φ mismatch despite restored 𝒞 fidelity (which would re-locate the fault as genuine Mode 4c — see P17). P17 (Mode 3 vs. Mode 4c senolytic-rescue diagnostic — forward hypothesis). Operational core (intervention orthogonality). Per §6.2.3, Mode 4c is defined operationally by its response signature under three orthogonal controller-targeted interventions: it responds to V_set-translating recalibration agents and does not respond to bandwidth- acceleration (Mode 4a target) or pinning-release (Mode 4b target). P17 specialises this to senolytic intervention, which acts as a sensor-side intervention reducing senescent-cell- driven 𝒞 corruption: a putative Mode 4c phenotype that responds to a senolytic was Mode 3 all along (sensor fault rescued by senolytic-mediated 𝒞 restoration); a phenotype that does not respond to a senolytic is genuine Mode 4c (controller-internal calibration drift unaffected by sensor restoration). The diagnostic is therefore not contingent on measuring V_set,fitness directly — it requires only the response signature under one sensor-side intervention plus the controller-side interventions of P13 and P14. Status note. P17 is a forward hypothesis, not a deployable diagnostic. Its empirical validation requires direct experimental demonstration of the predicted bimodal response stratification under senolytic intervention in a properly-stratified V-Φ dissociation cohort. The cohort regressions establishing V_set,fitness and δ directly (§6.2.3) would tighten the diagnostic further but are not prerequisites for the intervention-orthogonality test. Until the orthogonal-intervention experiment is conducted, P17 should be read as a structural prediction whose deployment in clinical decision-making is premature. The two phenomena that present as V-Φ dissociation — Mode 3 with downstream controller-action consequence (V_set,actual unaltered, applied to corrupted Φ) and genuine Mode 4c (V_set,actual itself shifted as a controller-internal property) — are predicted to be operationally distinguishable by senolytic intervention. Prediction. In any patient cohort presenting with V-Φ mismatch, stratification by senolytic response should produce two clinically meaningful sub-populations: (i) Mode 3-driven cases — V-Φ relationship returns to V_set,actual-prescribed form post-senolytic without changing V_set,actual; clinical outcome improves; intervention target is sensor repair (further

discriminating endpoint is the pre/post V-vs-Φ slope under an intervention that reduces senescent-cell-driven 𝒞 corruption. The framework specifies the structural form of the test, not a particular pharmacological agent: the architectural prediction is that any intervention removing senescent-cell-driven 𝒞 corruption should yield concordant Mode-3-vs-Mode-4c stratification, and naming a particular senolytic regimen is beyond the framework’s structural commitment. Selection of agent, dose, cohort, and follow-up window is a matter of trial design; the framework supplies the structural hypothesis under test and the discriminating endpoint, nothing more. Falsification of the diagnostic. If senolytic-responsive and senolytic-non-responsive sub- populations are indistinguishable on V-Φ trajectory pre/post intervention, or if no V-Φ mismatch dissociation is observed in either group, the diagnostic fails. 12. Numerical Verification We verify each of the four failure modes numerically in the four-variable closed-loop

pulse height; slow γ_V (Mode 4a regime, γ_V·τ_β ≈ 0.01) keeps β_c at ~1.0. All four panels use the same parameter set apart from mode-specific switches. 12.5 Data-anchored validation: framework predictions in published literature The numerical verification of §12.1–12.4 demonstrates that the framework’s closed-form thresholds match its own dynamical simulation. A more substantive test is whether the framework’s closed-form predictions stand against published clinical and experimental data without parameter fitting. Figure 5 overlays the framework’s key thresholds on representative empirical anchors from four independent literatures, one per failure mode, with no free parameters beyond the V-mapping in each domain. Page 50 of 213Dose Response

minimum risk at moderate selenium status and elevated risk at both low (Mode 1 vulnerability) and high (Mode 2 cascade via Mode 4b pinning) selenium status. The framework’s healthy-strip-width prediction (Eq. 9) recovers the U-shape’s interior optimum V* without fitting; the qualitative match between the framework’s 1/healthy- width prediction and the meta-analytic risk curve is striking. Panel C (Mode 3 — sensor rank reduction). Compartment-resolved redox measurements (Kojer et al. 2012 [32] and downstream literature) show that in young/healthy cells, mitochondrial GSH/GSSG ratios track cytosolic GSH/GSSG ratios tightly (rank-1 coupling, faithful 𝒞). In aged, SASP-rich tissue [14,30], the mitochondrial ratio decouples from the cytosolic ratio, producing a rank-reduction window where single- compartment biomarkers are non-veridical with respect to the true mitochondrial state. This is the empirical signature of Mode 3, predicted by the framework’s Theorem 3 multi- compartment proof. Panel D (Mode 4a + Mode 2 cascade — exercise + antioxidants). The Ristow et al. [10] and Paulsen et al. [11] data on exercise + vitamin C/E supplementation show that antioxidant supplementation blocks PGC-1α-driven mitochondrial biogenesis. The goodness-of-fit comparison is performed. Quantitative testing — fitting the framework’s closed-form thresholds to original-data points with confidence intervals, residual analysis, and out-of-sample prediction — is the natural next step. The figure’s present role is to demonstrate that the framework’s predictions point in the right direction across four independent literatures. We note also that the framework’s threshold criteria (β > β_c, Φ < Φ_surv, etc.) should be interpreted in a probabilistic sense when comparing with single-cell data: noise smears each crisp threshold into a probabilistic transition zone, and observed clinical event rates

Figure 5. Conceptual overlays of the framework’s closed-form predictions on representative empirical anchors from four independent literatures. Each panel illustrates qualitative alignment between the framework’s structural predictions and published findings. (A) Mode 1 — V is the residual G6PD enzymatic activity normalised to wildtype mean. The β_c(V) line is plotted with κ ≈ 0.05 from [16]. (B) Mode 2 — V is the plasma selenoprotein-P concentration normalised to moderate-status cohort mean. The U-shaped risk curve is the published Vinceti et al. meta-analytic finding. (C) Mode 3 — Schematic

β_c (Mode 1 collapse). The framework does not require ROS to be a positive signal in itself; the U-shape comes from the geometry of the (V, β) plane. Discriminating prediction. Mitohormesis predicts that compartment-specific mitochondrial- ROS interventions (mito-targeted antioxidants vs. cytosolic antioxidants) should differentially affect adaptive responses. The four-component framework predicts that any intervention reducing β (regardless of compartment) blocks adaptation if it drops Φ* into Σ’s toe — and Mode 3 (compartmental isolation) is when the two predictions diverge. In ageing tissue with high SASP burden and Mode 3 already active, mito-specific antioxidants may fail to block adaptation while cytosolic antioxidants may block adaptation. This is testable in single-cell flow studies. 13.2 Two-Hit Hypothesis for NRF2 in cancer The two-hit framework [13] proposes that NRF2 activation in normal tissue is protective (first hit prevents transformation), while subsequent KEAP1 mutation (second hit) constitutively activates NRF2 in established tumours conferring chemoresistance. The four-component framework recovers this as Corollary 5 with a structural reading: the supplies the violated threshold. Within the redox/NRF2 instantiation, all four modes are derivable in closed form, three are empirically anchored in published clinical and experimental data, and one (Mode 4c) is a forward structural prediction conditional on cohort regressions described in §6.2.3. Page 53 of 213 Dose Response

continuous deformation cannot connect them without crossing the role boundary. The diagnostic and intervention implications follow: Mode 4 → 3 → 2 → 1 intervention ordering, Mode 3 vs Mode 4c discrimination via P17, and the cascade-corrected fragility index. 14.3 What the framework does not offer The framework does not predict individual cell fate from individual cell parameters; it makes population-scale and cohort-scale claims under A5. It does not specify which molecular pathway implements Σ for a given tissue and readout — that is empirical input. It does not address sub-cellular signalling spatial dynamics within a single cell (concentration gradients), which would require an extension of 𝒞_full from a vector point structure that noise probabilistically samples — but the sharpness of the classification depends on signal-to-noise ratios that are tissue- and readout-specific. A full stochastic treatment is a worthwhile extension that would yield event-rate predictions rather than crisp threshold criteria. The framework as presented should be understood as the deterministic skeleton; stochastic flesh remains to be added. Mode 4c provisional status. As flagged in §6.2.3 and §11 P17, Mode 4c remains a structural prediction without empirical validation. Its operational deployment via P17 Page 54 of 213 Dose Response

depends on cohort regressions that have not yet been performed. The framework’s claim is that Mode 4c is in-principle measurable and structurally distinct from Mode 3 effects on closed-loop behaviour; whether the predicted V-Φ-misalignment-tracks-fitness pattern obtains in real cohorts is the empirical question that future work must answer. 14.5 Future directions Five directions look productive. (i) Empirical anchoring of A4 for non-DDR readouts. Single-cell flow dose-responses for UPR, PGC-1α, and HIF-1α readouts would either firm up should distinguish Mode 3 phenotypes (resolved by senolytic) from genuine Mode 4c phenotypes (controller-internal calibration drift, persistent post-senolytic) in ageing populations — operationalising P17. (iii) Quantitative δ for Mode 4c. Population-scale studies of V_set,actual versus environmental V_set,fitness in tissues with diverse exposure histories would calibrate the calibration tolerance δ. (iv) Mode 4a controller-bandwidth pharmacology. Constitutive low-grade NRF2 induction (sulforaphane, low-dose bardoxolone methyl, dimethyl fumarate co-administration during disturbance-rich