Errata to the Corpus

What this page corrects, and what it does not

An independent adversarial review of the published corpus, completed in October 2026, found eight places where a stated result was wider than the mathematics or specification that supports it. Each is corrected below. The corrections narrow statements or add a missing condition. None of them removes a result the architecture depends on.

Each correction is now carried into the paper it corrects and marked there in place, as every correction in this series is. This page remains the single list.

The reset guard must test the latch

As published. Definition 2 decides whether an ordinary principal may restore TOP by examining the current node states σ(v). Arbitrary autonomous rules may change those raw states. A rule can therefore raise every raw node back to TOP while the aggregate latch λ still holds BOT, after which an ordinary principal satisfies the guard.

step  event                    raw states   latch λ
0     authorized               TOP, TOP     TOP
1     payload mismatch         BOT, TOP     BOT
2     rule raises raw states   TOP, TOP     BOT
3     ordinary grant request   TOP, TOP     TOP   (guard reads raw states)

Correction. Ordinary re-arming is refused whenever the authoritative trip latch is BOT, whatever the raw node states report. Only the escalated effective reset clears a latched trip.

ordinary GRANT admissible  ⇔  λ_t ≠ BOT  ∧  (existing conditions)
λ_t = BOT  ⇒  only the escalated effective reset may act

Effect. Theorem 4 (no autonomous ascent) is unaffected, because step 3 still requires an external principal. The correction restores the stated reset-privilege distinction. The hardware filings already implement the latch-based rule.

The regularized update is an approximate correction

As published. Section 2 requires exact correction, θ_k+1(x_f) = y_true. Section 7 realizes it with (K + λ₁I)α = y_true − θ_k(x_f). For λ₁ > 0 the two are incompatible. With θ_k(x_f) = 1.2, y_true = 2.8 and K(x_f, x_f) = 1:

α          =  1.6 / (1 + λ₁)
θ_{k+1}(x_f) =  1.2 + 1.6 / (1 + λ₁)  <  2.8   for λ₁ > 0
λ₁ = 1     ⇒  θ_{k+1}(x_f) = 2.0

The worked example uses α = 1.6, which corresponds to λ₁ = 0.

Correction. Exact correction is realized by interpolation at the falsifier, λ₁ = 0 on that constraint. With λ₁ > 0 the update is an approximate correction whose residual at a single falsifier is (y_true − θ_k(x_f)) · λ₁ / (K(x_f, x_f) + λ₁), and the paper now says so. Separately, the term λ₂R(Ω_k+1) as written does not depend on θ and so cannot constrain the successor rule; it is replaced by the θ-dependent invariant penalty of Section 2.

The exclusion region is narrower along the gradient

As published. Section 2 describes the carve-out B_δ = {z : zᵀGz ≤ δ²}, with G = I + α v vᵀ and v = ∇φ, as elongated along the barrier gradient. The worked example correctly calls the gradient direction the minor axis.

along v̂ :      r ≤ δ / √(1 + α‖v‖²)
perpendicular : r ≤ δ

Correction. With this G, the excluded region is narrower along the gradient, and Section 2 is corrected to say so. Where elongation along the gradient is the intended design, the region is defined with G⁻¹ = I − α v vᵀ / (1 + α‖v‖²), which gives radius δ√(1 + α‖v‖²) along v̂. Positive definiteness and the Sherman–Morrison inverse are unaffected.

Proposition 9.1 bounds displacement, not re-entry

As published. The proposition states that the radius δ = √(2 Tr(σσᵀG) Δt ln(1/ε_risk)) bounds the probability of re-entering the ball around x_f, and the text then calls it a bound on leaving the ball. These are different events. For zero-drift Brownian motion started at δ + a, the probability of entering the interval by time T approaches 1 as a → 0, so no radius gives a uniform re-entry bound without a minimum starting separation.

Correction. Proposition 9.1 is restated as a displacement bound: over an interval Δt, the probability that the state moves farther than δ from its starting point, measured in the G-norm, is at most ε_risk under the stated disturbance model. A re-entry guarantee is withdrawn as stated. Any future re-entry result will define the event explicitly, require a minimum separation from the excluded region, and use a hitting-probability bound.

Lemma 4.1 needs a control-authority assumption

As published. The lemma states that the projection program is strictly feasible whenever D_R > η. Recoverability alone does not imply that. For ẋ = −x with U = {0}, D_R(x) = x, η = 1 and γ(h) = h, the state x = 2 is recoverable, yet the constraint reduces to 0 ≥ 1.

Correction. The lemma now states the assumption it uses: on the margin set, D_R − η is a control barrier function over the admissible inputs.

∀x with D_R(x) ≥ η :  ∃ u ∈ U  such that  ∇D_R(x) · f(x, u)  >  −γ(D_R(x) − η)

Effect. The counterexample does not satisfy Law 3, so Theorem 2 with all of its assumptions is not refuted. The correction attributes feasibility to the assumption that actually supplies it.

Pinning the statistic does not discharge the supermartingale hypothesis

As published. The risk bound uses M_k = M₀ ∏ e_j with E_P₀[e_j | F_j−1] ≤ 1, and argues that pinning the function that computes e_j keeps the bound valid under arbitrary rewrites. Pinning fixes the code. It does not fix the distribution of the inputs: a statistic with expectation 1 under P₀ can have expectation 2 under a rewritten process.

Correction. Ville's inequality holds under the supermartingale hypothesis, and the bound is stated relative to the reference model P₀. Pinning the statistic is necessary and not sufficient. Detecting departure from P₀ is a separate obligation, and mapping a monitor-threshold probability to a dangerous-failure rate remains the open item already listed in Section 9.

The identity theorem needs an injective or collision-resistant binding

As published. Theorem 2 argues that substitution changes the canonical form, hence the binding, and therefore causes denial. A finite digest over a larger domain is not injective, so o ≠ o′ does not by itself imply β(o) ≠ β(o′).

Correction. Theorem 2 is stated in three forms, and each claim in the corpus names which one it uses:

• Comparison: the gate compares full canonical objects. The theorem holds absolutely.
• Injective encoding: the binding is injective over a restricted finite admitted domain. The theorem holds absolutely on that domain.
• Cryptographic digest: the binding is a collision-resistant hash. The probability that a substitution goes undetected is at most the adversary's collision advantage, which makes this a computational security claim rather than an impossibility theorem.

The PCR table needs an explicit exit from RUN

As published. The temporal specification requires G(RUN → MonitorHealthy ∧ AuthFresh ∧ Ψ ⪰ 1). In the displayed cascade, case 4 requires MonitorHealthy to enter RUN, and case 5 otherwise keeps the current state. With Z = RUN, Ψ = 1 unchanged and MonitorHealthy false, case 5 keeps RUN.

Correction. A rule is inserted before case 5:

3a. PAUSE   if Z = RUN ∧ ( ¬MonitorHealthy(t) ∨ ¬AuthFresh(t) )

An implementation may instead treat loss of monitor health as a fault that sets Ψ(t) = ⊥, in which case case 1 moves the machine to DENY. Either way the invariant now follows from the table. The separate effect-boundary invariant, which already requires monitor health, kept the output de-energized in this case; the correction makes the state machine say so too.

What this review covered

The review read the corpus index and the available text of Genesis Rev 3, WP-10 Rev 4.4, WP-12 Rev 1.1, WP-13 Rev 1.1, the WP-14 Canonical Edition and WP-20. It did not audit WP-15, WP-16, the filed patent embodiments or their implementations. A review of WP-15 and WP-16 at the same depth is planned.