INDEPENDENT AUDIT OF READER ADDITIONS — 9 October 2026
Scope: editorial additions versus reader-baseline; not a repeat audit of the
original manuscript's full proof. Files checked: reader-guide.tex,
receiver.tex changed definitions, core-cold.tex Gaussian-weight rename,
assembler and current assembled source.

Verified additions:
1. Profile/seed definitions preserve W_0=-1_{B_rho}+rho^2 1_{B_1}, rho^2=3/5,
   fixed smoothing, growing/stable moment cancellation and seed covariance.
2. Stack, individual actual scalar colours, positive envelopes and packet
   definitions retain the common actual velocity. No independent evolution
   is attributed to an interacting colour.
3. Clock/amplitude/length normalization and kappa_j(nu_N) are consistent.
   The rotating coordinate y -> R_{Omega_<j s}y removes the signed older
   rigid rotation. At the outer scale this rotation is zero.
4. Exact phase ratio compares the child's complex cap coordinate to the
   canonical small-cap coordinate; both have modulus delta. The canonical
   first-cap infimum s_q is well-defined for small q on the protected
   ancient branch, since A(Omega_ref(u))->0 as u->-infinity and
   |A(Omega_ref(0))|=delta_ref>delta.
5. t_ref=tau_c-s_q is a child clock, t_0=t_ref/beta is a receiver clock,
   and u=s_c-t_ref gives actual cap u=s_q, reference u=0.
6. Controlled source history is truncated and zero-extended at its actual
   controlled endpoints. The canonical transform has domain 0<Re(mu)<sigma.
   C_*=gamma_epsilon F_ref(mu_beta) has no spurious beta factor.
7. phi_c=phi+4t_0/5 and B_c=e^{i phi_c}mathcal B_q retain the receiver-reference
   gauge. The remaining forcing rotation is e^{4i(t-t_0)/5}, not e^{4it/5}.
8. Density stop, prospective endpoint and coordinate first cap are distinct.
   Completed C_q is used only after the upper estimate closes T_s>H_+.
9. Homotopy amplitudes xi_j^{N,r}=1 at j=N and r otherwise, with phase theta
   only at N, reproduce the proof's auxiliary initial datum. For N>=2 its
   outer initial colour is W+alpha r Phi_{vartheta_1}. At r=0 the phase map
   is exact degree-one rotation; at r=1 only its degree/surjectivity is used.
10. Delta_tail(m) equals the sum of the separate L^1 and L^p geometric norm
    bounds, with factor 2 for the difference of two rotated seeds. It
    tends to zero and correctly supplies simultaneous fixed-viscosity
    continuity radii in the sparse construction.
11. Added definitions of C, M_j and E_j^r represent the two fixed derivative
    collars and finite angular-sector spaces already used in the proof.
    The derivative reserve and recursive finite polynomial are unchanged.
12. Gaussian beta_G renaming affects only the local Gaussian-weight proof.
    Direct comparison to the baseline shows all mathematical numerical
    factors, coercivity constants and exponents unchanged. Macro uses in
    subscripts are now braced in the assembled source.

One precision edit recommended (sent to root):
After the E_j^r display, state that h_m is extended by zero outside I and
f(0):=0. Then the whole-plane function in the displayed definition is
literally defined. Since C lies in the interior of I, the support condition
forces coefficients to vanish near the endpoints of I, preserving the
stated equivalence with the full-plane H^r norm. This changes no theorem.

No changed theorem assertion or additional mathematical hypothesis was
found in the reader guide, local definition conversion, or Gaussian rename.
This is an audit of the new editorial content, not a blanket certification
of every unchanged original argument.

FOLLOW-UP: EXPLICIT SPARSE ASSIGNMENT AND CONTINUITY RADIUS
Checked eq:reader-sparse-assignment and eq:reader-continuity-radius in
selection.tex. The recursive phase assignment updates one coordinate per
strictly increasing selected depth and retains the previous coordinates.
The final coordinatewise phase limit therefore exists and determines the
same single datum in X_p by the geometric tail estimate.

The half-supremum continuity radius is rigorously defined. Its admissible
radius set is nonempty by fixed-viscosity solution/colour continuity and
common protected caps, and is downward closed. Its supremum lies in (0,1].
Half that supremum lies strictly below it; an admissible radius larger
than the half-supremum exists by the definition of supremum, so downward
closure proves the claimed universal error property at r_k itself.
The universal quantifier over all phase vectors with theta_1=0 is valid:
each such datum has the same bounded initial outer colour W+alpha Phi_0,
and the uniform stage theorem supplies protected caps for every such
phase assignment at the chosen positive viscosity.

The strict tail condition Delta_tail(N_{k+1})<min_{i<=k}r_i controls all
future phase changes at once, giving the final error <2^-k from the datum
assigned at step k. No accumulation of successive phase errors is needed.

One clarity condition sent to root: explicitly specify N_1>=2 (and hence
N_k>=2 for all k), ensuring the outer phase stays fixed and the surjective
phase proposition applies. This requirement was already implicit in the
original construction and is not a new mathematical hypothesis.
The requested zero-extension clarification in E_j^r is now present and
verified. No uncorrected mathematical defect was found in these additions.
