RESPONSES TO SUBSTANTIVE REVIEW OBJECTIONS
Manuscript version 1.1 -- 9 November 2026

R1-01: Ambiguous future output alone does not show an online impossibility;
earlier observations might distinguish the paths.
Response: Lemma 1 now constructs an attainable common physical prefix ending
at z in [-u-D,-u+D). Two final disturbances from that same prefix give opposite
next bits. Even an exact current-state observation cannot distinguish them
before the required report. Closed by the proof reviewer on final source.

R1-02: A binary leaf lower bound is not enough to prove balanced threshold
attainability for arbitrary B and a restricted finite library.
Response: Lemma 2 explicitly orders the finite signature atoms, shows whole
word groups occupy consecutive atoms, and uses the supplied separating
threshold at each balanced split. B need not be closed or connected. The
K=1 zero-query stop is explicit. Independent minimax tree checks corroborate
21845 bounded instances; the analytical proof carries arbitrary B.

R1-03..07: Clarify horizon, units, endpoints, randomness and batch semantics.
Response: H is a positive integer; b counts probes and money is c*b;
half-open intervals and sign-at-zero are stated; random correctness is
probability one for each physical execution with a hard budget; only a finite
intersection of representative correctness events is used; batch queries
are adaptive but all occur at time zero. No implicit nonadaptive comparator,
free current labels, free event detection, or support-sensitive legality.

R2-01 / H1 (identified independently): The explanatory text said feasibility
was the only improvement 'when comparing with a feasible batch optimum',
contradicting the corollary.
Response: Replaced with the exact conclusion: strict improvement requires
batch infeasible and online feasible; feasible batch admits no improvement.
The theorem statements and calculations did not change. Both reviewers
verified closure against the final SHA256.

H2: 'No added value' could sound as though no possible extra input helps.
Response: Reworded to 'with no additional input value a separation is
impossible'. Minimality counts added alphabet elements only, not numerical
distance, energy, or general model perturbation. Closed in hostile round 2.

H3 / priority: Do not relabel classical sequential testing, the parent
acquisition report or adaptive repair-order results as a new general theorem.
Response: Section 1 adds primary comparisons and precise comparator
differences. The negative scalar obstruction leads; the extension is its
boundary example. Classical reachability, decision trees and transcript
arguments are attributed. The package recommends an integration-ready
addendum. No exact duplicate found in a targeted search is not priority proof.

Production limitation: the compiler stopped during installation initialization.
Response: A fresh narrowly scoped approved build resolved the limitation.
The unchanged source compiled twice; all seven pages were rendered and visually
inspected. Site integration remains with the central publisher. The proof
closure still applies to the same source hash.