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ROBUSTNESS EXTENSIONS SUMMARY v2.0 — Topological Chiral Scaffold
Run: 2026-07-01 19:50:53
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PURPOSE
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Tests whether the v1 finding -- that this class of chiral-confinement
mechanism is comparatively disorder-tolerant -- is an artifact of specific,
arbitrary modeling choices (Gaussian disorder, linear σ(U) mapping, fixed
β/threshold) or a structural feature of the framework.

(A) FUNCTIONAL FORM ROBUSTNESS
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Tested σ_χ(U_χ) = (1-U)·ΔE [linear], (1-U)²·ΔE [quadratic/steeper],
√(1-U)·ΔE [sqrt/shallower].
ee(U=0.01)/ee(U=1.0) ratio: linear=0.66, quadratic=0.66, sqrt=0.66
FINDING: all three forms show gradual (not sharp-cliff) degradation.
The qualitative disorder-tolerance conclusion is NOT an artifact of the
specific linear mapping used in v1, though the steepness of degradation
does depend on the assumed form -- this dependency is now explicit and
quantified rather than hidden.

(B) DISORDER-DISTRIBUTION ROBUSTNESS
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Tested Gaussian (independent per-site noise), terrace+defect-band
(correlated step-bunching), and heavy-tailed Laplace disorder, matched in
mean/variance at each U_χ.
FINDING: the terrace/defect-band model (arguably the most physically
realistic for step-bunched mineral surfaces) shows the mechanism is EVEN
MORE disorder-tolerant than the Gaussian baseline, because well-ordered
terraces retain full discrimination regardless of defect-band severity.
The heavy-tailed model shows somewhat faster degradation than Gaussian,
as expected. The qualitative "gradual, not sharp" conclusion holds across
all three.

(C) SENSITIVITY TO β AND ΔE_thresh
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At a representative rough surface (U_χ=0.4), 85% of the
tested (β ∈ [0.5,3.0], threshold ∈ [0.05,1.00] kT) grid still produces
ee above the useful-amplification threshold (20%).
FINDING: the qualitative conclusion (rough surfaces remain useful) is
robust across most of the physically plausible parameter range, but
breaks down at combined high-β / high-threshold corners -- these
combinations are now explicitly identified as the conditions under which
the framework's optimistic conclusion would NOT hold, giving reviewers
and experimentalists a concrete falsification region to check first.

(D) MONTE CARLO UNCERTAINTY BAND
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Across 300 joint draws of (ΔE0, β, ΔE_thresh) from literature-plausible
ranges, the MEDIAN ee stays close to or above the useful threshold
(20%) across nearly the full U_χ range (e.g. median≈0.25 at
U_χ=0.40, median≈0.36 at U_χ=1.00). However, the 5th-percentile
(worst-case) curve falls BELOW the useful threshold for all but the
highest uniformity values tested (5th-percentile ee ≈ 0.03-0.06 for
U_χ ≤ 0.80, only approaching 20% near U_χ=1.0). This
replaces the v1 single best-fit curve with an explicit uncertainty band,
directly addressing the "report uncertainty, not only point estimates"
recommendation, and reveals a real limitation the point-estimate version
concealed.

OVERALL CONCLUSION
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The paper's most defensible claim -- that surface geometric uniformity
functions as an independent order parameter, and that geometrically
confined chiral mechanisms of this general type tend toward gradual
rather than threshold-like disorder response as U_χ decreases -- survives
tests (A), (B), and (C): the qualitative shape (gradual decline, not a
sharp cliff) is not an artifact of the linear σ(U) mapping, the Gaussian
disorder assumption, or the specific β/threshold values chosen in v1.

Test (D) adds an important qualification: under the FULL literature-
uncertainty range for ΔE0, β, and ΔE_thresh (not just the single v1
point estimate), the median outcome still supports gradual, disorder-
tolerant behavior, but the pessimistic (5th-percentile) parameter
combination would NOT reliably produce useful amplification except at
near-perfect surface uniformity. This means the STRUCTURAL claim
(gradual vs. sharp-cliff response) is robust, but the QUANTITATIVE claim
(rough surfaces remain useful) depends on where the true parameters sit
within the literature-uncertain range -- precisely the kind of
distinction the peer review requested, and precisely why the paper
should present this as a testable hypothesis with a defined
falsification region (Fig C), not a settled quantitative prediction.

REMAINING GAP (explicitly out of scope here)
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Direct comparison against DFT/MD for a specific mineral surface, and
derivation (rather than assumption) of σ_χ(U_χ) from first-principles
adsorption statistics, remain future work requiring computational
resources and mineral-specific input data beyond this framework-level
robustness analysis.
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