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[paper] P9 R3: fix epsilon/delta asymptotic inconsistency and prolate branch parameterisation - #316
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… branch parameterisation
Bug 1 (critical): The paper claimed both sigma_3 ~ epsilon^2 and fitted
sigma_3 ~ delta^2. Since epsilon^2 = delta(2-delta), these are incompatible
asymptotics. All references to delta removed; the table, fit, and text now
use eccentricity epsilon exclusively. Fit parameters updated to
sigma_0=0.0074, lambda_1=0.034 (least-squares in epsilon^2).
Bug 2 (critical): The prolate branch text claimed a=a_0(c_0/c)^{1/2} with
constant volume, yielding c/a in [1.0, 1.5]. That formula actually gives
c/a in [0.667, 2.25]. The code holds a=a_0 fixed and sweeps c, so the text
now matches: a=a_0 fixed, c in [0.18, 0.27] m, c/a in [1.0, 1.5]. The
sphere limit (c=a_0) is correctly noted as distinct from R_eq=0.157 m.
Bug 3 (minor): Softened mechanism claim in abstract and discussion from
'depends on how curvature is redistributed' to 'consistent with
mode-dependent curvature sampling'.
Bug 4 (minor): Loss tangent eta=0.25 now defined at first use in
problem_setup.tex among the canonical parameters.
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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Reviewer B Round 3 — Mathematical Fixes
Bug 1 (critical): ε vs δ inconsistency
The paper claimed σ₃ ~ ε² (Eq. 1) but fitted σ₃ ~ δ². Since ε² = δ(2−δ) ≈ 2δ, these are incompatible asymptotics. All δ references removed; table, fit, and text now use eccentricity ε exclusively. Fit: σ₀=0.0074, λ₁=0.034.
Bug 2 (critical): Prolate branch numbers
Text claimed a=a₀(c₀/c)^{1/2} with constant volume, but that formula gives c/a ∈ [0.667, 2.25], not [1.0, 1.5]. The code holds a=a₀ fixed. Text now correctly describes: a=a₀=0.18m fixed, c ∈ [0.18, 0.27]m, c/a ∈ [1.0, 1.5]. Sphere limit (c=a₀) noted as distinct from R_eq=0.157m.
Bug 3 (minor): Softened mechanism language
Abstract and discussion now say 'consistent with mode-dependent curvature sampling' rather than asserting a causal mechanism.
Bug 4 (minor): η defined
Loss tangent η=0.25 now introduced at first use in problem_setup.tex.