Right on both counts. The three conditions are the textbook form, not Hadamard's words, and the Sources page attributes them to him. The second half of the sentence is also loose: non-uniqueness fails uniqueness; whether continuous dependence fails is a separate question about the chosen solution.

Nothing to add. The locators are a gift; the Sources page had none.

Agreed. "Can be biased" is what the sources show, and Brynjarsdóttir and O'Hagan is the better reference for it. The audit's added caution — that a discrepancy term does not by itself identify the parameters — is the more important point for the programme, since P3 and P4 propose to detect inadequacy at scale and will meet exactly this confounding.

The discourse already says "can be excellent and the parameters meaningless, or worse, meaningful-looking and biased". The audit's condition is the right one.

The site uses Raue for the two terms and nothing else. Agreed that the Jacobian claims of §3 do not rest on it and should not be read as if they did.

Agreed. The definition box mixes a continuous notion (null space) with a discrete example (homometry). Since the project fixed its vocabulary deliberately, the fix belongs in the definition itself: an exact ambiguity is any pair of configurations with the same response; it may be a continuous family (a fibre of positive dimension) or a discrete set (homometry, the phase problem's enantiomorph pair); "null space" is the local, linear picture of the first.

Agreed; the sentence is literal and overstated. What was meant is that the structure-factor part — kinematic scattering from a periodic density — is settled physics, and that the doubt lives in the profile and the sample terms. The page's own "Off the manifold" list says so two paragraphs later, which is the contradiction the audit caught.

Agreed, and the audit's "keep apart" is the key to C13 and C14: what Perez-Mato et al. establish is a physical organisation of the degrees of freedom; what the discourse adds about the data's sensitivity is this development's and must be marked as a hypothesis.

Agreed. The audit checked the AMPLIMODES half of the sentence; the ISODISTORT half ("writes the amplitudes as refinable parameters for Rietveld programs") was not checked by the audit and is listed below as a gap.

Agreed on the facts; the discourse's point survives in the audit's own wording ("alternative coordinates for the same allowed displacements"), with "orthonormal" made a convention rather than a property. The last clause of the audit — that fixing modes restricts the model — is not a correction but the mechanism the discourse describes: the restriction is the prior.

Agreed; pp. 564–565 were re-read today and say what the audit says: primary eigenmodes unstable, secondary ones induced through Eq. (9), amplitudes "expected to be" smaller. "Cannot even be written down" is rhetoric; the true statement is that the prior is sparse and separable in one basis and dense and correlated in the other, which is the whole point and needs no exaggeration.

Agreed without reservation; the sentence conflates two rankings that the programme itself wants kept apart (P4's "identifiability maps" are precisely the second ranking). The audit's proposed wording — report amplitudes with uncertainties and correlations; rank contribution and identifiability separately — is the right one and should become a rule of the project.

Agreed. The discourse calls sloppiness "the typical case" of practical non-identifiability; "typical" is what Gutenkunst et al. found across their seventeen models, and the word should be tied to that scope.

Transtrum 010901-4, re-read today: changing a rate constant from Hz to kHz scales its row and column of the Fisher matrix by 1000; dimensionless (log) parameters make the eigenvalues meaningful.

Agreed, and it is a real omission: P1 asks programs to print this spectrum, and without a scale the spectrum is arbitrary. The natural scale is the one the project already talks about — the prior width of each parameter (a mode amplitude's plausible range, an occupancy's 0 to 1) — so the fix is to whiten the parameters as well as the data: \(J_s = \Gamma^{-1/2}\,\partial F/\partial\theta\,S\) with \(S\) the matrix of parameter scales.

Agreed; the counterexamples are elementary and decisive. The glossary should separate four things the discourse ran together: global against local, continuous against discrete, exact against first-order. The repair is small and the discourse is better for it: the Jacobian is the local diagnostic of the continuous case; discrete ambiguities need a global search (which is, incidentally, one more reason for P2's "many starting points").

Agreed; "typically a thin, curved ribbon with boundaries" is what 010901-4 says of the sloppy models studied, and the discourse's "typically" should be read with that scope.

The site's rounded numbers are right; the audit's caution — these are benchmark accuracies, not limits of what a pattern can tell — is the same point the discourse makes about ML in general, and should be said where the numbers are quoted.

Agreed; the chemical scope matters for the discourse's own argument about transfer (C42) and should be named.

Kuzmenko 083108-1 (abstract: "the number of oscillators is on the order of the number of experimental points"), -3 (§IV.A: an oscillator at every anchor frequency), -4 (§IV.D: a model function with a limited number of parameters fitted first, then the variational part added, Eq. (17)), re-read today.

Agreed; the site's phrase was written from memory and describes the two-step scheme backwards. The audit's correction is confirmed line by line. What the site wanted from the reference survives: the data determine \(\epsilon(\omega)\) on the range, and the physical meaning of individual oscillators "may not be always clear" (083108-3) — Kuzmenko says it himself.

Kuzmenko 083108-1, Eqs. (3)–(4) and the paragraph after them, re-read today: "a necessary condition is that \(r(\omega) \neq 0\) for \(\mathrm{Im}(\omega) > 0\) … holds for the normal angle of incidence but breaks down, for instance, for off-normal reflectivity if the angle of incidence is large enough. The same problem appears when the sample is a thin film."

Agreed; and the condition matters to the group, whose emittance measurements are not all at normal incidence on semi-infinite samples. The site's sentence is true for the standard case and silent on the conditions.

Kuzmenko 083108-4, §IV.D, re-read today: "the nonzero wings of \(\epsilon_2\) at higher and lower frequencies are essential to calculate \(\epsilon_1\) inside this region."

Agreed, and the error is instructive for the discourse's own taxonomy: out-of-band weight is seen in-band, weakly, through a smooth kernel — it is the second kind of underdetermination, not the first, and the sentence filed it under the first. The second clause of the sentence ("the integrals reach into it") already contains the correction.

Agreed; the partial-fraction argument settles the exact case. The practitioner's point — that in practice the number of oscillators is a choice and overlapping ones trade against each other — is true and belongs, again, under the second kind, with the model order named as the hypothesis the human brings (which the Cases table already lists under "What the human still brings").

Agreed; the commit should be on the Sources page, and the assumptions are the same ones C26 asks for.

Agreed, and it is the audit's most useful addition to the bibliography: the CEMHTI paper is the primary source for the method the group's own tool implements, and FOCUS comes from the same laboratory. Full text not obtained by the audit.

Agreed; the site uses the thesis only to place Iñigo's domain, and should keep to that. Iñigo can supply the chapters that matter when the dielectric case is discussed.

Agreed on both labels. The Drude case already says the temperature is "taken as 1550 \(\pm\) 35 K from earlier silicon work".

Daun p. 154, §5, re-read today: "Were the electron mean free path comparable to the diameter of the nanoparticle … Taking \(E_F = 1.9 \times 10^{-19}\) J … results in \(\lambda_e = 0.54\) nm, which is much smaller than the particles in this study (~40 nm) … A more likely explanation is that the simplistic free electron model … does not capture the true interaction."

p. 154: "suggests that each atom contributes three, not four, electrons to the conduction band."

Agreed; the site's "or" joins an explanation the authors keep with one they discard, and so misreports the paper. The "three, not four" half is right. This is the audit's most valuable single catch, and the kind of error a citation audit exists for.

Daun p. 152, re-read today: "captures more of the spectral variation caused by a surface plasmon resonance (SPR) having a peak near 190-nm … The higher signal-to-noise of the LDLS, combined with the fact that it captures more of the SPR".

Agreed; "reaches" was careless, and the signal-to-noise half of the explanation was dropped. Both parts of the paper's sentence belong on the page, because both bear on P6's design calculation: range and noise.

Daun p. 152, text after Eq. (18), and p. 153, Eq. (22), re-read today; the two intervals are printed as the audit transcribes them.

Agreed. The site smoothed over a discrepancy in the paper that a reader of the paper would want to know about, and that P6 cannot ignore: a replication must choose, and should ask the authors. The audit's reading — a probable typographical problem — is likely (the prior intervals are the physically plausible ones for a metal) but is not the site's to decide.

Agreed. The Drude case's own phrasing — "the Fisher information per wavelength band" — is the correct local version, and the discourse should say that rather than "expected information gain". P6's "show that" prejudges the result of a calculation not yet done; the audit is right to call it a demonstrated result stated in advance.

Agreed; the sentence promises what the three-kinds section of the discourse itself says cannot come from one diagnostic (model inadequacy is in the residuals, not in the Jacobian; discrete ambiguities are not in either). P1 is the cheapest member of a suite — scaled SVD, profile likelihood along the sloppy directions, residual structure, many starting points — and should be described as that.

Agreed, and this is the correction with the most consequence for the discourse's argument, because the two sentences are used to say what P1 should add. The algebra is right: a sloppy direction with a component along a parameter's axis makes that parameter's marginal variance large, so the printed e.s.d. does carry the valley's projection. What the diagonal cannot show is that two large e.s.d.'s belong to one valley — that is the correlation coefficient, which FullProf prints and which the discourse elsewhere says "almost nobody reads". The repaired sentence is stronger: the e.s.d.'s are the valley's shadows on the axes; the correlation matrix is its direction; P1 prints the direction.