inverse problems · configuration space what the projection keeps · underdetermined experiments, collapsed configuration spaces, and the tools brought from outside · started October 2026

Sources

Sources

Every reference the discourse and the cases lean on, with its DOI, source URL and access status. Read means read in full in this project; checked means its bibliographic identity has been verified. Downloading a PDF does not mean it has been read in full or that the claims made about it have been independently reassessed.

The reference audit of 14 October 2026 (L007) covers these 21 sources and all 44 numbered references in Daun et al. The local collection in sources/library/ contains a searchable index, BibTeX, a verification manifest, citation corrections and a list of missing full texts. The PDFs remain outside this public site. Public full-text links below identify the copies actually downloaded, including manuscripts and preprints where indicated.

Project review record

Citation support audit — 14 October 2026. Prepared by Codex (AI assistant); recorded in L009 and published as a dated report in L010. It assesses 42 claim groups against source passages and separates evidence, limitations and proposed corrections. This project report is awaiting author review; it is not a peer-reviewed source or an approved revision. The scientific text remains unchanged. The report includes a suggested citation, source links, page locators and a downloadable copy.

The audit reviewed — 14 October 2026. Prepared by Claude (AI assistant) at Josu's request; recorded in L012. Each of the 42 findings re-judged against the printed sentence and, where the PDF is on disk, against the locator re-read: 32 agreed and to apply, 5 agreed with a narrower reading of the text, 3 partly agreed, 2 open, none rejected; the audit's method assessed, its gaps listed, and one revision proposed. Awaiting Josu's and Iñigo's reading; nothing applied.

Third audit report — 14 October 2026. Prepared by Codex (AI assistant); recorded in L013. Seven review findings distinguish exact website wording from stronger paraphrases, qualify the earlier assessments, record newly accessible full-text evidence from Raue, and identify additional coverage gaps. The report states where it differs from the second review, preserves both earlier records, and includes a downloadable edition and provenance. Awaiting author review; no scientific corrections applied.

31 sources: 2 read in full here, 26 confirmed by a search on the date given, 3 cited from memory and still to be confirmed. Generated from data/sources.yml; do not edit by hand.

In the project

Key Reference Status Used for
daun2019 K. J. Daun, J. Menser, M. Asif, S. Musikhin, T. Dreier, C. Schulz, Evaluation of Drude parameters for liquid germanium nanoparticles through aerosol-based line-of-sight attenuation measurements, J. Quant. Spectrosc. Radiat. Transfer 226 (2019) 146–156.
doi: 10.1016/j.jqsrt.2019.01.021
Source / publisher
read 2026-10-14
Local PDF: published; pre-existing
The second case: Bayesian inference of (\(\omega\)_p, \(\tau\)) from extinction spectra with Rayleigh, Mie and approximate-Mie models; the ill-posedness shown in its Fig. 9; model error after Kaipio and Somersalo. The PDF is in sources/.

Mode crystallography

Key Reference Status Used for
perezmato2010 J. M. Perez-Mato, D. Orobengoa, M. I. Aroyo, Mode crystallography of distorted structures, Acta Cryst. A66 (2010) 558–590.
doi: 10.1107/S0108767310016247
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
The symmetry-mode parameterisation of distorted structures; its stated uses — hidden correlations, fundamental and marginal degrees of freedom, fewer effective parameters — are the external tool of T07 in the authors' own words.
orobengoa2009 D. Orobengoa, C. Capillas, M. I. Aroyo, J. M. Perez-Mato, AMPLIMODES: symmetry-mode analysis on the Bilbao Crystallographic Server, J. Appl. Cryst. 42 (2009) 820–833.
doi: 10.1107/S0021889809028064
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
The program that decomposes a distorted structure into symmetry-adapted modes; the tool a script would call.
campbell2006 B. J. Campbell, H. T. Stokes, D. E. Tanner, D. M. Hatch, ISODISPLACE: a web-based tool for exploring structural distortions, J. Appl. Cryst. 39 (2006) 607–614.
doi: 10.1107/S0021889806014075
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
The other mode tool (now ISODISTORT); mode amplitudes as refinable parameters in Rietveld programs.
rietveld1969 H. M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Cryst. 2 (1969) 65–71.
doi: 10.1107/S0021889869006558
Source / publisher
checked 2026-10-14
Full text not obtained
The method of the first case.
patterson1944 A. L. Patterson, Ambiguities in the X-ray analysis of crystal structures, Phys. Rev. 65 (1944) 195–201.
doi: 10.1103/PhysRev.65.195
Source / publisher
checked 2026-10-14
Full text not obtained
Homometric structures: different structures with identical diffraction intensities — an exact null space of the forward map.

Inverse problems and identifiability

Key Reference Status Used for
hadamard1902 J. Hadamard, Sur les problèmes aux dérivées partielles et leur signification physique, Princeton University Bulletin 13 (1902) 49–52.
Source / publisher · Public full-text copy
checked 2026-10-14
Original Princeton University Bulletin 13(4), April 1902, pp. 49–52. No DOI was confirmed. Unrelated Crossref search hits were rejected.
Local PDF: scan of original publication
The definition of a well-posed problem (existence, uniqueness, continuous dependence); an underdetermined inverse problem fails the second and third.
tarantola2005 A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 2005.
doi: 10.1137/1.9780898717921
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published book
The probabilistic formulation: the solution of an inverse problem is a probability density on the model space, not a point.
kaipio2005 J. Kaipio, E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2005.
doi: 10.1007/b138659
Source / publisher
checked 2026-10-14
Same book as Daun reference [40]. Springer gives copyright 2005, hardcover release 1 December 2004, and eBook release 30 March 2006; these dates explain the 2005/2006 citations. Full book not obtained; free front/back matter is not counted as the book.
Full text not obtained
The approximation error model: the discrepancy between an exact and an approximate forward model treated as a random term with its own mean and covariance; used by Daun et al. for the approximate Mie model.
kennedy2001 M. C. Kennedy, A. O'Hagan, Bayesian calibration of computer models, J. R. Statist. Soc. B 63 (2001) 425–464.
doi: 10.1111/1467-9868.00294
Source / publisher
checked 2026-10-14
Full text not obtained
Model inadequacy as a discrepancy term to be inferred together with the parameters; the parameters lose their physical meaning when the discrepancy is left out.
brynjarsdottir2014 J. Brynjarsdóttir, A. O'Hagan, Learning about physical parameters: the importance of model discrepancy, Inverse Problems 30 (2014) 114007.
doi: 10.1088/0266-5611/30/11/114007
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: author manuscript
The demonstration that calibrated parameters are biased and over-confident when the model's discrepancy is ignored.
raue2009 A. Raue, C. Kreutz, T. Maiwald, J. Bachmann, M. Schilling, U. Klingmüller, J. Timmer, Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood, Bioinformatics 25 (2009) 1923–1929.
doi: 10.1093/bioinformatics/btp358
Source / publisher
checked 2026-10-14
Full text not obtained
The distinction between structural and practical non-identifiability, and the profile likelihood as the diagnostic.

Sloppiness

Key Reference Status Used for
gutenkunst2007 R. N. Gutenkunst, J. J. Waterfall, F. P. Casey, K. S. Brown, C. R. Myers, J. P. Sethna, Universally sloppy parameter sensitivities in systems biology models, PLoS Comput. Biol. 3 (2007) e189.
doi: 10.1371/journal.pcbi.0030189
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
Fisher-information spectra spanning many decades: the data fix a few stiff parameter combinations and leave the rest free; 'focus on predictions rather than on parameters'.
transtrum2015 M. K. Transtrum, B. B. Machta, K. S. Brown, B. C. Daniels, C. R. Myers, J. P. Sethna, Perspective: Sloppiness and emergent theories in physics, biology, and beyond, J. Chem. Phys. 143 (2015) 010901.
doi: 10.1063/1.4923066
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
The model manifold: the image of the configuration space in data space, its thin directions, and the manifold boundary approximation that reduces the model along them.

Machine learning for inverse problems

Key Reference Status Used for
cranmer2020 K. Cranmer, J. Brehmer, G. Louppe, The frontier of simulation-based inference, Proc. Natl Acad. Sci. USA 117 (2020) 30055–30062.
doi: 10.1073/pnas.1912789117
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: arXiv preprint
Amortised inference: a network trained on simulations returns the posterior for any new measurement; the whole fibre, not one point.
park2017 W. B. Park, J. Chung, J. Jung, K. Sohn, S. P. Singh, M. Pyo, N. Shin, K.-S. Sohn, Classification of crystal structure using a convolutional neural network, IUCrJ 4 (2017) 486–494.
doi: 10.1107/S205225251700714X
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
About 150 000 simulated powder patterns; crystal system, extinction group and space group classified at 95, 84 and 81 %: what a projection keeps of the symmetry.
lee2020 J.-W. Lee, W. B. Park, J. H. Lee, S. P. Singh, K.-S. Sohn, A deep-learning technique for phase identification in multiphase inorganic compounds using synthetic XRD powder patterns, Nature Commun. 11 (2020) 86.
doi: 10.1038/s41467-019-13749-3
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
1.8 million synthetic patterns from 170 compounds; the knowledge is in the generator of the training set — T09 and T10 in practice.
szymanski2021 N. J. Szymanski, C. J. Bartel, Y. Zeng, Q. Tu, G. Ceder, Probabilistic deep learning approach to automate the interpretation of multi-phase diffraction spectra, Chem. Mater. 33 (2021) 4204–4215.
doi: 10.1021/acs.chemmater.1c01071
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
Simulated spectra augmented with physics-informed perturbations; an ensemble that returns probabilities, not labels — the form the output must take when the problem is underdetermined.

Infrared spectra and dielectric functions

Key Reference Status Used for
kuzmenko2005 A. B. Kuzmenko, Kramers–Kronig constrained variational analysis of optical spectra, Rev. Sci. Instrum. 76 (2005) 083108.
doi: 10.1063/1.1979470
Source / publisher · Public full-text copy
checked 2026-10-14
Local PDF: published
The dielectric function as a free, causal function anchored by a few oscillators: the data determine \(\varepsilon\)(\(\omega\)) on the measured range, not a unique set of oscillators.
difes2026 J. M. Igartua, difes: dielectric function, inversion, fitting, emissivity, simulation, private repository jmigartua/difes and its site ftir-ecosystem-site, 2026.
Source / publisher
read 2026-10-14
Software/repository citation, not a paper. Existing project read status retained. No DOI or paper PDF expected; repository not cloned or independently audited in this reference check.
Software source; no paper PDF expected
The third case's machinery: oscillator models, the Fresnel link, Kramers–Kronig with finite-range corrections, recipes (the expert's steps in a text file).
gonzalezdearrieta2020 I. González de Arrieta, High-temperature infrared emissivity of materials for alternative energy applications, PhD thesis, UPV/EHU, 2020.
Source / publisher
Reported deposit DOI: 10.13140/RG.2.2.14502.55365
checked 2026-10-14
Thesis confirmed by EHU. ResearchGate reports a deposit DOI, recorded separately from independently verified publication DOIs. The ADDI handle and indexed PDF returned HTTP 404 during this audit; the thesis PDF is not local.
Full text not obtained
The domain of the author of the ideas: emissivity measured directly at high temperature, and interpreted through dielectric-function models.

Inference before refinement and the family's tree (the diff-ref-struct assessment of 15 October 2026, L014)

Key Reference Status Used for
fancher2016 C. M. Fancher, Z. Han, I. Levin, K. Page, B. J. Reich, R. C. Smith, A. G. Wilson, J. L. Jones, Use of Bayesian inference in crystallographic structure refinement via full diffraction profile analysis, Sci. Rep. 6 (2016) 31625.
Source / publisher
checked 2026-10-15
Open access; not downloaded
Bayesian Rietveld for one structure: MCMC over the model's parameters, posteriors for all of them, on the NIST silicon standard; its uncertainties larger than Rietveld's. The nearest existing thing to P1 done by sampling, and the reference for why Rietveld's \(\chi^2\) is not a likelihood.
gagin2015 T. Gagin, I. Levin, Accounting for unknown systematic errors in Rietveld refinements: a Bayesian statistics approach, J. Appl. Cryst. 48 (2015). not checked
Cited from memory; pages and DOI to confirm
An explicit correlated systematic-error term in a Rietveld model: one of the two misfit models the assessment asks the toy to compare by calibration (the other is the tempered \(\chi^2\)).
markvardsen2001 A. J. Markvardsen, W. I. F. David, J. C. Johnson, K. Shankland, A probabilistic approach to space-group determination from powder diffraction data, Acta Cryst. A57 (2001).
Source / publisher
checked 2026-10-15
Abstract seen; full text not obtained
Relative probabilities of the extinction symbols of a crystal system from integrated intensities (the program ExtSym). The k-point test proposed in the assessment is this idea carried from extinction symbols to the irreps of a parent.
kerman2012 S. Kerman, B. J. Campbell, K. K. Satyavarapu, H. T. Stokes, F. Perselli, J. S. O. Evans, The superstructure determination of displacive distortions via symmetry-mode analysis, Acta Cryst. A68 (2012) 222–234.
Source / publisher
checked 2026-10-15
Public reprint on the ISOTROPY site; not read in full
The symmetry modes of a P1 supercell as on/off switches and a global search for the active ones, with ISODISTORT and TOPAS: the closest existing work to a search of the configuration space in mode coordinates, and a point search rather than a posterior.
ozaki2020 Y. Ozaki, Y. Suzuki, T. Hawai, K. Saito, M. Onishi, K. Ono, Automated crystal structure analysis based on blackbox optimisation, npj Comput. Mater. 6 (2020) 75.
Source / publisher
checked 2026-10-15
Open access; the Optuna sampler page seen, the paper not downloaded
Bayesian optimisation of a refinement's settings to minimise R_wp (BBO-Rietveld), beating an expert on \(\mathrm{Y_{2}O_{3}}\) in about 100 trials. 'Bayesian' in the optimiser only: one point out, nothing about the posterior over the structure.
riesel2024 E. A. Riesel et al., Crystal structure determination from powder diffraction patterns with generative machine learning, J. Am. Chem. Soc. (2024); the model Crystalyze.
Source / publisher
checked 2026-10-15
Seen through MIT's news release; the paper not opened; author list and pages to confirm
A generative network that proposes structures from a powder pattern, right on about 67 % of 100 RRUFF patterns: the point-generator approach the discourse's §7 says must give way to a distribution.
howard2003 C. J. Howard, B. J. Kennedy, P. M. Woodward, Ordered double perovskites — a group-theoretical analysis, Acta Cryst. B59 (2003) 463–471.
Source / publisher
checked 2026-10-15
Confirmed through papers that cite it; full text not obtained
The twelve space groups of the rock-salt-ordered double perovskites and their group–subgroup tree: the finite list of candidate subgroups the assessment's first idea compares by evidence, and the reason Q3 can be answered by this family.
howard2004 C. J. Howard, H. T. Stokes, Octahedral tilting in cation-ordered perovskites — a group-theoretical analysis, Acta Cryst. B60 (2004).
Source / publisher
checked 2026-10-15
Public reprint on the ISOTROPY site; not read
The 1:2 and 1:3 ordered perovskites (ten and eleven structures): the next families' trees, once the first works end to end.
howard1998 C. J. Howard, H. T. Stokes, Group-theoretical analysis of octahedral tilting in perovskites, Acta Cryst. B54 (1998) 782–789. not checked
Cited from memory
The fifteen Glazer tilt systems of \(\mathrm{ABX_{3}}\) as a group–subgroup tree: the \(\mathrm{ABX_{3}}\) family's tree, if that family comes after the double perovskites.
skilling2006 J. Skilling, Nested sampling for general Bayesian computation, Bayesian Analysis 1 (2006) 833–859. not checked
Cited from memory
The sampler that returns the evidence and the posterior together, with several modes: the assessment's candidate for the cases where a Laplace approximation around each minimum is wrong.