The sources of the diff-ref-struct assessment added to the Sources page with their status: seven checked by search, three from memory

Josu saw that L014 pointed at the assessment without bringing its literature here, against this project's rule that every new source goes on the Sources page with its status. Added, in a group of their own: Fancher et al. 2016 (Bayesian Rietveld by MCMC), Markvardsen et al. 2001 (probabilities over extinction symbols; ExtSym), Kerman et al. 2012 (the symmetry-mode on/off search with ISODISTORT and TOPAS), Ozaki et al. 2020 (BBO-Rietveld), Riesel et al. 2024 (Crystalyze), Howard, Kennedy and Woodward 2003 (the twelve space groups of the ordered double perovskites) and Howard and Stokes 2004 (the 1:2 and 1:3 orderings), each checked by a web search of 15 October 2026 with the page seen; Gagin and Levin 2015, Howard and Stokes 1998 and Skilling 2006 not checked, from memory. None is read in full here. Each entry says what the assessment uses it for.

From diff-ref-struct: an assessment of inference before refinement and of the family's configuration space, which proposes answers to Q2 and Q3

Josu put two ideas to the diff-ref-struct project on 15 October 2026, both grown from this project's discourse: a Bayesian search of the configuration space before any refinement, from the data, the parent and the candidate subgroups; and the same search over the configuration space of a family of materials along its chemical axes. The assessment is on that project's site, "Inference before refinement, and the family's configuration space" (its design pages, log L286). What it says that bears on this project:

• The first idea is P1 and P2 made concrete on the diffraction case: evidences across the family's subgroup tree in mode coordinates, the domain-equivalent amplitude sets folded, the nuisances solved, the region as the result, and the design question (which measurement decides) answered from the posterior. Its weak point is the likelihood: Rietveld's \(\chi^2\) is not one, and the toy must test calibration before anything is claimed.
• The second idea is P3 for one family where the corpus already exists: Josu's Perovskite Atlas holds the rock-salt-ordered double perovskites (47 materials, 41 structures with their mode decompositions by irrep, 13 series) with every value sourced. The family's map c ↦ p(\(\theta\) | c) is a hierarchical model over tens of compounds, not machine learning; it is the measured prior the first idea needs, and each refinement updates it.
• Proposed answers, for Josu and Iñigo: Q2, diffraction leads (the tool, the toy, the corpus and the engine exist there); Q3, the double perovskites with Fm-3m as parent and the tree of Howard, Kennedy and Woodward 2003, rather than \(\mathrm{ABX_{3}}\). Q4's "hypothesis as recorded input" is met by the family file carrying the Atlas's commit as provenance. Nothing is decided here; the discussion of phase 0 still waits.

Third audit report: qualify the verdicts, record new evidence and preserve the earlier reviews

At Josu's request, published Codex's further review from the project conversation as the third audit report, alongside the original citation audit and Claude's L012 review. Its seven findings R01–R07 preserve the substantive conclusions of that conversation review, with stable anchors, source locators and links to the earlier C01–C42 findings. The same generated claim-card layout is used, with a public Markdown download and provenance hashes. Navigation, Sources and the roadmap link to the report.

The report distinguishes the three-paper comparison from field-wide novelty claims (C24), the resonance feature from its peak (C34), and Kuzmenko's limited-parameter background from the dense variational contribution (C25). It keeps the discrepancy between Daun's printed sampling intervals separate from the unresolved question of what was computed (C35). Mathematical corrections retain their force with explicit assumptions about coordinates, local and global identifiability, covariance and oscillator parameterization.

During the preceding conversation review, Raue's full online article became accessible: selected sections, especially Definition 1 in section 2.3.2, show that its operational criterion is more specific than broad practical imprecision. This evidence update is recorded here; neither the source's historical access record nor its read-in-full status is silently changed. Additional gaps include categorical rejection of point estimates, unconditional temperature smoothness, residual patterns as a unique diagnosis, database selection and the distinction between sloppiness and absolute precision. Verdict counts are explicitly not a quality score.

This is an AI-assisted review awaiting Josu's and Iñigo's assessment, not an independent external review or approval to apply changes. Differences from L012 are made explicit. Both earlier reports, the original local audit, the scientific pages and the founding brief are preserved.

The audit reviewed: its 42 findings re-judged, its Daun and Kuzmenko locators confirmed, 32 accepted whole, none rejected, and a revision proposed

Josu asked for the audit of the audit, as a page beside the audit, in the same style, and logged the same way. Each of the 42 findings (L009) was read with the sentence the site actually prints, and where the audit's evidence was on disk its locator was re-read: Daun pp. 152–155, Kuzmenko 083108-1 to -4, Transtrum 010901-4, Perez-Mato pp. 564–565. Every locator re-opened says what the audit says it says.

• 32 findings agreed and to apply, among them the three factual errors about the Daun paper (C33: the site reversed the authors on surface scattering, who rule it out on a 0.54 nm mean free path; C34: the plasmon peak near 190 nm lies outside the 205–585 nm range; C35: the model-error sampling ranges on p. 152 and the priors of Eq. (22) differ by a power of ten and the site equated them), the dielectric case's misdescription of Kuzmenko's method (C25–C27), and the discourse's statement that the printed e.s.d.'s hide the valley's length (C41: they are its projections; the correlation matrix is its direction).
• 5 agreed with a narrower reading (C18, C20, C23, C37, C42): the audit's "website claim" is a paraphrase stronger than the printed sentence; the corrections apply to the sentence.
• 3 partly agreed (C13: the symmetry basis as the sensitivity basis is a hypothesis, marked as such, that P2 tests; C24: the Rietveld page's sentence is about three papers and is right, the discourse's novelty claim needs a search; C36: the Hagen–Rubens example is a limit and belongs under the practical kind).
• 2 cannot be settled here (C03 the Kaipio book, C40 the Daun supplement); none rejected.
• Gaps in the audit: the Cases comparison table was not read and carries a claim C26 contradicts (G1); the ISODISTORT half of the mode-output sentence was not checked (G2).
• Three rules drawn from it: quote the sentence verbatim before paraphrasing it; report a parameter's contribution and its identifiability as two rankings; make a claim about the field only after a search. Nothing on the scientific pages was changed. The proposal is one revision of the discourse, the cases, the table, the programme and the Sources page, each change naming its finding, to be logged when Josu decides. The page is generated from its source.md by tools/audit_page.py, now shared by both records.

The citation audit set in the site's style: claim cards by verdict, citations as chips, generated from its source

Josu asked for the audit page in the style of the site, with the citations told apart visually. The wording of the report is unchanged; only its presentation is. The page's Markdown body (the public edition with its mathematics in LaTeX) is now source.md next to the report, and tools/audit_page.py, run by build.py, renders index.qmd from it: report.md and the hashes in provenance.json are untouched.

• Each of the 42 claims is a card with its id and a verdict badge; the card's edge, the badge and the index entry take the verdict's colour (supported: the kit's ok green; needs qualification: warn; incorrect as written: bad; not fully verified: faint; proposal presented too strongly: amber).
• Each piece of evidence is one citation: the locator (printed pages, section, equation), then chips — the source key linked to its row in the Sources table, the publisher record, the DOI, the pages of the reviewed copy, and the kind of access (full text, abstract only, indirect, bibliographic only, software source).
• The website claim is set apart in italics, the proposed wording in a tinted box, the independent reasoning under a dashed rule; the file locations are mono chips linking to the pages.
• At the top: the review notice, the suggested citation and version as a facts list, five verdict tiles with the counts, and a two-column index of the findings coloured by verdict in place of the folded list; the source-coverage table carries the same chips. The claim cards are kept out of the page outline. The rules are in project.css under "The citation audit"; index.qmd joins the generated files that are not edited by hand.

Archive the citation audit on the website for review and future reference

At Josu's request, added the L009 citation support report as a dated, readable website page, linked from this log, the Sources page, the navigation and the roadmap. The full 42-claim assessment is retained, including the website claims, evidence, source locators, limitations, independent reasoning and proposed wording. The scientific pages and founding brief are unchanged.

The report is explicitly attributed to Codex as an AI-assisted project review, awaiting author review, not a peer-reviewed publication or an approved set of corrections. It identifies the website commit assessed, supplies a suggested citation and retains stable claim anchors C01–C42. Future decisions and corrections should be logged separately from this historical report.

Adapted local file links to public source records and website pages; preserved the reviewed-copy PDF page numbers as locators. Added a downloadable public Markdown edition and SHA-256 provenance for the original and public reports. The original local report and structured findings are preserved; collected PDFs and private software snapshots are not included in the public site.

Citation support audit: compare website claims with source passages

Clarified the purpose of the reference work: a verified bibliographic record does not establish that a particular website statement is supported. Reviewed all 21 source-table entries and their associated uses in the Discourse, Cases and Programme, grouping the assessment into 42 claims. The local report records website locations, source pages or sections, evidence limitations and proposed wording.

Relevant passages were inspected in 14 local PDFs. Four unavailable articles were checked only against their author/publisher abstracts; the Kaipio–Somersalo attribution was checked through Daun, not the unavailable book; difes documentation and relevant code were inspected at a recorded commit; the thesis remains bibliographic context only. No source was promoted to read in full by this review.

Eleven claim groups are supported within their stated scope, thirteen need qualification or a better citation, eleven are incorrect as written, three remain not fully verified, and four describe proposals more strongly than the evidence permits. These are assessments of website claims, not ratings of papers. Principal issues include Daun's discounted surface-scattering explanation being presented as viable; Kuzmenko's dense variational mesh being described as a few oscillators; missing conditions for reflection phase recovery; and conflation of symmetry coordinates, local sensitivity, global identifiability and posterior probability. Correct dataset sizes and benchmark accuracies were also confirmed.

Identified De Sousa Meneses et al. (2007), DOI 10.1366/000370207783292163, as the more direct primary reference for the finite-range correction named in difes, distinct from Kuzmenko's variational method. Its full text remains to be reviewed. The report separates source evidence from independent mathematical reasoning. Proposed revisions have not been applied to the scientific pages or founding brief.

Reconcile the website's unchecked citations with the verified bibliography

Compared the live website with the L007 audit. Its Sources page still showed eight unchecked references: Hadamard 1902, Tarantola 2005, Kaipio and Somersalo 2005, Brynjarsdóttir and O'Hagan 2014, Raue et al. 2009, Kuzmenko 2005, Patterson 1944 and Rietveld 1969. All eight now have verified bibliographic identities: seven have exact DOI records, and Hadamard has the original publication scan. The audit was already committed locally but had not reached the published site.

Reconciled these statuses and the older DOI warnings with the audit, and linked the seven affected citation occurrences in the Discourse and Cases pages to their Sources entries. Added an explicitly dated update to L004 so its original unchecked list remains a historical record, not a current warning. Download availability remains separate: four of these eight have local PDFs, and four do not. No source was promoted to read in full, and no scientific claim was revalidated by this status update.

Reference audit: DOIs, source links, local PDFs and explicit access gaps

Audited all 21 project sources and all 44 numbered references in the existing Daun 2019 paper: 65 citation occurrences representing 64 distinct sources, including one software source. Checked exact Crossref metadata for 58 entries (57 distinct DOIs); retained a separately reported ResearchGate thesis deposit DOI without claiming independent registration verification. No DOI was invented for historical articles or books; book-review and chapter DOIs were rejected as whole-book identifiers.

The local collection contains 21 validated PDFs: 20 newly downloaded plus the original Daun paper. Fourteen of the 21 direct project sources have local PDFs. Forty-two distinct sources remain without full text; one source is software. The Bohren–Huffman copy is the 1998 edition, whereas Daun cites 1983. The local index, BibTeX, manifest, download failures and missing-items list make these limits explicit. PDF signatures, pdfinfo, page counts, first-page identity and SHA-256 hashes were checked.

Found a malformed reference [27] already in Daun's published PDF: it combines reference [12] with Sorensen, Maughan and Moosmüller, JQSRT 226 (2019) 81–86. The probable intended work and its DOI are recorded as a reconstruction, with the original citation preserved. Also recorded corrected author lists, names, titles and the Rhim–Ishikawa page range (429–443). Kaipio–Somersalo 2005 and Daun's 2006 citation refer to the same book with different print, copyright and eBook dates.

Updated the Sources page with DOI, publisher and available full-text links. Preserved the distinction between bibliographic verification, downloading and reading in full; no scientific claims were reassessed. All 11 original source files (PDF, OCR text and images) remain unchanged. PDFs stay outside the public site. This entry records local work; it does not assert deployment of the updated site.

The programme P1–P7 and the questions Q1–Q6 for Josu and Iñigo

Seven proposals, ordered from the cheapest to the largest, on the Programme page: P1 the diagnostic every fit should print (stiffness spectrum, sloppy directions in parameter names, credible region); P2 a toy that makes the thesis visible on a synthetic perovskite distortion, refined in coordinates and in mode amplitudes from many starting points; P3 the corpus — one structural family, patterns simulated under instrument models, the expert's analysis scripted (mode decomposition against a chosen parent, release strategy), the whole result stored, not one point; P4 learning over the corpus: identifiability maps, amortised posteriors over mode amplitudes, inadequacy flags; P5 the same scheme for infrared spectra with difes' recipes and libraries; P6 the Daun problem redone with a Mie surrogate and the design computation of which spectral band pins (\(\omega\)_p, \(\tau\)); P7 a perspective paper, after P2.

Six questions wait for the discussion: the name of the thing; which case leads; which family for the corpus; the parent-structure hypothesis as recorded input; what counts as a result (a value, a region, a diagnosis); and who writes the first script.

The first discourse: three kinds of indeterminacy, the projection made geometric, and the mode-crystallography move generalised

Written on the Discourse page, from the twelve theses. What it adds to the brief:

• A distinction the brief folds into one word, "underdetermined": an exact null space of the forward map (structural non-identifiability: powder averaging, the phase problem, homometric structures); a near-null space at the resolution and noise of the instrument (practical non-identifiability, the sloppy valleys of Gutenkunst and Transtrum; Daun's Fig. 9a); and model inadequacy, where the truth is not on the model manifold at all (Rayleigh against Mie; the free-electron model against liquid germanium). The three need different external tools.
• The projection written down: a forward map from a configuration space to a data space, its fibre over a measurement, the tube the noise makes of the fibre, and a refinement as one point of that tube chosen by the starting point and the strategy. The singular values of the weighted Jacobian as the local stiffness spectrum; its singular vectors as the coordinates the experiment actually sees.
• Why symmetry modes work, stated so that it can be carried elsewhere: an orthogonal change of basis in which the physics' prior is sparse (a few primary amplitudes, the rest near zero) and in which the correlations the data cannot break become single coordinates. The parent structure is a hypothesis brought from outside; that is the irreducible expert input. The analogues named for the other two cases: Kramers–Kronig and sum rules for the dielectric function; other experiments and the model-error term for the extinction problem.
• What machine learning can and cannot do here: it cannot recreate what the projection destroyed; it can return the whole fibre instead of a point (amortised inference), learn priors from corpora, replace expensive forward models, flag model inadequacy that recurs across data sets, and say which measurement would cut the fibre best. The output must be a distribution; a point estimate from an underdetermined problem is a confident guess.

The bibliography of the discourse: what was confirmed today and what is still from memory

Confirmed by web search on 14 October 2026 (authors, title, journal, year): Perez-Mato, Orobengoa and Aroyo 2010 (Acta Cryst. A66, 558–590, doi 10.1107/S0108767310016247); Orobengoa et al. 2009 (AMPLIMODES, J. Appl. Cryst. 42, 820–833); Campbell et al. 2006 (ISODISPLACE, J. Appl. Cryst. 39, 607–614); Gutenkunst et al. 2007 (PLoS Comput. Biol.); Transtrum et al. 2015 (J. Chem. Phys. 143, 010901); Cranmer, Brehmer and Louppe 2020 (PNAS); Kennedy and O'Hagan 2001 (J. R. Statist. Soc. B 63, 425–464); Park et al. 2017 (IUCrJ, about 150 000 patterns, 81/84/95 %); Lee et al. 2020 (Nature Commun. 11, 86; 1 785 405 synthetic patterns from 170 compounds); Szymanski et al. 2021 (Chem. Mater.); Iñigo González de Arrieta's thesis (UPV/EHU, 2020, high-temperature infrared emissivity).

Still from memory, marked "not checked" on the Sources page: Hadamard 1902, Tarantola 2005, Kaipio and Somersalo 2005, Brynjarsdóttir and O'Hagan 2014, Raue et al. 2009, Kuzmenko 2005, Patterson 1944, Rietveld 1969, and some DOIs. Nothing in the discourse rests on a detail of those that the checked sources do not also carry.

Update, 14 October 2026 (L007–L008): the eight references listed above have since been bibliographically verified. Their earlier "not checked" status is historical; the Sources page now gives the current status, DOI or original-publication link, and full-text availability. This does not mean they have been read in full.

Daun et al. 2019 read: the ill-posedness is shown as a credible region, and the external tools are other experiments and a model-error term

The paper infers the Drude parameters (\(\omega\)_p, \(\tau\)) of liquid germanium nanoparticles from line-of-sight extinction spectra measured across an aerosol in a plasma reactor, with a halogen lamp (410–700 nm) and a laser-driven source (205–585 nm). Three forward models: Rayleigh, exact Mie, and a fourth-order approximation to Mie. The inference is Bayesian (MCMC, \(10^{6}\) samples), with a noise model fitted to the residuals of a smoothed spectrum and, for the approximate model, a model-error term after Kaipio and Somersalo. What matters for the thesis:

• All candidate models reproduce the shape of the measured spectra, and the Drude parameters they return differ: ellipsometry 2.81 and 1.87; bulk density and resistivity 2.40 and 2.66; Rayleigh 2.85 and 4.5; Mie 2.04 and 1.97 (\(\omega\)_p in \(10^{16}\) rad/s, \(\tau\) in \(10^{-16}\) s; Table 3). The paper's own words: "the fact that different Drude parameters can produce similar extinction spectra highlights the ill-posedness of this problem".
• Fig. 9 is the collapse made visible: with the halogen lamp and Rayleigh the 90 % credible region is a long curved valley in (\(\omega\)_p, \(\tau\)); with the approximate Mie model it is narrow; with the laser-driven source, which reaches the surface-plasmon resonance in the ultraviolet, it is narrower still. The information is in a part of the spectrum one source does not reach.
• The external tools are other experiments (ellipsometry, bulk density and resistivity) and the explicit model-error term; and they disagree with the extinction-derived values in a statistically significant way. The conclusion is not a value but a diagnosis: the free-electron model is inadequate (perhaps three conduction electrons per atom, not four).
• A simplified model (Rayleigh) that fits the data superficially gives a wrong picture; the credible region, not the fit, tells.

The protocol inherited from diff-ref-struct: one private repository with `ecosystem/`, a public site repository, the family kit

Read before anything: CLAUDE.md, README.md, ecosystem/tools/build.py, data/*.yml, the site's _quarto.yml and includes of diff-ref-struct, and the Action publish-site.yml. The pattern is the difes one (L002–L004 of that project): data in YAML, a generator, a Quarto site with theme none and the family design kit, a dated log with ids that never change, and a push to main that renders the site and replaces a public repository whole.

Decided here, the same way:

• Private repository jmigartua/inverse-problems-configuration-space, with ecosystem/ (data, tools, site) and sources/ (the papers read). Working name; the project's name is open.
• Public repository inverse-problems-configuration-space-site, GitHub Pages from main, written only by the Action with a deploy key (SITE_DEPLOY_KEY), as diff-ref-struct's L007.
• Copied unchanged: theme.css, site.css, fonts.html, docs-close.html, the favicon, mathtokens.py, mathify.py. Written new: build.py (navigation, theses, log, sources, home), the header, the footer, the pages.
• Ids: theses T01…, log L001…, proposals P1…, open questions Q1…, sources by a short key.
• No core/ and no app/: this project is thought, cases and a programme; code appears only when a proposal of the programme is taken up, and then in a folder named by it.

The brief

Josu writes down ideas that are Iñigo González de Arrieta's, shared with him, to think on them and develop them. The ideas: inverse problems whose theory is known but whose parameters are poorly known and too many for what the experiment can tell apart; the experiment as a projection that collapses the configuration space; the extraction of the parameters from the projection as something not evident, perhaps impossible, without an external tool; Rietveld refinement as the known case and mode crystallography as the external tool there; the proposal to bring in machine learning over massive data sets treated automatically by scripts into which the expert's knowledge has been written, instead of applied by hand to one data set at a time. The paper in the folder (Daun et al. 2019) is another example, not the subject.

Asked for: analyse, sort into a coherent discourse, think and rethink, elaborate, propose, innovate; then discuss. The protocol of the FOCUS–difes and FullProf (diff-ref-struct) projects: a website holding everything, a repository, the log on the site, the sources used.

The brief is kept verbatim and organised into twelve theses (T01–T12) on the Brief page.