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

Roadmap

Phases

Think first, then make the thought visible on one small problem, then build the corpus and learn over it. Each phase ends with a named artefact and a log entry. Only phase 0 is detailed; the later phases are the programme's proposals in order, and their detail is written when the discussion of phase 0 closes.

PHASE 0 · open

The discourse, the cases, the programme

Sort Iñigo's ideas into a discourse that holds together, test it against three cases, and propose what to do next — so that the discussion with Josu and Iñigo starts from something written.

  • Private repository, site skeleton, the brief organised into theses T01–T12, working method in CLAUDE.md. done (L001, L002)
  • The paper in the project read and placed as the second case. done (L003)
  • The bibliography checked, with DOI and source links, a local PDF collection and explicit access gaps. metadata audit and citation statuses reconciled (L004, L007, L008); full-text collection partial
  • The website's use of its sources compared with relevant passages: 21 source entries and 42 claim groups. citation support audit recorded and archived on the site (L009, L010); proposed scientific corrections await review
  • The audit reviewed: its 42 findings re-judged, its locators re-read, a revision proposed. done (L012); the revision waits for Josu
  • A third report qualifies the audit's assessments and records further evidence and coverage gaps. recorded (L013); differences among the reports await author review
  • The discourse written: three kinds of indeterminacy, the projection as a forward map with its fibres, the mode-crystallography move generalised, what machine learning can and cannot do. first version (L005)
  • The three cases side by side: Rietveld and modes; Drude from extinction; dielectric functions from infrared spectra. first version (L005)
  • The programme P1–P7 and the questions Q1–Q6. proposed (L006)
  • The discussion with Josu and Iñigo: theses added or struck, questions answered, the first proposal chosen. waiting
Done when Q1–Q6 each have a logged answer and one proposal of the programme is chosen to start phase 1.
PHASE 1

The thesis made visible (P1, P2)

On one synthetic displacive structure, show the fibre of the diffraction experiment in atomic coordinates and in mode amplitudes, and print the diagnostic every fit should print.

  • The diagnostic: the stiffness spectrum of a fit, its sloppy directions named in parameters, the credible region of the pair that matters (P1).
  • The toy: a perovskite distortion, patterns simulated, refined from many starting points in both bases, the valley drawn (P2). A figure series and a page.
Done when the figure that shows the valley in coordinates and its alignment with the mode axes is on the site, with the script that made it.
PHASE 2

The corpus and the learning (P3, P4)

One structural family, treated whole by scripts that carry the expert's knowledge, with the full result of each treatment kept; then learn over it what no single refinement can show.

  • The pipeline: structures from a database, patterns under instrument models, mode decomposition against the chosen parent, the release strategy, everything stored (P3).
  • Identifiability maps, amortised posteriors over mode amplitudes, inadequacy flags (P4).
Done when for the chosen family the site can say, for any pattern of the corpus, which mode amplitudes the pattern determines and which it does not.
PHASE 3

The other two cases (P5, P6) and the write-up (P7)

Carry the scheme to the infrared spectra with difes, and to the extinction problem of Daun et al.; then write the perspective.