Finding 2026.2A deterministic synthetic corpus for the amorphous-carbon Raman inverse problem

§2026.2(i) Purpose

An inversion pipeline that reads crystallite size, amorphisation stage, and sp³ fraction out of a carbon Raman spectrum cannot be trusted on measured data until it has recovered known parameters from spectra whose parameters are known exactly. This finding describes the corpus built for that purpose. It is a forward-model output: every spectrum in it was synthesised from declared physics and declared distributions, regenerates byte-identically from its seed, and carries no information about any real device or film. Results obtained on it, reported in Finding 2026.3, regression-test the pipeline; they support no physical claim.

§2026.2(ii) Forward model

The model follows the three-stage interpretation of Ferrari and Robertson [FR00]. In stage 1, from graphite to nanocrystalline graphite, the disorder ratio obeys the Tuinstra–Koenig relation [TK70],

and in stage 2, from nanocrystalline graphite to amorphous carbon, the relation reverses,

The two branches meet at the turnover $L_a=20$ Å, where both give a ratio of 2.2, so that the ratio is continuous but not invertible on its own: a ratio below 2.2 corresponds to one crystallite size on each branch. The G band is given a Breit–Wigner–Fano line shape and the D band a Lorentzian, disorder-activated, as in [FR00].

The second corpus version adds three effects declared as next steps in the first. Both constants scale with excitation wavelength as

which leaves the turnover invariant. Compressive stress shifts the G band upward at 5 cm⁻¹ per GPa, to 8 GPa in sp³-rich films, relaxed by hydrogen; the rate is a declared model parameter. Hydrogenated films carry three effects. The photoluminescence background has a slope that rises with hydrogen content, following the trend reported by Casiraghi, Ferrari and Robertson [CFR05]. The D band is suppressed by a factor $(1-0.6h)$ for hydrogen fraction $h$, and the G band shifts upward with hydrogen; the factor and the shift are declared model parameters chosen for the corpus, not literature values, and the measured phase will test them.

§2026.2(iii) Corpus design

The corruptions are not noise in the ordinary sense; they are the failure modes of real acquisitions, planted so that a pipeline can be scored on whether it notices them.

§2026.2(iv) Tasks

Five tasks are scored on the held-out test split. T1 assigns the amorphisation stage and is scored by macro-F1. T2 recovers $L_a$ and is scored by mean relative error, reported separately for the degenerate subset near the turnover, where the ratio alone cannot decide the branch. T3 recovers the sp³ fraction and is scored by mean absolute error. T4 scores resolution of the degenerate branch directly: the T2 error on the 100 test rows at 514 nm whose noise-free disorder ratio lies between 0.35 and 2.05. T5 scores robustness as the mean absolute $L_a$ error, in ångström, on the 45 corrupted rows of the split.

§2026.2(v) Determinism and provenance

The corpus is regenerated from its seed before every evaluation and the SHA-256 digest of the regenerated files is compared with the digest recorded in the append-only ledger of §2.2; a mismatch fails the release gate described in Finding 2026.4. Any change to the generator is therefore a change to the corpus that the ledger records, and a result quoted against the corpus is quoted against a specific digest.

§2026.2(vi) What the corpus is for

The corpus answers one question: does a given pipeline recover the parameters that generated a spectrum, including under the planted corruptions? It cannot answer whether the forward model is complete, which is a question for measured spectra; the physics baseline of Finding 2026.3 shows the consequence of the turnover between equations 2026.2.1 and 2026.2.2 directly. The next step, in the programme's own terms, is to replace the synthetic spectra with measured ones from characterisation partners and to run the unchanged harness.