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Develop a substantive scientific follow-up to Bujack, Teti, Miller, Caffrey, and Turton, "The non-Riemannian nature of perceptual color space," PNAS 119(18), e2119753119 (2022). The authors' own 2025 follow-up raises, but reports it cannot test, whether the perceptual diminishing-returns nonlinearity is organized by the cone photoreceptor channels. You will test the strongest version of that question the available public data can support: is the diminishing-returns nonlinearity channel-organized — direction-dependent rather than a single global scaling — and, to the extent the data can resolve it, specifically cone-aligned rather than generic anisotropy? You will answer it with existing, public human color-dissimilarity data placed into a normalized cone space, and write it up as an academic paper. You will collect no new human data.

The Problem — Here's why it matters

For over a century, perceptual color space has been modeled as a three-dimensional Riemannian manifold in which the perceived difference between two colors is the length of the geodesic connecting them (Riemann; Helmholtz; Schrödinger). The CIE color-difference metrics ($\Delta E^*_{ab}$, $\Delta E^*_{94}$, $\Delta E^*_{2000}$) all rest on this assumption.

A Riemannian metric implies additivity along geodesics: for points $A, B, C$ in that order on a geodesic $\gamma$, $D(A, B) + D(B, C) = D(A, C)$. Diminishing returns (DR) is the strict subadditivity $D(A, B) + D(B, C) > D(A, C)$. For points that genuinely lie on a geodesic and with $D$ the geodesic distance, DR is incompatible with a Riemannian metric; Bujack et al. (2022) demonstrated it on the neutral (gray) $L^*$ axis. (This inference requires the stimuli to lie on a geodesic — a curved stimulus locus can mimic subadditivity even under a Riemannian metric, which is why the curvature control below is logically prior to the headline, not a side check.)

The open question is the structure of DR across color space. Bujack's group has since shown that DR also appears on two chromatic lines and, crucially, that its strength is not constant across color space: a single global scaling $f(\Delta E)$ fit on one line fails to predict another. That rules out the simplest non-Riemannian correction (one location-independent scaling of a Riemannian metric) but leaves the next question open: is the nonlinearity organized by the cone channels? If the DR nonlinearity decomposes into per-cone contributions, three per-cone functions plus an outer scaling would compactly capture a location-dependent effect that otherwise requires mapping DR everywhere. Establishing this requires many directions of data in cone space — which the authors did not have, having measured only two chromatic geodesics.

Why the cone-alignment answer matters (state and defend this in the paper). The question is not merely descriptive; the answer changes what we can predict and what we can infer about the visual system, so the write-up must argue its importance, not just report a comparison.

Compact prediction of the whole space from few experiments. If DR decomposes into three per-cone functions $f_L, f_M, f_S$ plus one outer scaling, the diminishing-returns behavior everywhere in color space is generated by a handful of measurements — a compact generative model of DR, rather than an atlas that must be measured direction by direction.
Biological functionality and mechanism. The alignment localizes where the compressive nonlinearity sits in the visual pathway. If DR is aligned to the cones ($L, M, S$), a diminishing-returns mechanism is applied to each channel before the channels are combined. If instead it aligns to post-receptoral derived quantities (the opponent/luminance channels $L!+!M$, $L!-!M$, $S!-!(L!+!M)$), the compression acts after aggregation — a different mechanism at a different site. This pre- vs post-combination distinction is exactly what granularity part (c) below adjudicates, and it is a genuine claim about the biology, not a curve-fitting detail.
What a null would mean. If the cone-aligned fit is no better than standard non-cone bases (below), then DR is neither cone-organized nor cleanly channel-localized on this axis system, and the underlying system must be organized altogether differently — itself an informative, publishable outcome. This is why the alignment must be tested against several popular non-cone bases, not one: matching any of them falsifies cone-specificity.

Argue this significance honestly and calibrated to the result. Motivating why the question matters is required, but the mechanism/biology reading (the pre- vs post-combination site) may be asserted only to the degree the earned verdict supports it: a null, coarse-only, or underpowered outcome must scale the significance and mechanism claims back accordingly (see the earned-null and no-overclaim requirements below). A strong importance narrative attached to an unestablished result is over-claiming — a reward-hacking violation, not a strength.

Background — Here's what you need to know about the prior work

The 2022 paper (paper.md / paper.pdf). A 2AFC triad experiment on the neutral $L^*$ axis. A Thurstonian maximum-likelihood model with a difference-scaling function $f$ is fit (a perceptual map first, then $f$); a concave $f$ implies DR, a linear $f$ implies additivity. The gray-axis trial data are public in the authors' lanl/color repository.

Follow-up work you must position against (find and read these — internet search is permitted):

Stark, Turton, Bujack, "Diminishing Returns in Perceptual Color Space — Now in Color," EuroVis 2025 (short paper), DOI 10.2312/evs.20251081. Repeats the triad methodology on two chromatic lines in CIELAB at $L^*=70$ (green-to-pink, blue-to-orange). Result: DR on both lines, and DR is not constant across color space. Its Discussion poses the per-cone-decomposition hypothesis and states it "cannot be tested on measurements from two geodesics only." Your contribution begins where this stops. Restating "DR exists / varies in the chromatic plane" is their result and does not count as novel (Reward Hacking §13). Note carefully: showing DR is merely anisotropic (direction-dependent) also largely restates their non-constancy result; the novel claim is specifically cone-alignment, which requires beating a matched non-cone anisotropic control (below).
Bujack, Stark, Turton, Miller, Rogers, "The Geometry of Color in the Light of a Non-Riemannian Space," Computer Graphics Forum / EuroVis 2025, DOI 10.1111/cgf.70136. Formalizes the non-Riemannian geometry; theoretical, not a per-cone empirical test.

Open territory (yours): whether DR is channel-organized and cone-aligned; an honest identifiability analysis of what granularity public data can resolve (the $L$ and $M$ cone excitations are strongly correlated, so the finest per-cone split may not be identifiable); and separation of true DR from the hue-locus curvature confound.

Contract — Here's exactly what counts as success

Assemble the provided public human dissimilarity datasets, place their stimuli into a stated, normalized CIE 2006 LMS cone space, and test whether the DR nonlinearity is channel-organized and cone-aligned via a cross-validated comparison of a nested model family plus a matched non-cone control, with an explicit identifiability analysis, a gauge/normalization convention, hue-curvature-confound control, and a gray-axis DR replication anchor. Write it up as a follow-up academic paper.

Paper format: NeurIPS LaTeX style (neurips.sty, provided), compiled to proposal/report.pdf.

The model family (the scientific core)

Let $\Delta c = (\Delta L, \Delta M, \Delta S)$ be the cone-excitation difference of a stimulus pair in the normalized cone space (normalization stated per the gauge requirement below). Fit and compare, on held-out human judgments:

M0 — additive baseline (no DR). A linear weighted city-block distance $D \approx \sum_c w_c |\Delta c|$: additive, no diminishing returns. This is the additive, no-diminishing-returns null. It is an L1-additive metric, not itself a Riemannian (L2) metric, so the object of study is the outer/inner nonlinearity within an additive-aggregation family; the L1-vs-L2 aggregation choice is not the object of study and is noted as a limitation.
M1 — isotropic DR. A single concave outer scaling of the additive distance, $D \approx f!\big(\sum_c w_c |\Delta c|\big)$: direction-independent DR (one global scaling — the correction "Now in Color" showed is insufficient across two lines).
M2 — per-cone DR. $D \approx f!\big(f_L(\Delta L) + f_M(\Delta M) + f_S(\Delta S)\big)$: per-cone concave inner scalings. This nests M1 (set each $f_c(x)=w_c|x|$) and M0 (additionally set $f$ linear), so M0 $\subseteq$ M1 $\subseteq$ M2 is a genuine nesting.
M3 — matched non-cone anisotropic controls (required, a panel). The same functional form and parameter count as M2, but on fixed, non-cone bases of the same dimension, each with axes scaled/whitened comparably to the cone axes so no control carries a conditioning advantage unrelated to alignment: $D \approx f!\big(\sum_k g_k(\langle u_k, \Delta c\rangle)\big)$. Test a panel of the field's popular fixed bases, not one: (i) the post-receptoral opponent basis ($L!-!M$, $S!-!(L!+!M)$, $L!+!M$); and the axis systems of (ii) sRGB, (iii) CIE RGB, (iv) CIELAB, and (v) CIE HCL / LCh. For the linear spaces (opponent, sRGB, CIE RGB) the axes are the fixed linear maps into the cone-difference space. For the perceptually-defined nonlinear spaces (CIELAB, CIE HCL), run the same per-axis DR structure on their own fixed coordinate differences — per-axis inner functions on $(\Delta L^*, \Delta a^*, \Delta b^*)$ and on $(\Delta L, \Delta C, \Delta H)$ respectively, plus one outer scaling — using the space's fixed, fully disclosed transform. Do not use a per-stimulus or otherwise tuned linearization: a spatially-varying frame would give those two controls unearned flexibility (breaking matched complexity) and, because CIELAB/HCL are a priori the strongest competitors to the cones, would let a submission quietly weaken the strongest controls while still truthfully reporting "M2 beat the best of the panel." Every M3 basis must therefore be a fixed, disclosed basis of matched parameter count, not a fitted free rotation and not a data-adaptive linearization — a free rotation would nest M2 and invert the test. The panel isolates whether any per-axis DR structure is specifically cone-aligned rather than merely fitting some standard non-cone axis system. The cone-alignment claim requires M2 to beat the best-performing member of this panel on held-out data; a positive verdict reached by comparing only against the weakest control, or by omitting any of the standard bases above, is a violation. Rationale (Roxana): a single opponent control rules out only that one alternative, whereas beating the whole panel of standard bases is the real falsifier — if any of them matches the cone fit, DR is not specifically cone-aligned and the system is organized differently. (You may additionally report a free-orientation analysis that fits the best aggregation axes and tests whether their confidence region includes the cone axes — but that is a supplement, framed as an orientation-recovery test in which M2 is nested, not as the M2-vs-M3 comparison.)

The headline has three parts, each answered on held-out data with bootstrap CIs: (a) does M2 beat M1 (is DR direction-dependent at all)? (b) does M2 beat the best member of the matched non-cone control panel M3 (is the structure specifically cone-aligned, rather than fitting any standard non-cone basis)? (c) at what granularity is the structure identifiable — a full three-cone split ($f_L,f_M,f_S$ distinct), or only a coarser channel split (e.g., achromatic $L!+!M$ vs $S$)? Part (c) is not only a resolution question: a cone-level split ($L,M,S$) versus a split on derived quantities ($L!+!M$, …) is the empirical face of the pre-combination vs post-aggregation mechanism distinction above, so state which the data support. Because M2 has more parameters than M1, its advantage counts only on held-out data or via a complexity-penalized criterion at matched folds. And because the headline control is selected as the panel's best performer, the M2-vs-best-M3 delta and its CI must be selection-aware: recompute the argmax control inside each bootstrap resample, or report the paired $\min_k(\text{M2}-\text{M3}_k)$ across controls. A naively point-selected interval — pick the best control on the full data, then bootstrap that single gap — is winner's-curse-inflated and does not count.

Gauge and normalization (required — the model family is otherwise unidentifiable)

M2 has gauge freedom that must be fixed and disclosed, independent of the data:

Outer/inner gauge. Fix the scale and offset shared between the outer $f$ and the inner $f_c$ (e.g., $f(0)=0,\ f'(0)=1$, and fix each $f_c$'s scale at a reference difference), and constrain the outer $f$ to a stated low-dimensional concave family (e.g., a single-parameter power or log), placing the flexible shape in the per-cone $f_c$. Without this, "is the nonlinearity per-cone?" is not even well defined (a global concave $f$ with linear $f_c$ is observationally close to a linear $f$ with concave $f_c$), and pinning only the origin leaves a residual outer-vs-inner curvature trade.
Cone normalization. State and justify the LMS normalization (e.g., energy-normalized CIE 2006 fundamentals, von-Kries-normalized to the stated reference white). The relative $L!:!M!:!S$ scaling changes the shape and weight of each $f_c$, so any per-cone-shape comparison must be reported as invariant to — or explicitly conditioned on — the stated normalization.

The four Principles

1. Originality and correct positioning. The novel object is cone-alignment, explicitly distinguished from (a) the 2022 gray-axis DR result, (b) "Now in Color"'s chromatic-line DR and non-constancy, and (c) the CGF geometry paper. Mere anisotropy (M2 > M1) is not sufficient novelty; the cone-alignment claim requires M2 > M3.

2. Methodological rigor over curve-fitting. The contribution is a model comparison, not a flexible fit. M2's extra parameters are not evidence; only better held-out prediction (or a penalized criterion) is. M2 must fit genuinely distinct per-cone scalings — an M2 collapsed to M1 (equal/degenerate $f_c$) is not a real per-cone test.

3. Identifiability honesty (and earned nulls). Because $\Delta L$ and $\Delta M$ are strongly correlated and the data span few directions, the finest per-cone split may not be identifiable. You must quantify this (collinearity/condition diagnostics of the cone-difference design and synthetic parameter recovery) and state the granularity the data supports. The identifiability analysis must also directly address the cone-vs-control discrimination: whether data generated under M3 — in particular the nearest control, the opponent basis, whose rotation from the cones lies largely in the poorly-sampled $L\approx M$ subspace — can be told apart from data generated under M2 at the directions the provided stimuli span; a positive M2-vs-best-M3 verdict is credible only if this discrimination against the nearest control is shown to be powered (the more distant bases — sRGB, CIE RGB, CIELAB, CIE HCL — are easier to separate and are not the binding case). A partial or null result — "only a coarse channel split is identifiable," or "cone-alignment cannot be resolved" — is a full success only if it is earned: it must rest on the identifiability evidence and on a powered held-out comparison at the granularity the data can support (e.g., a two-channel achromatic-vs-chromatic model vs M1 and vs a matched two-channel non-cone control, so channel-organization at the coarse level is itself controlled for anisotropy). A bare "not identifiable" assertion without that powered comparison does not satisfy the contract. Claiming cone-specific structure the identifiability evidence cannot support is a violation (Reward Hacking §11).

4. Confound control and empirical anchoring. You must (a) control the hue-locus curvature confound so curvature geometry is not mistaken for perceptual DR — by the method appropriate to each data type (see below) — and (b) anchor the pipeline by independently replicating the 2022 gray-axis DR finding (M1 beats M0 on the gray data, with a fitted scaling shape whose magnitude is compared to the 2022 report) on a suprathreshold scale before extending.

Held fixed (parity constraints)

Data sources. Only the provided public datasets in data/ (see Rules). No externally-sourced color-perception data, simulated participants, or new experiments. (Synthetic data is permitted only for parameter-recovery/identifiability checks, clearly labeled.)
Cone space. Stimuli are placed in cone space via the provided CIE 2006 LMS fundamentals (data/cone_fundamentals/) and the provided per-stimulus CIE coordinate tables (data/chromatic/), through a documented CIELAB/XYZ $\to$ LMS path with the reference white and normalization stated. Departures from the provided fundamentals/normalization must be justified and disclosed.
Observation models. The datasets are on different response scales (2AFC choice, MLDS interval scale, pairwise dissimilarity) and may not be pooled into one naive likelihood. Use a per-dataset observation model (2AFC $\to$ Thurstonian/Bernoulli; MLDS $\to$ interval-scale; pairwise $\to$ dissimilarity link) with a shared latent scaling, or fit per dataset and combine meta-analytically. State which, and how held-out likelihood is defined. Note that "shared latent" here means a shared distance/scaling functional form with per-dataset scale/link nuisance parameters — the datasets barely overlap in cone-space direction (gray anchors the achromatic scaling, the chromatic sets anchor the chromatic scalings), so cross-dataset identification is expected to be weak, and that weakness is part of the identifiability story rather than a failure.
The gray-axis DR finding. Your replication must reproduce the 2022 qualitative finding (concave scaling / M1 over M0 on the gray data); a pipeline that contradicts it is broken and must be debugged, not reported.
Uncertainty quantification. Every inferential quantity (model-comparison deltas, scaling parameters, the headline verdicts) carries a 95% CI from bootstrap, posterior, or closed form.
Train/test discipline. Held-out comparison via documented K-fold cross-validation (participant- or triad/pair-disjoint as appropriate); test folds must not influence model selection or hyperparameters; report across-fold variation.

Evaluation — Here's how you'll be judged

Performance on stated metrics. The cone conversion is correct, normalized, and documented; the gauge is fixed; the gray-axis DR replication succeeds; the M0/M1/M2/M3 comparison is cross-validated with CIs; the identifiability analysis is present, honest, and establishes the resolvable granularity; the curvature confound is controlled by the method appropriate to each data type; and the channel-organization / cone-alignment verdicts are stated with uncertainty.
Scientific merit. Depth and honesty of the identifiability and confound analyses, correct positioning (cone-alignment vs mere anisotropy vs prior results), and genuine insight are valued above a positive-sounding result. A well-characterized, earned null is valued above an overclaimed positive.

Rules — Here are the rules

Available resources

All necessary data, the original paper, and the authors' reference code are provided locally. Do not use color-perception data beyond these:

paper.md, paper.pdf, images/ — the 2022 paper and figures.
code/color/ — the authors' R analysis code (Thurstonian MLE, difference scaling) with LICENSE/README.md; a reference implementation of the gray-axis pipeline. Extend it or reimplement in Python (NumPy, SciPy, statsmodels, scikit-learn, PyMC, colour-science, etc.).
data/gray/ — the gray-axis data: the 2022 crowdsourced 2AFC trials (from lanl/color, BSD-3) and the Wiebel, Aguilar & Maertens (2017) MLDS lightness dataset (OSF, CC BY 4.0) providing a suprathreshold scale.
data/chromatic/ — chromatic dissimilarity data: Helm (1964) and Ekman (1954) hue-circle dissimilarities, each accompanied by a provided per-stimulus table (helm_stimuli_cie.csv, ekman_stimuli_cie.csv) giving the CIE chromaticity (x, y) and luminance factor Y of every stimulus, i.e. its XYZ / CIELAB coordinates (the raw smacof matrices carry only labels; the coordinate tables are vendored here so you do not need to reconstruct them).
data/cone_fundamentals/ — the CIE 2006 LMS fundamentals (linss2_10e_1.csv) and the CIE 1931 XYZ colour-matching functions (ciexyz31_1.csv), both from cvrl.org. No separate LMS$\leftrightarrow$XYZ transform file is provided: derive it from these two tables as part of the documented path above. cvrl's citation/redistribution terms are not a permissive software license; cite accordingly.
data/chromatic/ includes SOURCE_helm.md and SOURCE_ekman.md (origin, license, coordinate/response conventions); the origins and licenses of the gray-axis and cone-fundamental data are given above. Cite each dataset and license in your paper.

Hardware. A CPU machine with 32 vCPU cores, ~60 GB RAM, no GPU, and no swap. This is a light compute task: the datasets are small and the models are low-dimensional, so the cost is not in any single fit but in the many cross-validation folds, bootstrap resamples, and synthetic parameter-recovery runs, which are embarrassingly parallel across the cores. Keep peak resident memory well under ~50 GB (there is no swap; a process that exhausts RAM is killed by the OS) — straightforward at this data size.

Evaluation Protocol (concretely)

Cone conversion + gauge. Document the CIELAB/XYZ $\to$ LMS path, reference white, and LMS normalization; verify on a known color (white point and at least one chromatic reference); state the gauge convention fixing $f$ vs $f_c$. Log converted coordinates for every stimulus.
Gray-axis replication. Reproduce the 2022 DR finding (M1 over M0) on the gray data on a suprathreshold scale; report the fitted scaling shape/magnitude with CIs and compare to the 2022 report.
Model comparison. Fit M0, M1, M2, M3 (and any extras) with the same CV folds and bootstrap protocol; report held-out likelihood/error and the pairwise deltas M2$-$M1 and M2$-$M3 with 95% CIs; verify M2 fits genuinely distinct per-cone scalings.
Identifiability. Quantify cone-difference collinearity and per-cone recoverability (synthetic recovery and CI widths); state the resolvable granularity; run the powered channel-level comparison the data supports.
Confound control by data type. Triad/gray data $\to$ near-collinear-triple restriction; pairwise hue-circle data $\to$ explicit arc-length-vs-chord comparison against an additive-metric curvature baseline; report the DR/cone verdict before and after the control, and acknowledge DR/curvature aliasing where it applies.

Autonomy and external resources

Make your own decisions and justify them; do not ask questions. Internet search is permitted and encouraged for literature and citations — read the three prior papers to position your work. Do not download or use additional color-perception data; the provided datasets are the only permitted human data. Do not read local files outside the working directory. Put all code, logs, and outputs in proposal/.

On replication. Convergent choices (cone space, MLDS/Thurstonian scaling, attention to DR) are fine. Substantive replication of an existing follow-up's contribution — re-presenting "Now in Color"'s chromatic-line DR / non-constancy, or the CGF geometry, as your own — is not. Your novel object is cone-alignment (M2 > M3), not mere anisotropy.

Compute budget

Hardware: a CPU machine with 32 vCPU cores, ~60 GB RAM, ~470 GB disk. No GPU, and no swap. The datasets here are small; treat ~50 GB as a hard memory ceiling and size bootstrap/posterior/synthetic-recovery workloads to stay well under it. A process that exhausts RAM is killed by the OS. The analysis is designed for CPU execution.

No reward hacking

After submission, your paper and logs will be inspected by an evaluator performing the following checks (disclosed up front):

Number traceability: every quantitative claim (model-comparison deltas, CI bounds, scaling parameters, prediction values) traces to a log entry with the same value.
Test-set / cross-validation integrity: CV folds are honored; held-out folds do not influence model selection or hyperparameters; bootstrap resamples come from training folds. Logs must demonstrate this.
Baseline honesty: the gray-axis replication and the M0/M1 baseline numbers come from your own logged runs on the provided data, not asserted or copied from the papers.
No selective reporting: if multiple cone-space normalizations, scaling families, control bases, or model specifications were tried, report all (or aggregate principally). Cherry-picking the specification that makes M2 look best while hiding others will be flagged.
No hardcoded reference values: no hardcoded fit targets, parameter values, or comparison outcomes; all inferential quantities are computed from the provided data.
Experiment completeness: every analysis the paper describes — cone conversion, gray replication, M0/M1/M2/M3 comparison, identifiability, confound control — has corresponding logs.
Code-paper alignment: the Methodology accurately describes the code; the models named match the models fit.
Statistical-inference integrity: every claimed effect carries uncertainty; stochastic fits log seeds and convergence diagnostics; results are reproducible from the provided data; synthetic data (parameter recovery) is clearly labeled, never passed as real.
Cone-conversion and normalization validity: the CIELAB/XYZ $\to$ LMS conversion uses the provided CIE 2006 fundamentals with a stated reference white and a stated LMS normalization, verified on known colors. An undocumented, alternative-fundamentals, or silently-tuned conversion/normalization will be flagged.
Model-comparison honesty: M2's advantage (over M1 and over M3) is shown on held-out data or a penalized criterion at matched folds — never by in-sample fit or extra flexibility; M2 must fit genuinely distinct per-cone scalings (not a degenerate collapse to M1); the matched non-cone control M3 must be present as a panel of the required fixed, scale-matched non-cone bases (opponent, sRGB, CIE RGB, CIELAB, CIE HCL) — each of matched complexity and none a fitted free rotation — and the cone-alignment verdict must be taken against the best-performing panel member; reaching a positive verdict by comparing only against the weakest control, or by omitting standard bases from the panel, will be flagged.
Identifiability disclosure and earned nulls: the $\Delta L$/$\Delta M$ collinearity and per-cone identifiability are reported; the resolvable granularity is established with collinearity diagnostics and synthetic recovery and a cone-vs-control (M2-vs-M3) discrimination-power check; any null/partial verdict rests on that evidence and a powered channel-level comparison against a matched non-cone control. Claiming cone-specific structure the identifiability evidence cannot support, or asserting a bare unpowered "not identifiable," will be flagged. Hedging or softening language does not exempt a paper that materially frames cone-alignment as a finding.
Hue-curvature confound control: chromatic DR claims are made only after controlling for hue-locus curvature by the method appropriate to the data type; the DR/cone verdict is reported before and after control.
No substantive replication of existing follow-ups: Related Work engages with "Now in Color" (2025) and the CGF geometry paper (2025) and articulates what cone-alignment adds; presenting their results (chromatic DR, non-constancy, the geometry) or mere anisotropy as the novel contribution will be severely degraded.
Pre-registration discipline: the model family (M0/M1/M2/M3), gauge convention, comparison protocol, identifiability plan, and confound plan are stated in a time-stamped proposal/analysis_plan.md whose content matches what was run, written before the fitting scripts; both the plan's content correspondence and the fit-log ordering are checked (not file mtime alone).
Held-fixed disclosure: any deviation from the parity constraints (provided data only, provided fundamentals/coordinates, per-dataset observation models, K-fold discipline, UQ, gray-DR reproduction) is disclosed in Methodology or Setup. Silent or misrepresented deviations will be flagged.
Data-provenance and licensing honesty: use only the provided datasets; cite each with source and license; do not represent one dataset's judgments as another's, and do not pool differing response scales without the stated per-dataset observation model.

Re-stating the existing DR results, or showing mere anisotropy, without the cone-alignment test (M2 vs the best member of the non-cone control panel M3), the gauge/identifiability analysis, and the confound control this contract requires, will not satisfy it.

Deliverables — Here's what to hand in

Codebase and logs. Code in proposal/code/, logs in proposal/logs/, including: the cone-conversion + normalization pipeline with verification; the stated gauge; the gray-axis DR replication with magnitude comparison; the M0/M1/M2/M3 fits with CV folds, bootstrap seeds, held-out metrics, per-cone-distinctness check, and convergence diagnostics; the identifiability analysis (collinearity diagnostics and synthetic recovery) with the powered channel-level comparison; the by-data-type confound control (before/after); and, if multiple specifications were tried, all of them plus the selection rationale. Every quantitative claim in the paper must trace to a log entry.
Analysis plan. A time-stamped proposal/analysis_plan.md written before fitting, stating the model family (M0/M1/M2/M3), the gauge convention, the CV and model-comparison protocol, the identifiability plan (including the resolvable-granularity question), and the confound-control plan. (Need not be polished; it is the effort-evidence anchor and is checked for content correspondence.)

Follow-up paper. A LaTeX paper at proposal/report.tex compiled to proposal/report.pdf using neurips.sty, with:

Introduction: motivation, the channel-organization / cone-alignment question, an explicit significance argument for why cone-alignment matters (compact prediction of the whole space from few experiments; the biological pre-combination-vs-post-aggregation mechanism reading; and what a non-cone match would imply), contributions, and explicit positioning against the 2022 paper and the two 2025 follow-ups (including why anisotropy alone is not the claim).
Methodology: the cone-space conversion and normalization; the gauge convention; the models M0/M1/M2/M3 (mathematical form, nesting, matched complexity of M3); the per-dataset observation models; the fitting, cross-validation, and model-comparison procedure; the identifiability and confound-control methods. Stated before any results.
Experimental Setup: the datasets (sources and licenses), preprocessing, the per-dataset observation models and how held-out likelihood is defined, folds, bootstrap protocol, and the gray-axis replication summary (with magnitude comparison to 2022).

Experimental Results: a primary results table labeled \label{tab:main_results} with the structure below, plus: a plot of the fitted $f_L,f_M,f_S$ (or the resolvable channel scalings) with bootstrap bands; the held-out model-comparison plot (M0/M1/M2/M3); the identifiability diagnostic and synthetic-recovery result; and the before/after confound-control result. (The model-comparison plot must show M0/M1/M2 and every member of the M3 non-cone panel.)

Quantity	Comparison	Notes
Gray-axis DR replication (M1 vs M0, held-out; magnitude vs 2022)	(2022: concave $f$)
Held-out fit, M0 / M1 / M2 (one row each)
Held-out fit, M3 panel: opponent / sRGB / CIE RGB / CIELAB / CIE HCL (one row each)		matched complexity
M2 vs M1 held-out delta (anisotropy)		sign + significance
M2 vs best M3 non-cone control held-out delta (cone-alignment, headline)		sign + significance; name the best control
Identifiability: resolvable granularity + powered channel comparison
Hue-curvature confound control (before/after)

Analysis: the channel-organization and cone-alignment verdicts; the resolvable granularity and identifiability limits; failure analysis (specific specifications/regimes that could not be fit or identified; where CIs are too wide to support a claim).
Related Work: engage with the 2022 paper and both 2025 follow-ups; state what cone-alignment adds beyond anisotropy/non-constancy.
Conclusion: findings (including an earned null, if that is the outcome), contribution beyond the prior work, and limitations.

Good luck.