The baryon acoustic oscillation (BAO) feature is usually compressed into one effective standard-ruler parameter per tracer and redshift interval. The present work asks whether that compressionremains information-complete once the observed galaxy field is resolved by cosmic-web environment,viewing direction, and tracer class. Motivated by the DESI light-cone map, but not inferred from theimage alone, we formulate an environment-resolved BAO program in which each sector a = (e, μ, t, z)carries its own effective dilation parameter αa. The primary observable is the sector-contrast tensor∆ab(z) = αa(z) − αb(z), together with directional and cross-tracer contractions of that tensor. Thenull hypothesis is not that every sector contrast must vanish in the data; it is that the full covariance-weighted pattern of contrasts is reproduced by survey-matched mocks and forward models includingnonlinear transport, redshift-space distortions, survey geometry, and tracer bias. We develop theestimator basis, a minimal transport expansion for the sector dependence of αa, and a benchmarkforecast model calibrated to remain in the sub-percent regime suggested by contemporary BAOtheory. The resulting hierarchy predicts voidward positive shifts, knotward negative shifts, largeranisotropy in filaments than in sheets, and a growth of contrast amplitude toward lower redshift.We then map those forecasts onto a DESI-ready implementation pathway using public clusteringproducts, public mock suites, and the public probabilistic DESI cosmic-web catalog. The paper iswritten as a full analysis blueprint: observables, benchmark numbers, figures, tables, discovery logic,and explicit rejection criteria are all given. The main claim is narrow. The primordial sound horizonremains unique; what may fail is the sufficiency of a morphology-blind late-time compression of theobserved ruler.
SIKX HILTON (2026) studied this question.