Structure Does Not Fix the Clock: Layered Underdetermination and Evidential Provenance in Metaphysics-to-Physics Reconstruction, with a Boundary-Preserving Dark-Energy Case

When a qualitative source underdetermines both the numerical representation imposed on it and the law by which that representation is traversed, empirical success at the downstream model cannot supply a derivation for either choice, though it can still bear on the model's own viability. This paper develops that claim as a defeat-sensitive provenance rule for metaphysics-to-physics reconstruction. Three separations are required. First, order or qualitative structure does not select a nonconstant numerical scalar without additional quantitative structure. Second, even a fixed profile does not select a unique map from physical time or scale factor onto that profile. Third, a downstream model's empirical viability cannot be spent backward as a derivation for the representation, the cross-domain identification, or the source that motivated it — a narrower claim than a general ban on evidential support, and one this paper states precisely rather than leaves ambiguous. The worked case is deliberately demanding. Agápēic Relational Metaphysics (ARM) supplies qualitative relational motivation but no published result fixes a canonical continuum metric or cosmological clock. A normalized reception–expenditure representation is therefore adopted, not derived, and the ratio wₛ=−(1−s²)/(1+s²) is exact only within that representation. Its further identification with the physical ratio p_DE/ρ_DE is stipulated and remains frozen: no route through covariant type-bridges, canonical restriction, effective-field-theory organization, or shift symmetry supplies the missing numerical selector, so the identification stands or falls on future work this paper does not undertake. Conditional on the stipulation, a two-parameter boundary-preserving clock yields w(a)=−B/(2aⁿ+B); matching the DES Year 6 + DESI DR2 low-redshift CPL central value and tangent fixes B=10.5 and n≈3.943. Held fixed, the resulting non-phantom history admits a canonical-scalar-like linear completion — genuine Hubble-scale negative curvature in the reconstructed potential is identified and bounded to horizon-scale modes rather than left undisclosed — and remains compatible with a joint Planck 2018 + DESI DR2 + DES-Dovekie likelihood, with Δ(−2 ln L)≈+4.08 from Planck, −6.72 from the low-redshift sector, and −2.64 in total relative to flat ΛCDM. Because the calibrating data overlap the tested data, and because the reported reproduction re-executes one pipeline rather than a second, independently designed one, this is a same-data compatibility result, not a held-out confirmation, and the raw likelihood difference is not a model-selection verdict absent a full posterior or Bayes factor, neither of which is computed here. The confrontation is then broadened to a genuinely held-out DESI DR2 Lyα distance, a growth-shape screen, and a joint refit against DESI's own compressed full-shape likelihood the fixed trajectory returns a lower χ² than flat ΛCDM throughout, including a narrowed but surviving margin under the one held-out anchor tested. The case succeeds only in the bounded sense the method permits: it shows how a source-motivated physical extension can be tested without converting modelling choices into metaphysical predictions