Constraint Ancestry in Cosmological Viability Networks

Fine-tuning arguments often count viability conditions one by one, although several of them may constrain the same combination of upstream parameters. This preprint proposes a constraint-ancestry audit: before any prior, metric or probability is chosen, viability conditions are pulled back to a common parameter origin and tested for transmitted rank, closure relations and hidden fibres. Applied verbatim to the general constraints of Table 4 of Tegmark, Aguirre, Rees and Wilczek (Phys. Rev. D 73, 023505, 2006), the audit gives exact results: (i) The seven parameters (α, β, m_p, |ρ_Λ|, Q, ξ, ξ_b) are transmitted through only six process coordinates, including the non-monomial cooling factor [ln α⁻²]^(16/3); a constant Jacobian minor −2 proves rank six on all of 0 < α < 1. (ii) The parameter domain is a trivial fibre bundle over these six coordinates: every set of parameters with identical scores is exactly one curve, parametrized globally by α in closed form; the image of the score map is cut out by exactly two closure relations; along each fibre m_p has a single maximum at α_c = e^(−16/33). (iii) A two-number test decides whether any additional log-monomial condition breaks the fibre. Recombination-before-equality, nucleosynthesis timing and supernova gas retention are exactly blind to the hidden direction; disk fragmentation breaks it only logarithmically; the first order-one breaking comes from stellar and planetary scales (close encounters, galaxy-to-star mass ordering). (iv) In the hyperplane picture of the source, the allowed region has a one-dimensional lineality space and therefore no vertices; power-law priors select a corner only if constraints transverse to the hidden direction are added. Further, halo, encounter and cooling factors satisfy HC = B², and Adams' 2026 vacuum-energy bound pulls back to the same node Q³ξ⁴. No probability for a viable universe is assigned. All algebra is exact; the embedded audit script and a machine-readable provenance ledger (CSV/JSON) reproduce every statement.