IndisputableMonolith.Foundation.ConfigDim_D3_v3
Module packaging a certificate that spatial configuration dimension is forced to three, via a non-negative domain cost and a positive canonical threshold. Foundation workers cite it when closing the T8 step of the forcing chain. The argument is definitional plus elementary positivity lemmas, not a deep existence proof.
claimA non-negative domain cost $C$ on configuration space, a positive canonical threshold $\theta>0$, and an inhabited certificate asserting that the admissible spatial dimension is $D=3$ under the Recognition cost structure.
background
Recognition Science forces geometry from a single cost functional. The J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) is the unique symmetric generator of the Recognition Composition Law; the self-similar fixed point of that law is the golden ratio $\phi$. The forcing chain then extracts discrete structure: an eight-tick octave (period $2^3$) and, at T8, three spatial dimensions.
This module sits in that foundation layer. It imports RS constants (including the native tick $\tau_0$) and the Cost library, then introduces a domain cost on configuration data together with a canonical threshold. The intended reading is that admissible spatial configurations are those whose cost stays below threshold; the certificate packages the claim that this selection rule forces $D=3$.
Sibling definitions supply non-negativity of the domain cost, positivity of the threshold, and an inhabited certificate type ConfigDimD3_v3Cert, so downstream code can treat three-dimensionality as a checked package rather than an open hypothesis.
proof idea
Definition-heavy module. It introduces domainCost and proves a pointwise evaluation identity plus non-negativity; introduces canonicalThreshold and proves positivity; then packages ConfigDimD3_v3Cert with an inhabited cert. No deep tactic proof: the work is naming the cost/threshold pair and discharging elementary Real inequalities so the D=3 certificate is constructible.
why it matters in Recognition Science
T8 in the unified forcing chain asserts $D=3$ spatial dimensions. This module is a versioned certificate surface for that claim: cost non-negativity and a positive threshold give a concrete selection rule on configurations, and the inhabited cert makes the rule usable as a hypothesis package elsewhere in Foundation.
No downstream edges are recorded on the page yet, so its immediate consumers are not wired in the graph. Its role is still clear in the RS stack: without a checked D=3 package, later geometric and physical constructions (octave timing, ladder masses, coupling bands) lack a forced ambient dimension. The _v3 suffix marks an iteration of that certificate interface rather than a new physical principle.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those are upstream.
- Does not prove uniqueness of D=3 from first principles inside this file alone.
- Does not construct physical constants (c, hbar, G, alpha) or mass rungs.
- Does not record downstream consumers; used_by is empty on the page.
- Does not address temporal dimension or the eight-tick octave beyond imports.