IndisputableMonolith.Foundation.ConfigDim_D3_v3
Module packaging the Recognition Science case that configuration cost forces spatial dimension D = 3. It defines a domain cost on candidate dimensions, a positive canonical threshold, and an inhabited certificate ConfigDimD3_v3Cert. Anyone citing the T8 step of the unified forcing chain uses this bundle. The argument is cost comparison plus nonnegativity, not a deep analytic construction.
claimOn candidate spatial dimensions one defines a nonnegative domain cost $C(D)$ and a positive canonical threshold $\theta_\ast$. The module asserts a certificate that the unique dimension meeting the cost threshold is $D = 3$, in the sense of the Recognition Science forcing chain (T8).
background
Recognition Science derives geometry from a single cost functional rather than postulating spacetime dimension. The forcing chain (T0–T8) ends at T8: spatial dimension $D = 3$. Upstream, the Cost module supplies the J-cost $J(x) = (x + x^{-1})/2 - 1$ and related defect measures; Constants supplies the RS tick $\tau_0$ and $\varphi$-native units.
This module works at the configuration level: it treats candidate dimensions as discrete labels and assigns each a domain cost. The siblings domainCost, domainCost_nonneg, and domainCost_at_eq fix that cost and its elementary properties. A positive canonicalThreshold marks the admissible band; the certificate objects package the claim that only $D = 3$ sits in that band.
The local setting is Foundation, not phenomenology: no mass ladder or coupling fit is attempted here. The module only closes the dimensional slot needed by later geometric and ledger constructions.
proof idea
Definition-heavy module with short positivity and equality lemmas, then a certificate record. Domain cost is introduced as a function on dimensions; nonnegativity and evaluation-at-equality are proved directly from the Cost import. The canonical threshold is defined and shown positive. ConfigDimD3_v3Cert (and the inhabited cert) packages those facts into a single witness that $D = 3$ is the forced configuration dimension. No long tactic script: structure is defs plus elementary inequalities and a bundled certificate.
why it matters in Recognition Science
T8 in the unified forcing chain states that spatial dimension is forced to three. This module is the v3 packaging of that claim: a cost-threshold certificate rather than an informal counting argument. Downstream pages currently list no direct used_by edges, so the module stands as a Foundation leaf meant for import by geometry, ledger, and eight-tick constructions that assume $D = 3$.
Together with T5 (J-uniqueness), T6 ($\varphi$ fixed point), and T7 (eight-tick octave, period $2^3$), it completes the discrete skeleton on which continuum fields and the mass ladder sit. Referees checking the forcing chain should verify that the domain cost is the same J-derived cost used elsewhere, not an ad hoc dimension penalty.
scope and limits
- Does not derive continuum Einstein equations or curvature dynamics.
- Does not prove uniqueness of J; that is T5 upstream in Cost/forcing.
- Does not fix units, alpha, or particle masses; only the dimension slot.
- Does not supply a used_by parent theorem in the current graph.
- Does not address time dimension or signature beyond spatial D = 3.