Consequences

6.1 — KS-2c is closed

Kill switch KS-2c asked: why N = 3 spatial dimensions?

This paper answers: because there are four independent axioms, one gives the temporal direction, three give the spatial directions.

N = 3 is derived, not assumed.

KS-2c is closed.

6.2 — Lovelock is unconditional

AP08 section 9 derived Einstein’s field equations via Lovelock’s theorem, conditional on N = 3.

With N = 3 now derived, the condition is removed.

Lovelock’s theorem (Lovelock 1971) applies in all dimensions; the uniqueness in 3+1 specifically — the divergence-free, symmetric, rank-2 tensor built from the metric and its first and second derivatives is uniquely G_μν + Λg_μν — is the Lovelock 1972 result. In other dimensions, the general theorem admits additional terms in the Euler density expansion; in 3+1 specifically those terms are topological or vanish, leaving only the Einstein tensor and the cosmological constant.

Einstein’s field equations with cosmological constant are now an unconditional theorem of the record algebra.

The derivation chain is complete:

Axioms {S, B, R, C} → independent (AP20 section 4.2, fenced at KS-P.2) and jointly exhibited by any existing record (AP20 section 6).

+ EH + QRA (proven, AP20) → Lorentzian manifold (section 4’s signature argument; fenced at KS-D.4).

+ Four independent axioms → four dimensions, signature (−, +, +, +). (This paper.)

+ Record density on M → Poisson forced by symmetry constraints (AP08 section 4).

+ Lovelock’s theorem (now unconditional) → G_μν + Λg_μν = (8πG/c⁴) T_μν. (AP08 section 9.)

No link in this chain is conditional on an empirical input for the number of dimensions.

The form of Einstein’s field equations is derived from the axioms alone.

6.3 — What this means for The 420 Code

After this paper, The 420 Code derives Lorentzian spacetime, special relativity, N = 3 spatial dimensions, the Poisson equation, Einstein’s field equations, the cosmological constant existence, and quantum mechanics — all unconditional.

No empirical inputs other than m_e (from AP24) and the value of G (identified but not independently computed, per AP08 section 5).

EH and QRA are proven (AP20). All results are unconditional.