The Quantum Error-Correcting Origin of Spacetime

Where do initial conditions come from? Causal dynamical triangulations [13], spin foams, and

tensor networks all face the same problem: the seed geometry must be specified from outside the

theory. Fine-tuned starts produce fine-tuned ends.

topological defect costs reproduce the mass ratios of the electron, muon, pion, proton, and neutron

to 0.12% — no fitting. The FCC lattice is taken as given there. Here we ask the prior question:

why that lattice?

Bang transition to K=12 FCC — is available at:

the Bell pair: the absolute origin, a single timeless entanglement bond, the minimum quantum

state from which everything grows. The Big Bang is a later, separate event: the P = e

transition in which three K=6 hexagonal sheets crystallise into the K=12 cuboctahedral FCC

bulk, creating three-dimensional space for the first time.

The complete chain, running from the established physics of Part I backward to the minimal

initial state, is:

Figure 1: The cosmological emergence chain. Top: Timeline from Bell pair to particle

spectrum, with the Big Bang (P = e

— (a) Bell pair; (b) triangle (minimal CSS stabilizer); (c) K=6 hexagonal sheet (2D pre-Bang

expansion); (d) K=12 cuboctahedral (Big Bang product); (e) ABC stacking mechanism (three

sheets + Lift).

We present three independent arguments, each sufficient on its own, that the [[192, 130, 3]] code

forces K=12 FCC coordination. Their convergence constitutes the strongest possible case that

this geometry is not a choice but a logical necessity.

The [[192, 130, 3]] CSS code is constructed on the FCC coordination cluster [2]. The cluster’s

combinatorial data — its f-vector — is (f

The CSS coupling matrix B ∈ {0, 1}

Part I [1] shows that this integer is the proton verification cost C

matching the proton-to-electron mass ratio to 0.008%. Equation (1) is not an approximation;

distance or breaks the identity dim(B) = 1836. No CSS code with dim(B) = 1836 and d = 3

exists on a lattice with K < 12.

dron with K = 12. Any reduction in coordination destroys either C

The Kepler conjecture, proven by Hales [7], states that no arrangement of equal spheres in three

dimensions achieves a packing fraction higher than π/(3

is achieved by the FCC lattice, where each sphere contacts exactly 12 others at the vertices of a

cuboctahedron.

number of nearest-neighbour contacts must have K = 12 and must be locally cuboctahedral. No

other coordination number is simultaneously achievable and maximal.

The two arguments above establish that K=12 is necessary (from the CSS code) and maximal

(from the Kepler/kissing bound). A third argument from Regge calculus establishes that K=12

FCC is the unique flat discrete geometry in three dimensions — independently of packing density

or code structure.

where θ

geometry requires δ = 0 at every interior hinge.

dihedral angles are:

structure on a simplicial complex is the plaquette: a closed loop enclosing minimal area. On a

triangular lattice, this is the triangle.

exactly the triangular faces of the lattice [2]. A two-node open link is not a stabilizer. The triangle

is the minimal structure that participates in the fault-tolerant verification machinery of the code.

simultaneously: (i) gauge-invariant (closed plaquette); (ii) a valid CSS stabilizer; (iii) the seed of

the hexagonal tiling. No simpler structure satisfies all three conditions.

A triangle has three edges. Each edge is a bond between two nodes — a unit of entanglement.

zero logical qubits, distance 2. It is the minimum bipartite entangled state: no entangled state

on fewer than two qubits exists.

entangled link. The remaining two edges of the triangle are generated by adding a third node

equidistant from the original two, at the apex of the equilateral triangle. This third node closes

the gauge-invariant loop, converting the open Bell-pair bond into a CSS stabilizer.

possible initial condition at minimal qubit count. A single qubit cannot be entangled with any-

thing. Two unentangled qubits carry no non-local correlations. The Bell pair is the boundary of

the possible.

pair origin — it requires it, as the backward chain shows. The forward and backward implications

together constitute a complete logical closure:

Closure into a triangle gives each node participation in 3 checks; further lateral growth into the

sheet interior raises this to 6 (first hop) and beyond (compound detection paths), exceeding the

equidistant from existing edges) is the path of least resistance: it requires satisfying 2 distance

constraints (1D solution manifold), versus the 3 constraints required for out-of-plane growth (0D).

The sheet-interior nodes achieve t ≫ d + 1 triangle membership and are fault-tolerant stable.

only half the Kepler bonding capacity. The out-of-plane Lift is suppressed by a topological barrier.

We derive its magnitude via two independent routes that converge on the same value.

We now evaluate this for the Lift.

The three constraints reduce the solution manifold from 3D to a discrete set of two points (the

two tetrahedral apices, ±h). Crucially, all three constraints are satisfied simultaneously at z = h;

there is no trajectory that satisfies them sequentially. The potential V (ϕ) therefore encodes a

The codimension of the solution manifold (Eq. 14) equals the bounce action in natural units:

states that logical error rates are suppressed below the fault-tolerance threshold when the num-

ber of independent stabilizer checks t on a defect exceeds d + 1. Below threshold, the survival

probability scales as: