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Barbero-Immirzi projection can only reach 0.437, 0.618 or 1.236 — never the physical 0.2375 #3

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quantumProjection cannot produce a physically admissible Barbero–Immirzi
parameter for any E8 root except through its own fallback branch.

The arithmetic. Every E8 root is either a permutation of (±1, ±1, 0⁶) or
(±½)⁸ with an even number of minus signs. So

gamma_base = |c[4]| + |c[5]|  ∈  {0, 1, 2}

and the projection (e8_lqg_bridge.zig:154) is

gamma = if (gamma_base < 0.1) GAMMA_PHI else |gamma_base * PHI_INV|

which leaves exactly three reachable values:

gamma_base γ produced in (0.1, 0.5)?
0 0.436992 — GAMMA_PHI = (φ−1)/√2, the fallback yes
1 0.618034 no
2 1.236068 no

The physical target is GAMMA_STANDARD = 0.2375 (Meissner, from black-hole
entropy matching; Immirzi/Rovelli's ln2/(π√3) ≈ 0.1274 is the other common
value). Neither is reachable. The only value inside the admissible range is
the degenerate branch taken when both coordinates are zero — that is, the
answer is physical exactly when the projection has no input.

How it surfaced. test "Barbero-Immirzi prediction" asserts
0.1 < γ < 0.5 and had never executed. src/quantum_gravity/root.zig
declares pub const e8_lqg_bridge = @import(...) and nothing referenced it,
so under Zig's lazy analysis the file was never part of the compilation and
its test blocks did not exist. zig build test reported success while
running zero tests. With reachability forced, 254 tests run and this is the
one that fails.

Not fixed here, deliberately. Choosing a different mapping from E8
coordinates to γ is a physics decision, and any formula I invented would be
fitted to the assertion it has to satisfy — which would make the test agree
with the code by construction and establish nothing. The test is marked
skipped with a pointer to this issue so that new regressions still show up;
it should be un-skipped by whoever fixes the projection.

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