measuredSmallKAlphaSymbolDir
plain-language theorem explainer
Banks the two-point small-wavevector intercept α ≈ −0.249884 for the axis-TT-plus / symbol-direction mode of the exact flat Regge Hessian. Gravity analysts cite it when comparing measured continuum intercepts against the Einstein–Hilbert TT coefficient −1/4. It is a bare rational constant definition, not a derived theorem.
Claim. Define the measured small-$k$ intercept for the axis-TT-plus symbol-direction mode by $\alpha_{\mathrm{meas}} := -249884/1000000 \approx -0.249884$.
background
The module studies the exact flat Regge Hessian Bloch symbol in 4D. At a flat background every deficit vanishes, so Schläfli reduces the second variation of $S=\sum_h A_h\delta_h$ to the cross term $S''=\sum_h (dA_h)(d\delta_h)$ in squared-length coordinates; no off-flat Schläfli primitive is needed.
On TT polarizations the algebraic $m^2$ density is isotropic $Q_{m^2}(H,k)=(-1/8)|H|_F^2|k|^2$. For the banked axis-TT-plus face ($|H|_F=\sqrt{2}$) this is exactly $-1/4$, matching the Einstein–Hilbert TT coefficient. Gauge modes give exactly $0$.
This constant is a Python-first two-point small-$k$ intercept stand-in for that same axis-TT-plus / symbol-direction channel, recorded as the rational $-249884/1000000$ rather than the exact algebraic value.
proof idea
No proof: a one-line definition binding a real constant to the rational $-249884/1000000$. Downstream closeness to $-1/4$ is discharged by norm_num in the companion near-quarter theorem.
why it matters
Feeds measuredSmallKAlphaSymbolDir_near_quarter, which asserts the intercept lies within $10^{-3}$ of the Einstein–Hilbert TT coefficient $-1/4$. That check is part of the Stage-1 face-coefficient battery for the exact flat Regge Hessian: confirming that the measured small-$k$ continuum intercept on the physical TT channel sits next to the algebraic oracle value banked for axis-TT-plus / symbolDir.
It does not inhabit the RS ledger or flip gap-action recovery; it is a decide-cert style numerical anchor beside the exact $-1/4$ and $0$ mode certificates. In the broader gravity analysis it supports the claim that the flat Hessian TT sector reproduces continuum GR kinematics before any curved-background or full coupling-table work.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.