[Draft] Complex supplier b ≈ 1.334e-3 (+5.2%): shared-donor kernel and entrance gauges on the E8 complex word

[DreamingOfClouds]

WIP. The claim is pending the full package and is conditional on two new lemmas. No κ is claimed.

Result so far (hosted b on #442's complex word, exact moment engine)

word	b (·10⁻³)	gain
#442 complex	1.267453
shared-donor kernel, 79 pivots	1.310216	+3.37%
entrance gauges, 80 helpers	1.310916	+3.43%
both (all residuals hosted, stock 7,680)	1.333854	+5.24%

If the complex side were the only constraint these give κ caps of 1.3085 / 1.3092 / 1.3321·10⁻³ against 1.2658·10⁻³
for #442's complex word, which is what binds the current frontier (#447, #445).

What passes

Exact arbitrary-dirt and inverse-transpose replay, the emitted program in both orientations on 800 columns, and the exact
Gaussian phase recipes of every used frame transition, for all three words (sh check.sh DIR).

What does not (read this first)

• The entrance lines are isotropic (even weight). The bit-style coordinate-entrance criterion of κ = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes #440
  (validate_isometries) is not met; for entrances that do meet it the gain is 0.
• Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442's shipped complex audit and emit assume w == 9 and start == 0; no shipped complex word has a nonzero helper
  entrance. The scripts here are patched copies.
• The result is conditional on two new lemmas, the review points: (A) the entrance adapter (E→FULL =
  monomial·C_[9−e]·monomial, exact for all 16 entrance frames; the residual-route claim is assumed), (G) nonzero-frame
  compensation and the centre scatter at the target levels (extends κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425's conjugation lemma).
• Pending: global template and owner tables for mixed residual widths (the hosted b is a model that reproduces Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442's
  complex b to the last digit), finite invoices, the outer assembly with a bit word, mutation controls, byte-for-byte
  regression at the Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442 defaults, two fresh replays.

Credits

#442 (DaysSky), #433 (icekylinx), #425/#386 (jacklightChen / Zhihao Chen), #417/#435 (chafreaky), #434/#440
(rohanarun), #401/#408–#416 (entrance gauges), #370 (Dylan Crow), Jacob Sussman's E8 unit.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code