The First Light protocol now points to three required engineering artifacts:
These pages convert the remaining H0 work into explicit evidence obligations. The theorem and Python reconstruction remain unchanged. Hardware verification begins only after these packets contain real values, build identifiers, reports, and sign-off.
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CITYWIDE BROADCAST STATUS · SYNCHRONIZED
This page is now the canonical source packet for Bulletin FL-E47-2026-07-19. The theorem and E1 reconstruction are accepted citywide. The universal dense-float64 $10^{-16}$ endpoint criterion is superseded by the corrected precision-aware residual budget. H0 hardware realization remains open and has been propagated to Engineering and Observatory queues.
Central Citadel broadcast · Canonical Bulletin Ledger · Machine Certificates
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FIRST LIGHT · HARDWARE-IN-THE-LOOP VALIDATION GATE
Document: KKP-R-HIL-FL-2026-REV1
City route: Blue Line → Verification Precinct → Spectral Theory interchange → Hardware engineering queue
Evidence class: E0 exact finite-dimensional theorem · E1 Python numerical reconstruction · H0 proposed hardware protocol
Audit date: 2026-07-19
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The mathematical contraction theorem is valid under the stated spectral hypotheses. The Python reconstruction verifies the $125=47+78$ decomposition, the normalized kernel ratio $\Omega_c=47/125=0.376$, the stability bound, projector idempotency, and geometric suppression of the transverse complement.
The proposed end-to-end acceptance bound of $10^{-16}$ after $n=500$ iterations does not pass in ordinary dense float64 execution. The observed limit is accumulated floating-point error in repeated matrix multiplication, not failure of the underlying contraction theorem.
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MACHINE VERDICT
Theorem: PASS
Dimension ratio: PASS
Stable step size: PASS
Projector reconstruction: PASS
Float64 residual ≤ $10^{-16}$ at step 500: FAIL
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$V=\mathbb R^{125}$
$Q:V\to V$