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| 1 | +# ADE Cascade Round 1 + M15 exp_05 + DNS Instrument v0 |
| 2 | + |
| 3 | +**Date**: 2026-07-17 |
| 4 | +**Branch**: research/ade-cascade-round1 |
| 5 | +**Context**: Re-founding the turbulence program on milestone-era machinery after the |
| 6 | +2026-07-17 stack audit (6 lore FDOs corrected). All experiments pre-registered per |
| 7 | +the midnight invariant-registration discipline (reg commit c5e05712) before any run. |
| 8 | + |
| 9 | +## New experiments |
| 10 | + |
| 11 | +- `foundational/experiments/ade_cascade/` — Dynkin graph-distance coupling for the |
| 12 | + PAC cascade engine (reuses milestone12 DynkinDiagram, milestone15 build_cycle). |
| 13 | + The legacy kernel exp(−|i−j|·cd) is nested exactly as the A-family arm. |
| 14 | + - **R1 CONFIRM**: at equal rank, A/D/E topologies produce distinct exponents |
| 15 | + (E < D < A at ranks 6–8; separations 20–90× CI half-width). Mode-count-only |
| 16 | + null is dead. [D] the legacy engine's 3.3% miss of −5/3 is an A-family |
| 17 | + artifact: D_8 = −1.6624 (0.26% from Kolmogorov). |
| 18 | + - **R2 KILL**: affine-vertex reading of the k−1 offset dead (median ρ = 0.91, |
| 19 | + direction reversed — cycle closure steepens). Registered kill; clue recorded. |
| 20 | + - **R3 CONFIRM**: mode-count monotonicity survives the kernel swap. |
| 21 | +- `foundational/experiments/dns_instrument/` — 2D pseudo-spectral NS v0, qualified |
| 22 | + (TG 2×10⁻¹⁵, budget 4×10⁻⁹, resolution 1.1×10⁻⁸). No physics claims at v0; |
| 23 | + GPU-phase measurement runs to be separately registered. |
| 24 | + |
| 25 | +## Milestone 15 |
| 26 | + |
| 27 | +- `exp_05_general_k_limit.py`: anchor k=2 reproduces 8/3 to 6×10⁻⁸; **both** |
| 28 | + registered candidates for the general-k limit die (L₃ = 5.4913 vs K1 3.0667 / |
| 29 | + K2 2.625; L₄ = 11.1863 vs 3.3524 / 2.619). The 8/3 = F₆/F₄ Fibonacci |
| 30 | + coincidence is formally retired; general-k limit OPEN, no post-hoc fit. |
| 31 | + K3: ℤ₂ even-reflection telescoping universal (det H = +1, k = 2,3,4, m ≤ 30). |
| 32 | + Anchor gate caught a sign-convention instrument bug (VOID first run, disclosed). |
| 33 | + |
| 34 | +## Engine change |
| 35 | + |
| 36 | +- `milestone4/core/utils.py::energy_cascade`: optional `coupling_matrix` injection |
| 37 | + (default bit-identical, gate-verified G1/G2 = 0.0 diff, G3 baseline reproduced); |
| 38 | + per-scale `psd_shift` now recorded (threat T1 monitoring). |
| 39 | + |
| 40 | +## Lore sync |
| 41 | + |
| 42 | +FDOs updated this session: `med-navier-stokes`, `she-leveque-fibonacci-turbulence`, |
| 43 | +`cascade-turbulence-mode-count` (incl. exp_15 audit: 800× is ~1063× CoV-of-CoV; |
| 44 | +B.2 CI excludes −5/3), `pac-dag-fluid`, `bidirectional-sec-pac-fluid`, |
| 45 | +`milestone15-representative-problem`. New FDO for ade_cascade round 1 created |
| 46 | +post-outcomes. |
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