D-029 — E-019 analysis: backend v2 validated; zero-flow at a=12 — NO transition; lattice stiffens

Date: 2026-08-18 | Session: 006 cont.4 | Task: 2.8(ii) Status: complete. a=12 reached (e²⁴ blockwise sieve). All measurements continue the a ≤ 10 trends; no transition signature of any kind. The a=13–14 push (e²⁶–e²⁸, hours) is DEPRIORITIZED by evidence (§8.4a).

1. Backend v2 (prime_backend_v2.py) [NUMERICAL-VALIDATED]

• Exact segmented Λ sieve (composites marked by base primes ≤ √hib; survivors = primes; higher prime powers by exact index), blockwise with running cumsums; answers C1/C0 at arbitrary m; npz cache.
• V-A1: max |dev| vs E-016 in-memory backend = 2.2e-7 over 10⁴ random t ∈ (0,20] — the float64 summation-reordering floor (both backends carry this rounding level; agreement here = exact).
• V-A2: full pipeline at a=10: stiffness Q dev 4.4e-8, z₁ dev 6.9e-9, zero count identical. e²⁴ sieve: 1579 blocks, ~11 min (Ryzen 9).
• Debugging note: an early version set lam on ALL multiples of pk (wrong for non-prime-powers) and missed primes > √hib — caught by the smoke test; an off-by-one (cumsum to floor(e^t) vs floor(e^t)−1) produced O(0.2) errors at small n (t−log n ~ 1/n not small there) — caught by V-A1. Both lessons logged.

2. Zero-flow at a=12 vs a=10 (θ=π, h=0.01) [NUMERICAL-VALIDATED]

3. γ-locking proximity is chance-level

Expected min over 30 γ's of distance to the nearest lattice point (spacing s): ~ s/(2·30) ≈ 0.005. Observed 5e-5–2e-4 is 20–80× smaller, BUT: (i) the h=0.01 zero-location noise is ~5e-4 (E-010 z₁ h-drift) — larger than the proximity itself; (ii) the minimizing γ CHANGES with a (γ_20 at a=10, γ_3 at a=12) — systematic locking would track a FIXED γ with monotonically decreasing distance. Verdict: coincidence, not locking. Future locking claims must (a) beat ~1e-4 proximity, (b) track a fixed γ across ≥ 3 a-values, (c) exceed h-noise control.

4. Verdict on task 2.8

At a = 12 the Cor 1.6 transition has not begun: inflow continues (z₁ = 4.495/a → 0), the lattice stiffens (gap CV ↓), no γ-locking, the (★) envelope is stationary at ~6.5e-3, and no new non-real zeros appear. Combined with D-023 (scale limitation, not a wall) and D-028 (open content = zero set of M): the transition, if it exists, starts at a ≫ 12. Task 2.8 CLOSED (question "does anything change by a = 12?" answered NO); the a = 13–14+ push is deprioritized by evidence, not by obstruction — it remains available (backend v2 + cache make a=13 a ~30 min run) and is the first thing to revive if any analytic estimate points at a specific transition scale.

5. Honesty notes

• All a=12 numbers at h=0.01, λ=−1 (same conventions as E-010–E-018).
• B3's first run showed excess −4 at y₀=0.1 — edge-undersampling artifact (400 pts/edge); dense rerun (4000/edge) gives clean +2.0000 at both y₀. Winding edges must sample the angle whipping near real zeros adequately — recorded as machinery guidance.
• quad_plain fallback (>64 integers per window) means the quadrature smooths prime-sum kinks at large t — same approximation as at a≤10 (validated there; V-A2 re-validates end-to-end).
• gap CV uses located zeros; window-edge effects < 0.1%.

ERRATUM (2026-08-19, D-043 §C)

The B2 "γ-proximity chance-level" conclusion is RETRACTED: the metric was wrong-direction (median over all ~10³ zeros to z ≤ 300 of distance to only the FIRST 30 γ's, z ≤ 77 — trivially ≈ 49). Correct direction (γ → nearest W-zero, E-022 data): mean min-dist ≈ 0.65/a² — strong, monotone-improving positional locking (15× tighter than chance at a=12). The B1/B3/B4 findings (maximal lattice, stiffening, no non-real zeros, stationary envelope) are unaffected. See D-043 §C.