Logbook — 2026-04-13 — Preflight kickoff

Context. Guardian cleared v0.3 for execution. This entry opens §4a preflight and codifies five residual Guardian flags as operational requirements before any numerics runs. Sequel entry: 2026-04-13-preflight-results.md will record outcomes.

1. Guardian flags → operational settings

Flag 3 — Integrator-tolerance threshold (must fix before any comparison)

Decision. Three engines "agree to within integrator tolerance" at the anchor point (δ₀ = 0, |α| = 0, φ_α = 0) iff

‖ΔC‖ = |C_A − C_B| < 10⁻⁴                  (complex coherence)
|Δ⟨σ_z⟩|           < 10⁻⁴                  (σ_z population)
max_n ‖ΔBloch_n‖   < 10⁻³                  (per-pulse, n = 1…22)

The per-pulse threshold is relaxed 10× because intermediate Bloch values accumulate floating-point error across 22 matrix exponentials whereas the final C is a single-point readout. These thresholds are defaults; if preflight discovers legitimate engine differences dominated by a specific cause (i.e. one of the four candidates in §4a), the cause is reported regardless of whether thresholds are met.

Flag 4 — Injectivity probe on raw C, not normalised

Decision. cond(J) is always computed on raw C = ⟨σ_x⟩ + i⟨σ_y⟩, not on |C|_normalised. The normalisation factor 1/|C(0, 0, 0)| is a constant over the entire map and therefore rescales cond(J) by that constant — harmless — but if |C(0, 0, 0)| turns out to be small in the Doppler-dominated regime, the normalisation amplifies numerical noise and corrupts the conditioning analysis. Normalised |C| is a visualisation device only, per §2.1 of v0.3.

Flag 2 — Finite-difference step per axis

Decision. For the Jacobian J = ∂(Re C, Im C)/∂(δ₀, |α|, φ_α):

• δ₀: central differences on the native grid (Δδ₀ = 0.05–0.1 MHz/(2π) depending on final resolution per Q4).
• φ_α: central differences on the native grid (Δφ_α ≈ 0.098 rad at 64 points).
• |α|: the Q4-sanctioned sparse grid {0, 1, 3, 5} gives finite differences of spacing {1, 2, 2} — non-uniform and coarse. cond(J) along the |α| row will therefore reflect sampling artefact, not physics. Mitigation: a dense sub-grid |α| ∈ {0, 0.25, 0.5, …, 2} at 0.25 spacing is run only where S1 shows cond(J) flagged as ill- conditioned; elsewhere the coarse grid stands with an explicit caveat annotated on the plot.

Flag 1 — Per-run cost quote for S2 budget

Decision. During preflight, measure wall time for a single anchor-point run in the candidate engine. Multiply by slice sizes: - S1 = 121 × 5 = 605 runs - S2 = 121 × 64 × 3 = 23,232 runs (expensive sheet) - S3 = 5 × 64 × 2 = 640 runs

If S2 × (per-run cost) > 24 h wall, triage options: drop to 48 φ_α points (Δφ_α ≈ 0.131 rad, still above 16-point sanity level); or reduce δ₀ resolution from 121 → 81 points; or run only the |α| = 3 sheet of S2 as the diagnostic slice and defer |α| ∈ {1, 5} to a follow-up. Decision deferred to the results entry; options stated here so they're not invented mid-sweep.

Flag 5 — Q3 and Q5 must both be resolved before S1

Decision. The preflight-results entry must explicitly state:

• Q3: whether a closed-form Lamb–Dicke linear prediction exists in the repo for C(δ₀, |α|, φ_α), or whether R1 will be evaluated numerically at η → 0 (e.g. η = 0.04 with linear extrapolation). Until this is stated, R1 residual plots cannot be generated.
• Q5: engine commitment — extend ../../scripts/stroboscopic_sweep.py or fork to a new phase_contrast_map.py. The decision depends on whether ⟨σ_x⟩, ⟨σ_y⟩ are already exposed or require a backend patch; see §2.

2. Immediate inspection targets

Before any engine runs, answer three questions by reading files:

Q5a — Does stroboscopic_sweep.py already return ⟨σ_x⟩, ⟨σ_y⟩? Expected finding: σ_z / P_↑ only, requiring a patch. To confirm, read the remainder of the script beyond line 200 (Hamiltonian block seen in the v0.3 code-reading pass).

Q3a — Is there a closed-form LD linear prediction anywhere in the repo? Grep for "Lamb" / "LD" / eta = 0 / small-η expansion in scripts/ and the HTML sources.

Anchor data — Where is the (α=0, δ₀=0) legacy data point? The data/alpha_0/ directory holds the HDF5 adaptive-learner outputs. The JSON uniform engine data is under data/runs/ (inferred from directory name). Read both and extract the contrast value + any phase info at the anchor point.

3. Plan of execution

1. Inspect scripts/stroboscopic_sweep.py completely (lines 200 onward) — answer Q5a.
2. Inspect data/alpha_0/ and data/runs/ — locate anchor-point legacy values.
3. Grep for LD closed form — answer Q3.
4. If Q5a = no, decide: minimal patch vs. new script. Document either way.
5. Run candidate at anchor point; record wall time and Bloch trajectory.
6. Three-way comparison; if disagreement, assign one of four candidate causes.
7. Write 2026-04-13-preflight-results.md with pass/fail determination, Q3 and Q5 resolutions, S2 budget calculation, and next-step call on main-sweep execution.

4. Non-goals for preflight

• No map-grid runs.
• No Jacobian computation.
• No modifications to v0.3 README (per Guardian's cadence recommendation: next README touch is v0.4 after preflight data exists).
• No modifications to legacy data.

Guardian cadence respected: single pass on §4a, then results entry, then — and only then — main sweep or README v0.4.