phugoid

A fixed-wing flight-mode lab in EigenScript, named for the slowest longitudinal mode it grades. phugoid is the consumer that stresses the half of the observer nothing else in the fleet touches: the cost and correctness of observation while observing, at a frame deadline — live predicate reads (stall warning, trim detection, oscillation onset) inside a hot real-time loop. The proposal and contract live at hq/proposals/flight-simulator.md; the falsifiable prediction recorded there is that the physics will not be what breaks first.

Oracle-first: rung 0 is the grader, rung 1 the first flight model

Rung 0 built and adversarially validated the grader before any model:

• DERIVATIVES.md / data/b747_approach.eigs — a complete public airframe dataset (Boeing 747, Mach 0.25 powered approach; Caughey 2011 ← Nelson ← NASA CR-2144) whose source publishes every link of the derivation chain.
• modes.eigs — nondimensional coefficients → dimensional stability derivatives → state matrices → characteristic quartic (Faddeev–LeVerrier) → complex roots (Durand–Kerner) → mode quantities (ωn, ζ, T, t½, N½). Every stage is checked against the published values: 180 pinned checks.
• measure.eigs — the estimators that will grade rung-1+ trajectories: period by extrema-spacing and by Hann-windowed DFT peak, damping by log decrement and by envelope fit (both baseline-free, on peak-to-trough spans), aperiodic t½ by exponential fit. 126 pinned checks against synthetic truth, with every refusal path pinned — the estimators must refuse rather than answer when a window can't support the estimate.
• ORACLE.md — the quality bar itself: published numbers, stated tolerances (with written justifications for every widening), an eighteen-plant fault matrix proving each checker can fail, and a boundary self-test of the comparators so a widened tolerance cannot pass silently.

Rung 1 (shipped 2026-08-24) is the first model, graded by rung 0:

• sim.eigs — the nonlinear longitudinal 3-DOF model: coefficient aerodynamics with the α̇ dependence solved in closed form, a Newton trim solver, RK4, and the SP-subspace excitation. Its Jacobian at its own solved trim must match the rung-0 A matrix entry-by-entry (S0), and its free responses grade to the chain's mode quantities: phugoid T within 0.03% measured, ζ within 0.2%; short period T within 0.17%, ζ within 0.15% (arms in ORACLE.md, twenty-two-plant fault matrix in tests/test_sim_planted.sh).
• tests/observer_check.eigs — the observer's verdicts graded against the same physics: 8 agreement pins, and 3 pinned divergences — the fixed 10-sample predicate window reads a 47 s mode at 1 Hz as diverging on its quarter-cycles (GAPS.md G4, the first measured instance of the proposal's two-timescale prediction).

Rung 3 (shipped 2026-08-25) is the first phugoid model that acts — a closed-loop autopilot, with the observer as its supervisory layer:

• autopilot.eigs — classical pitch-rate feedback on the rung-1 plant, graded against closed-loop pole predictions computed from the chain BEFORE the controller existed (A_cl = A + B·K, then the same charpoly4 → dk_roots → modes_of). Measured: ζ tracks the prediction to 0.0066–0.16% across the three graded gains and the phugoid row, and the whole grading apparatus transferred with no new oracle code.
• The observer in the loop. Two of three pre-registered predictions were refuted, which is the rung's main result. At inner-loop rate the observer is not noisy — but neither is it merely blind: on a smoothly decaying phugoid it never says oscillating (0 of 8000 reads) and instead alternates diverging (49%) and converged (51%), so an autopilot would fight a healthy mode half the time. Supervision does not hold cleanly either; it flickers 17 times in one phugoid episode for want of hysteresis. The corrected design law needs two conditions: a verdict is actionable only when the regime persists beyond ~1–2 observation windows and the observed channel still clears the deadband. The second condition is a horizon, not a gate: the onset never moves (the window filling), only the cutoff does, so as a mode decays under the band supervision runs out of time rather than switching off — EigenScript#1045 changing what an actuator does.
• tests/ap_profile.eigs — the observer's READ path, which no consumer had put under load. The whole read-bearing program costs 1.75–2.50× the write-only one on this shape; for a program that reads verdicts at all, ~75% of the observer cost is the reads themselves and ~25% is per-assignment write bookkeeping the reads keep armed. And the rung's second upstream find: EigenScript#915's write-path gate arms per interpreter state and monotonically, so one verdict read anywhere in a program — in a function that is never called, in a different file, or as a bare string constant — arms bookkeeping for every assignment in every module (+43–48% measured on dead code across three independent reproductions; GAPS.md G7, EigenScript#1046). It cannot help an autopilot by construction.

Rung 2 (shipped 2026-08-24) is the lateral model — three timescales and the level-set stress:

• latsim.eigs — the lateral 3-DOF (exact Ixz-coupled moments, exact-origin trim, mode-pure annihilator ICs via Cayley–Hamilton). Jacobian parity vs the rung-0 lateral A measured at machine epsilon; Dutch roll T within 0.1%, ζ 0.01%; roll and spiral t½ within 0.1%.
• tests/observer_lat_check.eigs — the level-set grading: the value channel correctly reads zero-symmetric motion the entropy channel is provably blind to (the mirror pin: a +5 → −5 assignment registers why == 0 exactly), and the rung's new find — verdicts are unit-dependent below |v| ≈ 1 (the same still-decaying bank angle reads converged in radians, moving in degrees; GAPS.md G5, EigenScript#1045).

Run it

bash tests/test_lint.sh        # every .eigs lints clean (planted-fault validated)
bash tests/test_comparator.sh  # 15 tolerance boundary self-tests
bash tests/test_modes.sh       # 180 chain checks vs published values
bash tests/test_measure.sh     # 126 estimator checks vs synthetic truth
bash tests/test_planted.sh     # 18 plants must each flip exactly their checks
bash tests/test_sim.sh         # 79 rung-1 model checks vs the rung-0 chain
bash tests/test_sim_planted.sh # 22 rung-1 plants, exact red sets + manifest
bash tests/test_observer.sh    # 11 observer-verdict checks + 2 plants
bash tests/test_latsim.sh      # 76 rung-2 model checks vs the rung-0 chain
bash tests/test_latsim_planted.sh # 22 rung-2 plants, exact red sets + manifest
bash tests/test_observer_lat.sh   # 13 rung-2 observer checks + 2 plants
bash tests/test_ap.sh          # 217 rung-3 closed-loop checks
bash tests/test_ap_planted.sh  # 16 rung-3 plants, exact red sets + manifest
bash tests/test_ap_profile.sh  # the observer read-path ratio gate

Requires eigenscript on PATH (or EIGENSCRIPT=/path/to/binary), pinned in CI at the version in .devcontainer/Dockerfile.

The rung ladder

Rung	Scope	Status
0	Oracle before code: dataset, mode predictions, measurement scripts	done
1	Longitudinal 3-DOF, trimmed; elevator pulse → phugoid, SP-subspace IC → short period, graded against rung 0; observer verdicts graded second	done
2	Lateral 3-DOF: Dutch roll, spiral, roll subsidence via mode-pure annihilator ICs; the level-set/value-channel stress graded	done
3	The autopilot: closed-loop control graded against closed-loop pole predictions; the observer as supervisory layer	done
3b	6-DOF + control tapes, byte-exact replay gate (deferred from rung 3: no nondeterminism source yet, so the gate would be vacuous)	—
4	The swarm: N aircraft, three-arm observer cost curve (ceiling/disciplined/floor), VM-vs-AOT	—

Headless by contract through rung 4; any instrument-panel phase comes after and rides the fleet UI-oracle standard.

Gap ledger: GAPS.md — upstream findings, never silent workarounds.

License

MIT — see LICENSE.