The Along-Track Cruise Floor Is Architectural
The ~0.14 m Along-Track Cruise Floor Is Architectural — the Pre-Risk Close-Out
The floor is the same ~0.14 m operational p_e maximum under every dynamic lever a velocity- or bandwidth-limited error would answer to. It is speed-invariant (Figure A): the operational p_e maximum moves 9% across a 2× speed range, while every forcing of the modeled steady-state floor carries a positive power of speed and so predicts a falling error. It is gain-invariant (Figure B): the operational p_e maximum runs 0.1493 → 0.1460 → 0.1449 m as the end-effector position gain doubles from [2,2,4] to [4,4,8], with engagement proven (the startup peak fell 30%, the fraction above 0.10 m halved from 0.554 to 0.218), so the inverse-gain quasi-static prediction is genuinely falsified. And it is arc-anchored: the four speed profiles overlay in arc space at mean pairwise Spearman rho 0.936, versus 0.587 in absolute time. The floor is locked to the helix parameter, not to elapsed time.
The end-effector regulation loop's natural frequency exceeds the orbital rate by a factor of 91 to 224, and the settled coupled-mode ripple carries at most 3.5% of the floor. The loop settles to its per-instant equilibrium within a small fraction of an arc period, so reading the settled state at each arc phase is legitimate: the measured profile is the per-arc static equilibrium, not an unsettled transient. This is the sense in which the floor is a quasi-static tracking error.
The standoff reference is self-referential. Guidance commands the end-effector to a point on a sphere of radius 0.20023 m about the arm's own whole-system centre of mass; the arm carries mass fraction 0.576, so reaching toward the target moves the centre of mass, which moves the target. At the episodes where p_e exceeds 0.10 m, the aim folds the commanded point toward the inner reachable boundary (required reach touches 0.099–0.106 m against an inner radius of 0.103 m). The arm is not degraded there — margin to the outer envelope exceeds +0.497 m and the episodes are better-conditioned — it holds a well-conditioned mid-reach posture and declines to follow the reference into the retraction fold. At the fold the elbow is an active constraint, pinned at its −2.891 rad lower singularity fence for about 99.5% of episode steps. The fold posture is the episode locus.
The episodes are a tangential sign flip. In the orbit's Frenet triad the error runs +0.04 to +0.05 m ahead of reference on healthy arc and falls to −0.05 to −0.08 m behind at the episodes, while the inward-normal component stays small (+0.02 to +0.03 m) throughout. The ceiling is an along-track lag localized in the tangential direction — not a constant standoff-geometry offset. This direction is the axis on which every candidate channel below is tested.
coverage 0.997–1.0 · gates 3/3
op p_e max at v_ref 0.90 / 0.75 / 0.60 / 0.45 m/s
op p_e max, K_e [2,2,4] → [3,3,6] → [4,4,8]
vs 0.587 absolute time; envelope spread 8.8%
0.078 / 0.089 / 0.237; ≥ 76% is non-static
architectural_close_gain (gain, AM0339)
comparison · baseline · from_log
Each channel was pre-registered before measurement, frozen, and — where flagged — independently audited. Each closes on data with a named falsifying invariant that fired. Numbers are the three gain-set runs unless a band is given.
| # | Channel | How it was killed | Killing number (band vs required) | Invariant |
|---|---|---|---|---|
| 1 | Reference-rate consistency (anchor-rate deficit) | Three independent ways: architecture, magnitude, gain-trend | Deficit 0.0173 / 0.0152 / 0.0093 m/s, in band [0, 0.09] and shrinking, vs required 0.157 / 0.373 / 0.515; transmitted mismatch ⇒ < 0.2 mm (< 0.4% of the 51–84 mm lag) | decision row 1 |
| 2 | Static re-anchor family (shoulder / base-CoM anchor) | By direction; candidate dead on paper | Anchor shift is near-pure normal (Δ·n̂ ≈ −0.078..−0.088) versus the tangential lag; open-loop gap g_B 0.154–0.177 m vs band [0.01, 0.08], kill > 0.10 | FI-cd-1 |
| 3 | Modeled static forcings (Coriolis + CoM coupling) | By magnitude — a minority carrier | Along-track closure 0.081 / 0.090 / 0.239 (8–24%) vs band [0.5, 2.0]; the modeled floor is real (norm 0.039–0.058 m) but 81–93% off-tangent | FI-sf-2 |
| 4 | Tikhonov reconstruction attenuation | By magnitude — three orders short | Denied along-track velocity ~0.03–0.08 mm/s vs required 157 / 243 / 217 mm/s; closure 0.000495 / 0.000246 / 0.000143; despite carrier-band alignment 0.561 / 0.731 / 0.739 | FI-tk-2 |
| 5 | Post-integration velocity kill (the clip) | As carrier — base-compensated | Closure 0.0019 / 0.0002 / 0.0000 (< 0.2%); reduced along-track denial ≈ 0; cross-gate reproduces the fence lane to ≤ 3×10−4 m/s | FI-cl-2 |
| 6 | Joint-6 posture regulator | Orientation-only (direction + magnitude) | End-effector position authority 1.177×10−8 m/rad (7 orders below the null band); closure 0.0019 / 0.0008 / 0.0007 | FI-po-3 + FI-po-2 |
The complete modeled static balance — Coriolis, CoM coupling, and the joint-6 posture forcing that closes it, all the same linear map on one balance — sums to a combined along-track closure of 0.078 / 0.089 / 0.237 on the three runs. The static balance accounts for at most 24% of the fold lag on every run. The remainder, at least 76%, is non-static: the quasi-static geometry-versus-stiffness equilibrium itself.
The committed target was p_e below 0.10 m throughout the orbit, ideally at the floor, with the mid-mission humps near 200 s and 450 s removed. The architectural verdict means below 0.10 m throughout is unreachable at this trajectory geometry and gain envelope without an architecture change. Every dynamic lever inside the current architecture has been measured inert. The candidate rungs that remain are all design-gated reference-side geometry changes: each is a new design half, a fleet campaign, and a full five-baseline re-pin. This document does not choose.
Re-scope pre-risk to "operational p_e at the characterized floor" and proceed to the risk phases.
Achieved today: pe_p99 0.1412–0.1483 m, coverage 0.997–1.0, gates 3/3 on the guarded logs, floor fully characterized, every named channel excluded.
Cost: accepts ~0.14 m as the nominal architectural floor and reports it honestly as the operating point. The "ideally at the floor" clause is met; "below 0.10 m throughout" is retired as out of reach. Unblocks the main thesis.
Open a reference-side geometry redesign — posture-aware reference shaping at the fold phases, or a re-derived decoupled standoff anchor that survives a fresh open-loop overlay — aimed at removing the fold that drives the humps.
Cost: a design half, a user-gated fleet campaign, a five-baseline re-pin, and a mission-clock re-check, with uncertain payoff (the closest prior candidate failed its paper gate) and a delay to the risk phases.