evidence_map

Evidence Map — sims logs

The curated window into the sibling run logs via the sims_logs/ symlink
(Inspection_Simple_2/logs, local-only, always-current). It points at the few figures and traces
that matter, keyed by subsystem — so you don’t grep ~1k
files. Paths resolve in Obsidian through the symlink, not on GitHub. Verified 2026-06-23 by
opening the figures named below.

What’s logged (per dated run)

Each sims_logs/logs_<date>/ holds figures/*.png (run-collection smoke figures) plus, per scenario,
<scenario>/{run,stem}/npz/run_<id>/<scenario>.npz (the time-series that back the figures). Two
scenarios recur: full_control_single and full_control_imex (the implicit–explicit
integrator variant — see below).

Key exhibits

Subsystem	Exhibit	Path (via sims_logs/)	What it shows
com	CoM smoke test	logs_<date>/figures/com_smoke.png	3 panels: CoM force $f_c$, arm torque $\tau$, base rate ${\omega }_b$.
base,ee	${\omega }_b$ ripple (cured)	same figure, bottom panel	${\omega }_b$ now at machine-epsilon ($\sim 10^{-14}$) — the forward-Euler ripple is gone.
base,ee	per-run time series	logs_<date>/<scenario>/run/npz/run_<id>/<scenario>.npz	raw channels (home of the ${\dot{\tilde{\mathbf{x}}}}_c$ trace for the §4 test).
com+base+ee	near-singular spike A/B	logs_Jun21_26/checkin_jun21_26/figures/run_PM0314/overlay_{p_c,v_c,omega_b}.png + …s_min_G.png	the CoM-spike exhibit; varies the Tikhonov onset (analysed below).

Verified reading (2026-06-23)

I opened com_smoke.png from the earliest (logs_Jun04_26, horizon $t=\mathrm{0..100}$) and latest
(logs_Jun23_26, $t=\mathrm{0..10}$) runs. Both show:

• CoM force $f_c$ — a smooth peak ($\approx 4.2$) then monotone decay. No singularity spikes.
• Arm torque $\tau$ — clean settling oscillation; no spikes.
• Base rate ${\omega }_b$ — scale $10^{-14}$ / $10^{-15}$ rad/s, i.e. numerical noise: the base is
  effectively non-rotating and the forward-Euler period-2 ripple is absent.

This is consistent with the fix already shipped in the code: the sims controller integrates the base
velocity-damping term implicitly (backward-Euler), which “cured the ripple” —
breve_controller (sims wiki) (the IMPLICIT warning
callout). That is the implementation side of our theory page
discretization_stability_omega_b /
omega_b_forward_euler_instability.md — the
two workspaces describing the same ${\omega }_b$ artifact from the math and code sides.

Found — the COM spikes (run_PM0314, A/B over Tikhonov onset)

Located 2026-06-23 (user pointer)

sims_logs/logs_Jun21_26/checkin_jun21_26/figures/run_PM0314/ — a 9-variant A/B that varies the
Tikhonov onset. These overlays are the missing spike exhibit; read directly ($t=\mathrm{0..1100}$ s):

• overlay_p_c.png (CoM position error) — a sharp shared transient at $t\approx 700$ to
  $\approx 0.34$ m across all variants (incl. the two noise-free ones), plus a distinct earlier hump
  ($t\approx 400$–$680$) in the Low-Tikhonov variant.
• overlay_v_c.png (CoM velocity error, ${\dot{\tilde{\mathbf{x}}}}_c$) — the same $t\approx 700$
  spike, to $\approx 0.22$.
• overlay_diagnostics.conditioning.s_min_G.png (${\sigma }_G$) — the Low Tikhonov onset 0.020
  (REJECTED) variant dips to ${\sigma }_G\approx 0.005$ (near-singular); all others hold $\approx 0.03$.
• overlay_omega_b.png (${\omega }_b$) — here ${\omega }_b$ is a real $\sim 0.15$ rad/s signal (not
  the cured machine-ε ripple); the Low-Tikhonov variant bursts $0.08$–$0.23$ rad/s near singularity.

What this settles. Lower Tikhonov onset → the [base, ee] block rides closer to singularity
(${\sigma }_G\downarrow$) → CoM tracking visibly degrades ($p_c$, $v_c$ worst for that variant) → the
variant was rejected. So Tikhonov does move the CoM — but indirectly, via singularity
proximity and base↔CoM coupling, not by acting on the decoupled $3\times 3$ CoM loop. This
refines (does not overturn) subsystem_decomposition: the
mechanism sits on [base, ee]; the observable propagates to com through coupling. The
near-singular ${\omega }_b$ bursts here are a physical singularity effect — distinct from the (cured,
machine-ε) forward-Euler ripple.

Source-verified (via the new sims_gnc/ symlink). sims_gnc/breve_controller.py L484–494 is
exactly eq 6.3, $\mathbf{v}=({\mathbf{\Gamma }}^{\top }\mathbf{\Gamma }+\lambda \mathbf{I}{)}^{-1}{\mathbf{\Gamma }}^{\top }\mathbf{y}$
with $\lambda =\max ({\beta }^2,{\text{floor}}^2-{\sigma }_G^2)$ — so the onset is g_reg.floor (the
$0.020$ in the rejected variant), and the schedule keys off the same s_min_G the ${\sigma }_G$ overlay
plots. The implicit cure is L455–467 (A = M_breve + dt*D_breve, gated by base.implicit_damping).
Theory ↔ code ↔ log now closed. (The code names it gamma_regularization, never “Tikhonov” — the
join is structural; see damped_least_squares → Code provenance.)

Corroborated by the dedicated sims_logs/logs_Jun19_26/mission_tikhonov_020_jun19/ run: with onset
$0.020$ the condition number ${\kappa }_J$ spikes to $\sim 10^6$ (near-singular) at $t\approx 200$–$290$ and
$820$–$1080$, EE-error bursts track them, and CoM velocity error peaks at $\approx 0.21$ — yet area
coverage still completes ($\approx 0.99$). The setting rides the singular edge.

Still open. Whether the sharp $t\approx 700$ transient is itself a forward-Euler signature needs
the lag-1 autocorrelation test below on the run’s .npz ${\dot{\tilde{\mathbf{x}}}}_c$ channel.

The decisive test (from error_floor.md §4): the
$dt$-independent lag-1 autocorrelation of the logged ${\dot{\tilde{\mathbf{x}}}}_c$ — $\approx -1$ at
$dt=0.03$ flipping to $\approx +1$ at $dt=0.01$ ⇒ the CoM spikes are the same forward-Euler artifact.
The data lives in the per-run .npz above; the channel↔name mapping is in the sims wiki
(plotter / data-classes pages). Tracked as a human task in
ONGOING.md.

How to add an exhibit

Cite a figure as sims_logs/<run>/figures/<f>.png, tag the subsystem it evidences, and one line on
what it shows. Keep this to load-bearing exhibits — this is a map, not a gallery.