Choose the token-guess operating point by measuring the instrument

[Al-does]

Stacked on #12. That PR showed the shipped MESS3 parameters leave almost no room on either reported axis. This one picks parameters deliberately and validates them on GPU.

How the point was chosen

process_design.py scores a candidate process before anything is trained: how far Bayes sits above the best short-window policy, and how much belief variance lies between what a short window already explains and what the task's own sufficient statistic can explain.

That upper end turned out to matter as much as the floors. A policy objective can only reward what the one-step predictive distribution distinguishes, so a two-token alphabet caps the probe at 0.60 no matter how far its floors drop — it looked like the best family until the ceiling was measured. Alphabet size is a ceiling, and three states need three tokens.

Three floors bind and they do not move together:

• a short token window falls as the channel gets noisier
• the Bayes argmax cell rises as the chain gets stickier
• a randomly initialised transformer, measured rather than derived, sits near 0.82–0.88 throughout and rises as alpha falls, because a smoother belief is easier for a random causal filter to track

stay = 0.96 is where the first two cross; alpha = 0.55 is where the third crosses them. At stay=0.96 the binding floor runs 0.859, 0.831, 0.852, 0.882 for alpha = 0.60, 0.55, 0.50, 0.45.

	shipped	proposed
stay, alpha	0.90, 0.85	0.96, 0.55
echo-to-Bayes range	0.0167	0.0568
floor, last token	0.805	0.235
floor, last two tokens	0.930	0.405
floor, 8-token window	0.964	0.802
floor, argmax cell	0.882	0.824
floor, untrained network	0.883	0.832
usable band	0.036	0.168

GPU validation

Matched PPO and IQN arms, 2.5M steps, three seeds, identical recipe, architecture, budget, seeds, and probe. Only the process differs. One rented RTX 4090, ~1.3 h, destroyed on completion.

Both operating points on all three axes

point	arm	belief R²	clears floor	share of accuracy range
shipped	ppo	0.8461 ± 0.0065	no	−0% ± 0%
shipped	iqn	0.9756 ± 0.0032	yes	47% ± 2%
proposed	ppo	0.8281 ± 0.0548	no	52% ± 22%
proposed	iqn	0.9646 ± 0.0056	yes	91% ± 1%

The biggest change is that the task becomes learnable. At the shipped point plain PPO sat at the echo policy on all three seeds to within 0.2% of the range, so its low belief R² was measuring an agent that never did the task. Gradient signal-to-noise for the beyond-echo improvement rises from 0.034 to 0.114.

The IQN-minus-PPO gap also comes back on-scale: 3.6× the usable band at the shipped point (an overflow, not an effect) versus 0.81 of it at the proposed point.

Reward-only PPO fails to clear the untrained-network floor at both points, which means that finding was not an artifact of a badly chosen process.

Costs, stated plainly

PPO's seed spread grows a lot (±0.0065 to ±0.0548) because it now sometimes learns and sometimes does not. That is the γ=0.99 variance problem from #12 rather than a property of the process, and it argues for γ=0 or more seeds at this point.

The mixed-state distribution also stops being the sparse Cantor-like fractal that makes the α=0.85 picture recognisable. That is why the token-window floors collapse, but it does change the figure:

Belief geometry at both operating points

Also here

within_branch_r2 at depth two is the most discriminating readout and is what future cycles should lead with: at the proposed point it separates untrained 0.72, PPO 0.71 ± 0.09, IQN 0.94 ± 0.01, where global R² compresses them.

Two library changes are in Al-does/RL-Harness on cursor/mess3-symmetric-model-0668: symmetric_model exposes chain memory alongside channel fidelity, and detect_profile no longer returns a profile that asks for 1.8 GPUs on a one-GPU box. That second one cost 20 minutes of rental before I caught it — Ray leaves the trial PENDING forever instead of failing, so it now raises up front.

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