# Finite verifier information and pool-headroom examples

These exact authored calculations illustrate standard finite decision theory. They are not empirical verifier results, a novel method, a learned controller, or an amendment to a frozen scientific study. No real model, dataset, serving configuration, or cost frontier is reproduced.

`matched-laws/` assumes exactly two already available candidates, exactly one correct with equiprobable correct index. Its 54 cells compare known class-conditional error couplings, discrete budgets and utility prices. `pool-headroom/` uses a general prior over all four two-candidate truth states (00,01,10,11), including no correct candidate and both correct. Its 108 cells distinguish observable selection value from the unavailable hidden-truth headroom ceiling. Across changed truth priors, unconditional judge marginals need not match. Within a fixed prior the compared couplings preserve each single judge's law.

Both assume known laws and conditional independence of errors across candidates given truth. Candidate generation and public execution costs are omitted. Query costs 0/2/4 are abstract units, not dollars, tokens or latency. Net utility is selected-success probability minus an explicitly authored nonnegative conversion price times abstract cost (prices 0,1/50,1/4). Positive prices are utility conversions, not inferred real billing. Optional choices are ex ante among fixed affordable arms, not adaptive sampling or full real-budget portfolio frontiers. Coverage-matched and same-charge information-retention controls are distinguished from economical cheaper single-judge arms. Natural consensus risk at reduced coverage does not establish equal-coverage superiority.

## Standalone computation (Python standard library)

From this directory:

```sh
(cd matched-laws && python3 -I -B regimes.py > reproduced-map.json)
(cd matched-laws && python3 -B -m unittest test_regimes)
(cd matched-laws && python3 -O -B -m unittest test_regimes)
(cd pool-headroom && python3 -I -B headroom.py > reproduced-map.json)
(cd pool-headroom && python3 -B -m unittest test_headroom)
(cd pool-headroom && python3 -O -B -m unittest test_headroom)
```

Compare parsed JSON to each retained `regime-map.json`; whitespace differences are immaterial. Derivations state exact assumptions and oracle limitations. Undefined zero-coverage risk remains null. Unaffordable arm metrics remain null; descriptive fixed-rule metrics in the headroom map must not be cited as affordable when their acquisition exceeds the displayed budget.

## Optional plotting

The supplied SVG/PNG figures are standalone. With Matplotlib already installed (no automatic downloads), run `cd figures && python3 -B build.py`, then `python3 -B -m unittest test_plot_data`. Exact rational plot data and captions are retained. Figure 2 contrasts cost-4 joint and cost-2 single information before cost penalty; it is not an equal-total-cost net advantage. Categorical dependence laws are not a single correlation axis. Rendering bytes may vary across plotting/font versions.

`publicmanifest.json` commits all distributed members and retains meaningful upstream source hashes without private paths, operational identities or logs. Computational sources/tests/maps and figure artifacts are unchanged from their reviewed versions; the derivation prose only removes private workflow references. This draft requires publication review; it conveys no installed-serving parity, H1 collection evidence, calibration guarantee, empirical power or novelty claim.