# Risk adjustment and missing care

**Correct reference-risk adjustment removes the published pattern in this finite model. Wrong subgroup adjustment can restore it—even when the risk model is right on average.**

BI-01-RA1 · 23 October 2026 · exact sensitivity extension to the companion research note. No CMS data, patient experiment, trained agent, clinical validation, Lean proof or new general-theory claim.

At the article's λ=1 and K=1/5, compare identical review coverage, payments, effort costs and outcome probabilities:

| Benchmark | Completion, review unknown | Completion, review known |
|---|---:|---:|
| Original common benchmark | 100% | 75% |
| Correct expected success at reference high effort | 100% | 100% |
| Halfway from correct adjustment to original bias | 100% | 100% |
| 90% of the original bias | 100% | 75% |

All four rows use the same λ and K. The 80%-bias threshold is an exact tie, not a guaranteed 100% or 75% result. The saved outputs retain both pure policies; their mixtures yield intermediate expectations.

The additional **average-correct, subgroup-wrong** example uses a separately stated λ=2: true reference success is 95% and 60%, but estimated success is 80% and 75%. Both population averages are exactly 77.5%, and the easier group still ranks above the harder group. Nevertheless, revealing review changes completion from 100% to 75%, while the adjusted residual among completed cases rises from 0 to +5 percentage points. There is no change in any case's success probability. This is model arithmetic, not observed mortality or patient benefit.

## Inspect and reproduce

- [Written propositions, assumptions, counterexamples and full-vision scope](proof.md)
- [Exact evaluator](risk_adjustment.py)
- [All exact outputs and check counts](results/risk-adjustment.json)
- [Scenario metrics and tied policies](results/scenario-metrics.csv)
- [Closed-form boundary evaluations](results/nested-frontiers.csv)
- [Independent reproducible audit](independent_solver_audit.py) and [receipt](independent-audit-receipt.json)
- [Primary-source insurance-ratings context](../REFERENCES.md#quality-ratings-context)

Run with Python 3, standard library only:

```sh
python3 -B risk_adjustment.py --output /tmp/bi01-risk-adjustment-check
```

The evaluator performs 1,026 exact checks grouped by purpose: independent Bernoulli-event expectations, original-model reproduction, boundary feasibility, tie preservation, correct-adjustment controls, average-calibration counterexample and diagnostics. This includes repeated parameterized checks, not 1,026 independent research findings. Full families are justified by the written proof. A second fresh run and source/output hashes are recorded in `manifest.json`.

The oracle benchmark is defined before effort is chosen. Adjusting for the effort actually selected removes the effort incentive and is a different experiment. The multiplier is a utility parameter, not an operational PTI voting weight. In particular, no risk model was learned from records here.

## Implications and next study

PTI estimation, care payment, training reward, future assignment and relevant Codex voting need separately evaluated mappings. Patient authority and rights do not depend on PTI. Codex can evaluate the proposed measure or contract; this analysis adopts neither. Pool/Treasury must account for future liabilities beyond this current-period budget, and Trust-Time needs its own capacity model. Humans, agents and robots retain distinct capabilities and authority. THEON's foundation-model, longitudinal/multimodal, multi-agent and governed RSI program is preserved; no weight learning or improvement was tested.

Next: add later discovery and lawful exit/fallback care with legitimate clinical exceptions. Separately test estimated risk with omitted variables and selection in training/evaluation data, using equally informed conventional-contract controls. CMS data stays deferred until a defined empirical question and an identifiable denominator justify its use. Medicare Advantage Stars provide contextual motivation, not validation of this model or grounds for a mortality/intent accusation.

The original model and v2.8 whitepaper remain unchanged. This extension tests the risk benchmark; it does not change the original proof. The companion article integrates the new finding and distinguishes its exact-model evidence from historical ratings research.


The separate independent audit adds 1,726 parameterized consistency/provenance checks, including 432 comparisons against the original utilities and 1,152 comparisons between direct best-response feasibility and interval feasibility. Counts are not independent scientific findings or evidence of clinical validity. To reproduce that audit from this directory:

```sh
python3 -B independent_solver_audit.py \
  --original ../exact_solver.py \
  --risk-adjustment risk_adjustment.py \
  --output /tmp/bi01-independent-audit.json
```

## Source provenance

The evaluator, independent audit and all results are byte-identical copies of the reviewed BI-01-RA1 study. The proof differs only in its relative link to the original model. This README is adapted for the public bundle. [manifest.json](manifest.json) records both source and distributed hashes. No new software license is granted.