# Nested Observer Tower Governance MVP — v2

## Purpose
Benchmark a multi-layer observer system with three observer towers and compare two epistemic regimes:

1. Global-first:
   global prior and tower-top summaries dominate initial interpretation.

2. Frontier-first:
   first-hand frontier evidence is primary; higher layers may interpret, summarize, and propose hypotheses, but cannot downgrade frontier evidence without an independently supported fault certificate.

## Hidden world
A 4D state generated by a 2D isotropic harmonic oscillator.

Each tower contains:
- frontier physical observation;
- middle interpretation transform;
- top summary.

All layers preserve provenance.

## Injected scenarios
- clean
- frontier sensor anomaly
- middle interpretation drift
- wrong global model/prior
- genuine physical anomaly

Noise sigma:
0.005, 0.015, 0.03.

Total v2 trials:
3300.

---

## v1: naive Frontier-first failed

The first Frontier-first implementation classified only:

**59.42%**

correctly.

Global-first classified:

**76.97%**

correctly.

However, Frontier-first already had much smaller raw state-estimation error:

- Frontier-first RMSE: 0.0256
- Global-first RMSE: 0.0697

The v1 failure was traced to the fault certificate.

The naive sensor diagnostic removed one tower and tried to predict it using only the other two towers at each instant.
Some two-tower coalitions have instantaneous rank 3 rather than 4.
Thus the diagnostic itself was partially blind but still attempted to certify a frontier sensor as faulty.

This violated the Frontier Observer Priority Principle:
a higher layer must not downgrade frontier evidence using a certificate that is itself informationally incomplete.

---

## v2: dynamics-aware fault certificate

The corrected certificate uses temporal history and the known nominal dynamics.

For a candidate excluded tower i:

1. fit a single physically consistent trajectory using the other towers across time;
2. require the retained towers to admit a low-residual physical trajectory;
3. predict the excluded tower from that reconstructed trajectory;
4. certify a frontier sensor fault only if:
   - retained observers are mutually and dynamically coherent;
   - the excluded observer remains strongly inconsistent.

Symbolically:

Other frontier towers + history
-> physically coherent trajectory
-> predict excluded frontier
-> only then FaultCert(O_i).

This is substantially stronger than instantaneous leave-one-out comparison.

---

## Results

Frontier-first v2 classification accuracy:

**94.545%**

Global-first classification accuracy:

**76.970%**

Frontier-first v2 localized-fault culprit accuracy:

**87.727%**

Global-first localized-fault culprit accuracy:

**64.470%**

Final state RMSE:

- Frontier-first v2: **0.0147323**
- Global-first: **0.0697424**

Relative RMSE ratio:

**0.211**

So Frontier-first v2 uses about 21.1% of the Global-first state RMSE in this benchmark.

---

## Per-scenario aggregate

|   sigma | scenario             |   frontier_v2_accuracy |   global_accuracy |   frontier_v2_culprit |   global_culprit |   frontier_v2_rmse |   global_rmse |
|--------:|:---------------------|-----------------------:|------------------:|----------------------:|-----------------:|-------------------:|--------------:|
|   0.005 | clean                |               1        |          0.231818 |              1        |         1        |         0.00430337 |     0.0184229 |
|   0.005 | global_model_error   |               0.977273 |          0.936364 |              1        |         1        |         0.00424225 |     0.176896  |
|   0.005 | interpretation_drift |               1        |          0.813636 |              1        |         0.813636 |         0.00423668 |     0.0295978 |
|   0.005 | physical_anomaly     |               1        |          0.927273 |              1        |         1        |         0.00430709 |     0.0875991 |
|   0.005 | sensor_anomaly       |               0.981818 |          0.813636 |              0.981818 |         0.813636 |         0.00235513 |     0.0325405 |
|   0.015 | clean                |               1        |          0.995455 |              1        |         1        |         0.0130167  |     0.0192885 |
|   0.015 | global_model_error   |               0.972727 |          0.918182 |              1        |         1        |         0.0130024  |     0.174685  |
|   0.015 | interpretation_drift |               1        |          0.681818 |              1        |         0.7      |         0.0126937  |     0.0299391 |
|   0.015 | physical_anomaly     |               1        |          0.940909 |              1        |         1        |         0.0128008  |     0.0861936 |
|   0.015 | sensor_anomaly       |               0.859091 |          0.8      |              0.831818 |         0.8      |         0.0119698  |     0.032535  |
|   0.03  | clean                |               1        |          1        |              1        |         1        |         0.0257158  |     0.0213319 |
|   0.03  | global_model_error   |               0.981818 |          0.9      |              1        |         1        |         0.0260096  |     0.183895  |
|   0.03  | interpretation_drift |               1        |          0.359091 |              1        |         0.363636 |         0.0260193  |     0.0321612 |
|   0.03  | physical_anomaly     |               0.931818 |          0.85     |              1        |         1        |         0.0256275  |     0.088035  |
|   0.03  | sensor_anomaly       |               0.477273 |          0.377273 |              0.45     |         0.377273 |         0.0346846  |     0.0330155 |

---

## What the benchmark actually supports

It does NOT support:

"Frontier observers are always correct."

It supports a conditional principle:

### Frontier Observer Priority Principle

First-hand physical evidence should constrain higher-level models unless an independent fault certificate demonstrates that the frontier channel itself is unreliable.

### Fault-Certificate Adequacy Principle

A higher layer may downgrade frontier evidence only if the evidence used to certify the fault is at least sufficiently observable to distinguish:
- a local frontier fault,
- a shared global-model error,
- and a genuine physical anomaly.

In this MVP, temporal dynamics supplied the missing observability.

---

## Observer tower ordering

Evidence flows upward:

Physical world
-> Frontier AI
-> Interpretation AI
-> Tower synthesis
-> Global AI.

Hypotheses and experiment requests flow downward:

Global AI
-> tower
-> frontier measurement policy
-> physical interaction.

Therefore the hierarchy is not a hierarchy of truth authority.

It is a division of epistemic roles:

- Frontier: measurement authority
- Middle: interpretation authority
- Global: synthesis and experiment-design authority

Global synthesis cannot retroactively rewrite first-hand evidence merely because it conflicts with the current global model.

---

## Nested Observer Drift

For tower k, define a provenance drift measure:

D_k = distance(back-project(top_k), frontier_k).

A nonzero D_k localizes disagreement introduced above the frontier layer.

This separates:
- sensor anomaly: already present in frontier evidence;
- interpretation drift: frontier evidence is coherent, but upper representation diverges;
- global-model error: multiple frontier towers agree with each other but disagree with the prior;
- physical anomaly: multiple frontier towers agree and show a time-localized break from nominal dynamics.

---

## Main conclusion

The benchmark supports the architecture:

Frontier evidence
-> cross-frontier consistency
-> dynamics-aware fault certification
-> provisional global model
-> global synthesis.

Rather than:

Global prior
-> decide which local observation must be wrong.

The important result is not merely that Frontier-first v2 scored higher.
It is that the naive Frontier-first version failed until the fault-certificate layer respected observability.

Thus "frontier priority" is not a weighting preference.
It is a constraint plus a burden of proof for overriding first-hand evidence.
