# Observer, state, and backreaction defense

Separate state choice, detector response, and geometric consistency before interpreting particles in curved spacetime.

## Learner edition

## 1. Reconstruct the observer-dependent particle model

**Task type:** derivation

Starting from two complete mode bases related by a Bogoliubov transformation, derive the normalization constraint and the expected occupation number seen by the second basis. Then connect the field result to a finite-time detector response without treating either quantity as observer independent.

### Deliverables

- A line-by-line derivation with conventions and inner product stated
- A table separating mode occupation, detector response, and stress-energy
- Two limiting-case checks

### Scoring criteria

- Correct transformation and normalization: 8 points
- Explicit assumptions and observer labels: 6 points
- Detector comparison and limiting checks: 6 points

## 2. Map the hierarchy before trusting the approximation

**Task type:** analysis

Construct a dimensionless hierarchy using curvature radius, detector gap, switching time, and renormalized stress scale. Evaluate at least six parameter points and identify where adiabatic reasoning, detector resolution, or negligible backreaction fails first.

### Deliverables

- A reproducible parameter table or dataset export
- Three dimensionless diagnostics with units canceled explicitly
- A boundary plot and a 250-word interpretation

### Scoring criteria

- Dimensionally valid diagnostics: 7 points
- Reproducible sweep and uncertainty treatment: 7 points
- Cautious boundary interpretation: 6 points

## 3. Discriminate state preparation from detector artifact

**Task type:** design

Design a blinded comparison that could distinguish two state prescriptions while controlling switching transients, finite sampling, and detector calibration. Include a conventional explanation capable of producing the same apparent response.

### Deliverables

- A preregistered primary contrast and null model
- Calibration, sham, and state-label blinding plan
- Stop rules and a replication package manifest

### Scoring criteria

- Identifiable primary contrast: 7 points
- Controls address leading artifacts: 7 points
- Decision and release rules are prespecified: 6 points

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Evidence rule: distinguish calculation, model-dependent inference, experimental observation, and unresolved claim in every response.