Oxygen return
with retained state

1. The question now has a testable form

Match present oxygen. Measure the retained state. Test the subsequent response.

The target paper proposes adaptation that persists after oxygen return. The tool represents that proposal with distinct oxygen, oxidant, scavenger and endpoint records. Its exact calculations establish what the submitted observations distinguish.

Target: Salvagno et al., IJMS 24(1), 82. Dataset: NOP_return_memory_synthetic_v0.1.

2. Retain both balance and magnitude

R and A are specified assay readings. Normalization preserves their separate baseline references. The positive pair (q, scale²) reconstructs both indices. If r=a=2, the ratio is one while scale² is four.

The explicit adapter C_redox = [[Φ, −1], [1, Φ]] carries these indices into the established operators H=G/√5 and S=(2Q−I)/√5:

Mirror exchange gives q → 1/q and η → −η. Magnitude remains a separate coordinate. Observations or a declared model supply the actual biological motion; the algebra supplies its reversible representation.

3. The exact adaptation result

For the proposed law τ da/dt = r−a, constant input during each interval gives the exact update below. Rational λ is chosen directly; a biological rate has yet to be estimated.

Starting at baseline, a pulse k>1 for d intervals leaves a persistent adaptation state during finite recovery. At return the prescribed oxidant input is one. The remaining state follows from the model's declared update.

The included example uses k=2, λ=½ and four intervals: a=31/16 and q=16/31 immediately after return. Input r is an assumed oxidant drive; its conversion from oxygen and its downstream HIF effect remain unassigned.

4. Exact observation ledger

Fractions preserve the entered data. Brackets show propagated interval bounds. A returned dry-gas read concerns that gas channel; tissue oxygen requires its own measurement. Green rows contain a returned read and a resolved difference in at least one redox index.

5. The next discriminating measurements

The preceding biological background enters here as a measurement interface: mitochondrial or cellular oxidant output, antioxidant adaptation, HIF regulation and gene-specific transcription. Each compartment and assay retains its identity. Repeated configurations and continuing events motivate the history record; biological rates are measured separately.

These are model-discrimination requirements derived for this tool. Exposure schedules and clinical decisions require the research team's experimental and clinical framework.

6. Evidence registry

Supporting and contrary results retain their populations, endpoints and limits. The included registry contains no imported individual measurements.

7. Run on a declared dataset

The package contains the CSV template, metadata example, exact audit, symbolic verifier, acceptance tests, source ledger, demonstration and receipts.

python nop_audit.py audit \
  --metadata examples/metadata.json \
  --data examples/synthetic.csv \
  --out results

python verify_all.py

python render_report.py \
  --audit results/audit.json \
  --algebra results/algebra_receipt.json \
  --out NOP_Research_Workbench_v0_2.html

The audit and report use Python's standard library. Symbolic checks use SymPy; optional static figures use Matplotlib. The README specifies the complete data contract and exact adapter.