47-PTN Template v1.0 | Chapter 10 — Results Presentation & Comparative Scoring

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Chapter 10 — Results Presentation & Comparative Scoring

I. Metrics Definition

1. Primary metrics
   • Arrival-time residual: ΔT_arr = T_arr(obs) − T_arr(ref) (unit s); report mean(ΔT_arr), std(ΔT_arr), and interval x̂ ± U (coverage factor k).
   • Phase consistency: r_phi = corr( Phi_ref , Phi_obs ); interval via Fisher-z and back-transform; report r_phi and p.
   • Paraxial conservation error: ε_flux (dimensionless; → 0 at O(θ^2)).
   • Dimensional-closure rate: p_dim ∈ [0,1] (pass fraction).
   • Robust residual metric: Q_res ∈ [0,1] (lower is better; robust quantile gap or Huber surrogate).
2. Secondary metrics
   • Mass-conservation deviation: ΔM = |∫ ρ dV|_{t2} − |∫ ρ dV|_{t1} (unit follows ρ).
   • Coherence-window adequacy: κ_coh = f(T_coh, L_coh, B_coh ; |∇ n_eff|, SNR, σ_y) (dimensionless).
3. Normalization & score mapping
   • Z-normalization: z_m = ( m − m_baseline ) / σ_baseline.
   • Sigmoid score: q_m = 1 / ( 1 + exp( a z_m + b ) ) (default a=1, b=0; invert sign if “larger is better”).
   • Aggregate score: Q = ( ∑_i w_i q_{m_i} ) / ( ∑_i w_i ), weights w fixed in the evaluation sheet.
4. Explicit path/measure
   Unified arrival-time display:
   T_arr = ( ∫ ( n_eff / c_ref ) d ell ) = ( 1 / c_ref ) * ( ∫ n_eff d ell ); show gamma(ell) and d ell in text; record delta_form in exports.
5. Units & dimensions
   Wrap any division/integral/composite operator in parentheses; all variables/symbols in backticks; attach check_dim report for closure.

II. Benchmarks & Comparators

1. Benchmark definition
   • Baseline model: baseline_id, baseline.version, train/calibration dates, fixed seeds and config.
   • Data splits: train/val/test or k-fold; stratify by device/region/batch to keep balance.
2. Comparator setup
   • Paired design: per record_id, compare method_A vs baseline with paired difference Δm = m_A − m_base.
   • Statistical tests: two-sided paired tests or permutation for core metrics; multiple testing via Benjamini–Hochberg with FDR ≤ 0.1.
3. Power & sample size
   Target power 1−β = 0.9, α_core = 0.01; follow Chapter 4’s preregistered plan.
4. Scorecard fields (publishable)
   method_id, dataset_id, metrics{ΔT_arr,r_phi,ε_flux,p_dim,Q_res,...}, score.Q, seeds, references[], version.
5. Decision thresholds (aligned with Chapter 4)
   • Positive: all core gates pass (e.g., improvement on |ΔT_arr| in the correct direction, r_phi ≥ 0.6, p_dim = 1.0); aggregate Q exceeds baseline by +δQ_min.
   • Negative: any core metric fails or citations/dimensions are non-compliant.

III. Visualization Standards

1. Dashboard
   Cards: ΔT_arr distribution (hist/KDE), r_phi bar with CIs, ε_flux boxplot, Q_res trend, p_dim gauge.
2. Residual & agreement plots
   • Residual-vs-fitted; Bland–Altman with mean bias and 95% limits.
   • Phase scatter: Phi_obs vs Phi_ref with y=x reference and interval bands.
3. Path & geometry
   • Path profile: n_eff(ell) vs ell; legend states gamma(ell) step Δell and delta_form.
   • Paraxial conservation: cross-section flux heatmap with ε_flux contours.
4. Error bars & intervals
   Means/medians must include ±U or quantile bands; state k or confidence level.
5. Figure format
   Axes with explicit units (s, rad, 1); annotate versions and data time windows; color/linestyle legend fixed to method IDs.
6. Export
   Provide both vector (PDF/SVG) and bitmap (PNG) versions; captions include see[] and version.

IV. Conclusions & Reporting

1. Conclusion structure
   • One-line takeaway: direction and magnitude vs baseline; then core-metric summary with uncertainty.
   • Evidence levels: statistical significance, engineering significance, and reproducibility; include FDR-adjusted statements.
2. Limits & boundaries
   State applicability (coherence window, paraxial, small-angle, slowly varying medium); mark “restricted mode” outside domain.
3. Publication package
   Include scorecard.json, results.md, audit.jsonl, check_dim_report.json, and figure bundle.
4. Citations & compliance
   Use the canonical “volume + version + anchor (P/S/M/I)”; keep text and exports consistent; path expressions show gamma(ell), d ell, and record delta_form.

V. Weights & Thresholds (example, drop-in)

Aggregate: Q = (0.35 q_ΔT + 0.25 q_r + 0.15 q_flux + 0.15 q_dim + 0.10 q_res).

VI. Machine-Readable Templates (ready to commit)

A. scorecard.json

{

"version": "1.0.0",

"dataset_id": "ptn-demo",

"baseline": { "id": "base-001", "version": "1.2.3" },

"method": { "id": "mA-010", "version": "2.0.0" },

"metrics": {

"DeltaT_arr_s": { "mean": -2.3e-9, "std": 4.8e-9, "U_k2": 1.5e-9 },

"r_phi": { "value": 0.72, "ci95": [0.61, 0.80] },

"epsilon_flux": { "median": 0.004, "p95": 0.011 },

"p_dim": 1.0,

"Q_res": 0.13

},

"score": { "Q": 0.78 },

"tests": {

"paired": { "DeltaT_arr": { "p_perm": 0.004, "B": 10000 } },

"FDR": 0.08

},

"see": [

"EFT.WP.Core.Equations v1.1:S20-1",

"EFT.WP.Core.Metrology v1.0:check_dim",

"Data.Benchmarks v1.0:PROTO"

],

"version_lock": true

}

B. results.md (outline)

# PTN Results — v1.0.0

## 1. Summary

- One-liner conclusion; core metrics with uncertainty.

## 2. Core Metrics

- Delta T_arr (s): mean±U, histogram, BA plot.

- r_phi: value + 95% CI; scatter vs identity.

- epsilon_flux: distribution; paraxial guard lines.

## 3. Secondary Metrics

- ΔM, κ_coh …

## 4. Visual Gallery

- Figures (PDF/PNG), legends, units.

## 5. Repro & Audit

- Seeds, configs, manifests; audit.jsonl hash.

C. bench_score.yaml (interface contract)

version: "1.0.0"

call: "I90-bench_score"

inputs:

results: "PTN_EXPORT/results.parquet"

baseline: "PTN_EXPORT/baseline.parquet"

metrics: ["DeltaT_arr_s","r_phi","epsilon_flux","p_dim","Q_res"]

weights: { DeltaT_arr_s: 0.35, r_phi: 0.25, epsilon_flux: 0.15, p_dim: 0.15, Q_res: 0.10 }

thresholds:

tau_T_s: "3*u(T_arr)"

r_phi_min: 0.6

flux_ok: "≈0@O(theta^2)"

p_dim: 1.0

mapping:

type: "sigmoid"

a: 1.0

b: 0.0

exports:

files: ["scorecard.json","results.md","figs/*.pdf","reports/check_dim_report.json"]

VII. Required Items on Results Page (aligned with Chapter 5)

• Data & methods: dataset_id, method/baseline IDs and versions, random seeds.
• Metrics & intervals: ΔT_arr, r_phi, ε_flux, p_dim, Q_res with units and uncertainties.
• Figure list: filenames, sizes, formats (PDF/PNG).
• Audit & compliance: audit.jsonl, check_dim_report.json, see[], references[], version.
• Decision & gates: positive/negative call, FDR, δQ_min, applicability and limitations.