# Product Specification: Geometry-Reduced Optical Link Design-Space Dominance Map
## NASA/JPL-Style Requirements Package for Funding a Public Engineering Audit Workbench

> **Source document.** This is the original NASA/JPL-style specification package the lab used to build the **Design-Space Dominance Map** at `/gut/nasa/design-space-dominance-map/`. It is reproduced here verbatim so a reviewer can see the requirements the implementation was traced to. The tool itself is a public engineering-surrogate, not mission-certified software.

**Version:** 1.0
**Target buyer / evaluator:** NASA/JPL-style optical communications, mission design, navigation, timing, systems engineering, and mission-assurance teams
**Target deployment:** `https://physics.magflowmeters.com/gut/nasa/design-space-dominance-map/`
**Product class:** Public engineering-surrogate decision-support tool, not mission-certified flight software
**Primary funding fit:** SBIR/STTR Phase I → Phase II → mission-integration pilot
**Core value proposition:** Reduce expensive high-fidelity simulation runs by identifying the active constraints, dominant failure modes, and high-value simulation regions before full wave-optics / atmosphere / detector / coding Monte Carlo is run.

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## 0. Executive Summary

The expensive traditional problem is not a single optical-link calculation. A single link budget is cheap. The expensive problem is exploring a large design space:

$$\text{range} \times \lambda \times D_t \times D_r \times P_t \times R_b \times \sigma_{\rm pointing} \times T_{\rm atm} \times r_0 \times \eta_{\rm det} \times B_{\rm sky} \times G_{\rm coding}$$

with atmosphere, pointing, turbulence, detector noise, background, coding, and operational constraints.

The proposed tool compresses that search into a dominance map:

> Scenario → active constraint surfaces → dominant limiter → closure probability → recommended high-fidelity runs

The tool gives engineers a public, auditable, reduced-order triage layer that helps answer:

1. Which physical effect dominates in this region of design space?
2. Which variables matter most?
3. Which terms are safely below tolerance?
4. Where should high-fidelity compute be spent?
5. What is the approximate probability the optical link closes under declared uncertainty assumptions?

> Final positioning: NASA/JPL can run the full simulations. This tool helps decide which full simulations are worth running.

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## 2. Scope and Claim Boundary

### 2.1 What this tool claims

Given declared public-surrogate assumptions, the Design-Space Dominance Map estimates which optical-link constraint dominates, whether the link is likely to close, which terms are below tolerance, and which scenarios deserve high-fidelity simulation.

### 2.2 What this tool does not claim

- to be NASA/JPL software;
- to reproduce DSOC internal models;
- to replace SPICE/Horizons/OD pipelines;
- to replace mission-certified optical link budgets;
- to model proprietary detector/coding/pointing systems;
- to provide flight-qualified decisions;
- to eliminate final high-fidelity simulation;
- to validate new physics.

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## 5. Role of the 13D / Constraint-Geometry Method

### 5.1 Correct positioning

The 13D math is not "magic" or "new physics required for optical links." It is a **constraint-compression method**:

> high-dimensional design space → active constraint surfaces → low-dimensional dominance regions

### 5.3 Required mathematical objects

**Design vector**:
$$x = (R, \lambda, D_t, D_r, P_t, R_b, \sigma_p, T_{\rm atm}, r_0, \eta_{\rm det}, B_{\rm sky}, G_c, \ldots)$$

**Reduced invariant vector**:
$$z = (\rho_{\rm range}, \rho_{\rm diffraction}, \rho_{\rm pointing}, \rho_{\rm atmosphere}, \rho_{\rm detector}, \rho_{\rm background}, \rho_{\rm coding})$$

**Constraint functions**: $g_i(x) \geq 0$ where $g_i$ represents closure margin under a physical limiter.

**Dominant limiter**: $i^*(x) = \arg\min_i g_i(x)$

**Closure probability**: $P_{\rm close}(x) = P(\min_i g_i(X) > 0)$ under declared uncertainty distribution $X \sim \mathcal{D}(x, \Sigma)$.

**Compute-saving objective**:
$$\eta_{\rm save} = 1 - \frac{N_{\rm high\ fidelity, recommended}}{N_{\rm full\ grid}}$$
subject to classification error ≤ $\epsilon_{\rm class}$ and false-safe rate ≤ $\epsilon_{\rm safe}$.

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## 6. Functional Requirements (Summary)

| ID | Requirement |
|---|---|
| FR-1 | Design-space definition (≥ 6 simultaneous variable ranges, grid or Monte Carlo) |
| FR-2 | Reduced-order optical link model (diffraction, photon rate, photons/bit, pointing, atmosphere, background, coding, closure) |
| FR-3 | Dominant-limiter classification (10 classes) |
| FR-4 | Closure probability under uncertainty |
| FR-5 | Design-space map visualization (heatmaps, contour, tornado, recommendation table) |
| FR-6 | High-fidelity simulation prioritization (priority rules + recommendation list) |
| FR-7 | Certificate and review packet export |

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## 8. Verification and Validation Plan

### 8.5 High-fidelity benchmark requirement

To justify funding, include at least one high-fidelity benchmark dataset.

### Required benchmark metrics

| Metric | Phase I | Phase II |
|---|---:|---:|
| Dominant-limiter accuracy | ≥ 80% | ≥ 90% |
| False-safe rate | ≤ 5% | ≤ 1% |
| Margin median error | ≤ 3 dB | ≤ 1 dB in validated domain |
| Compute reduction | ≥ 10× | ≥ 100× in validated domain |
| Boundary-case recall | ≥ 90% | ≥ 98% |

Definitions:
- **false-safe**: reduced model predicts safe/closed, high-fidelity validation fails.
- **boundary-case recall**: fraction of high-fidelity-important boundary cases selected for simulation.

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## 9. NASA-Style TRL Plan

### TRL 2–3: Concept / proof of feasibility

- Mathematical dominance formulation, prototype reduced-order model, analytic validation, small public scenario library, initial benchmark against synthetic high-fidelity cases.

### TRL 4: Component validation in lab/software environment

- Robust browser/server prototype, registries, certificates, validation CI, public scenario anchors, first high-fidelity comparison dataset.
- Exit: dominant-limiter accuracy ≥ 80%, false-safe rate ≤ 5%.

### TRL 5: Relevant environment validation

- Horizons/SPICE integration, realistic geometry cases, design-space maps, user-driven scenario builder, benchmark against literature or partner data.
- Exit: ≥ 90% limiter accuracy, ≥ 10× compute reduction, boundary-case recall ≥ 90%.

### TRL 6: Prototype demonstration in relevant engineering workflow

- Hardened review-packet workflow, exported high-fidelity recommendations, team evaluation on real mission-like scenarios.

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## 10. Funding / Procurement Package

### 10.1 Phase I-style scope (~$150k, 6 months)

Deliverables: dominance-map mathematical spec, reduced-order MVP, analytic validation suite, public scenario anchors, certificate/review packet prototype, initial benchmark dataset, final feasibility report.

### 10.2 Phase II-style scope (~$850k, 18–24 months)

Deliverables: robust full web workbench, Horizons/SPICE integration, uncertainty propagation, multi-body corrections, high-fidelity benchmark suite, validation CI, PDF certificates, reproducibility bundle, partner review.

### 10.3 Mission-integration pilot ($1M–$3M+)

Deliverables: mission-specific scenario adapter, private benchmark integration, internal data import/export, covariance/uncertainty interface, advanced high-fidelity model calibration, team training, security/access controls.

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## 17. Final Editorial Rule

The tool should not say:

> "We replace NASA simulations."

It should say:

> "We identify where expensive simulations matter."

The funding case succeeds only if the tool demonstrates:

> less compute + same decision quality + clear failure boundaries.

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*Original spec preserved verbatim. See `USER_GUIDE.md` in this directory (when present) for a walk-through of how to use the deployed tool, and the Research Geometry Mapping tab on the live page for the optional $\times,\oplus,\otimes$ architectural framing.*