# ⚛  L1 Principle — Cosmic Ray Propagation Inversion

**ID:** `L1-376` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Cosmic rays*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** CR spectral source distribution
> **📡 Carrier:** particle · **🌫 Noise:** observation gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555178

---

## 🧠 1. Introduction

**Cosmic Ray Propagation Inversion** is a **parameter-estimation problem** whose unknown lives in **CR spectral source distribution** space, within the **Cosmic rays** sub-domain of **Astrophysics**.

Measurements consist of particle interactions in a detector via a **diffusion loss transport** sensing mechanism.

The forward operator applies, in order: S · diffusion · galactic operator; operator inherits structure from a graph (mesh, network); O · chi2 · cr ratios operator.

Observations are corrupted by observation gaussian. Existence of the recovered CR_spectral_source_distribution is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); solar_modulation_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · diffusion · galactic → Structured graph operator → O · chi2 · cr ratios → **y** (detector).

```
y = `O.chi2.cr_ratios` G `S.diffusion.galactic` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.diffusion.galactic` | S · diffusion · galactic operator |
| `G.structured` | Operator inherits structure from a graph (mesh, network) |
| `O.chi2.cr_ratios` | O · chi2 · cr ratios operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Cosmic rays |
| Carrier | particle |
| Problem class | parameter_estimation |
| Solution space | CR_spectral_source_distribution |
| Noise model | observation_gaussian |
| Integration axis | galactic_volume |
| Difficulty delta | 3 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Existence of the recovered CR_spectral_source_distribution is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); solar_modulation_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | B_over_C_chi2 |
| Secondary | positron_fraction_chi2 |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `diffusion_loss_transport`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| D 0 cm2 s | s | 30000000000000000000000000000 |
| Z halo kpc | — | 4 |
| Solar phi gv | — | 0.5 |
| Delta diffusion | — | 0.35 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| D 0 cm2 s | s | 10000000000000000000000000000 – 100000000000000000000000000000 |
| Z halo kpc | — | 2.0 – 8.0 |
| Solar phi gv | — | 0.3 – 1.5 |
| Delta diffusion | — | 0.2 – 0.6 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.3 B_over_C_chi2

| Metric | Range |
|---|---|
| B over c chi2 | 0.8 – 3.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **B_over_C_chi2**, with κ = `1000` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x58d9b143d8d8ae3812b97c7640829efa78025eade0df37cbe9857437fa8c026c`
- **Chain tx hash:** `0xf6dc5c68c3e2e1c4e463c6d2434cd78b52f5036f66f2c9601423f5280ed3827d`
- **Chain block:** `41555178`

---

## File Mapping

This bundle consists of: `L1-376.md`, `L1-376.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-376.md` | Source of truth — edit this | Human or LLM |
| `L1-376.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-376`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._