# ⚛  L1 Principle — Neutrino Oscillation Parameter Extraction

**ID:** `L1-485` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Particle Physics — *Neutrino physics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** PMNS parameter vector
> **📡 Carrier:** particle · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555317

---

## 🧠 1. Introduction

**Neutrino Oscillation Parameter Extraction** is a **parameter-estimation problem** whose unknown lives in **PMNS parameter vector** space, within the **Neutrino physics** sub-domain of **Particle Physics**.

Measurements consist of particle interactions in a detector via a **neutrino disappearance appearance** sensing mechanism.

The forward operator applies, in order: an unspecified linear measurement operator; S · matter · msw effect operator; O · chi2 · event rates operator.

Observations are corrupted by Poisson counting noise. Existence of the recovered PMNS_parameter_vector 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 ~= 500); flux_normalization_uncertainty_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Poisson sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → Generic linear operator → S · matter · msw effect → O · chi2 · event rates → **y** (detector).

```
y = `O.chi2.event_rates` `S.matter.msw_effect` A x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.linear_op` | An unspecified linear measurement operator |
| `S.matter.msw_effect` | S · matter · msw effect operator |
| `O.chi2.event_rates` | O · chi2 · event rates operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Particle Physics |
| Sub domain | Neutrino physics |
| Carrier | particle |
| Problem class | parameter_estimation |
| Solution space | PMNS_parameter_vector |
| Noise model | poisson |
| Integration axis | neutrino_baseline |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Existence of the recovered PMNS_parameter_vector 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 ~= 500); flux_normalization_uncertainty_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | delta_CP_constraint_sigma_deg |
| Secondary | theta_23_octant_significance |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Pot 1e21 | — | 3 |
| Baseline km | km | 810 |
| N event bins | — | 100 |
| Flux uncertainty percent | — | 5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Pot 1e21 | — | 0.1 – 30.0 |
| Baseline km | km | 200 – 2000 |
| N event bins | — | 10 – 1000 |
| Flux uncertainty percent | — | 1.0 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 20 delta_CP_constraint_sigma_deg

| Metric | Range |
|---|---|
| Delta cp constraint sigma deg | 5 – 90 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **delta_CP_constraint_sigma_deg**, with κ = `10000.0` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x4e31736ad56c166b919769dd6080c356d7e344a2c958cc4b424151ce7e94efe4`
- **Chain tx hash:** `0x0066cb73cc2300fe093919607d36f1bd2857a008f5cb0c237134fe1daac3014c`
- **Chain block:** `41555317`

---

## File Mapping

This bundle consists of: `L1-485.md`, `L1-485.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-485.md` | Source of truth — edit this | Human or LLM |
| `L1-485.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 `L1-485`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._