# ⚛  L1 Principle — Jet Reconstruction (Anti-kT)

**ID:** `L1-487` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Particle Physics — *QCD jets*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** jet 4vector list
> **📡 Carrier:** particle · **🌫 Noise:** pileup detector gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555317

---

## 🧠 1. Introduction

**Jet Reconstruction (Anti-kT)** is a **parameter-estimation problem** whose unknown lives in **jet 4vector list** space, within the **QCD jets** sub-domain of **Particle Physics**.

Measurements consist of particle interactions in a detector via a **sequential jet clustering** sensing mechanism.

The forward operator applies, in order: S · antikt · sequential clustering operator; S · select operator; O · jet · energy scale correction operator.

Observations are corrupted by pileup detector gaussian. Existence of the recovered jet_4vector_list 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 ~= 100); pileup_contamination_residual dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Pileup detector gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · antikt · sequential clustering → S · select → O · jet · energy scale correction → **y** (detector).

```
y = `O.jet.energy_scale_correction` `S.select` `S.antikt.sequential_clustering` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.antikt.sequential_clustering` | S · antikt · sequential clustering operator |
| `S.select` | S · select operator |
| `O.jet.energy_scale_correction` | O · jet · energy scale correction operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Particle Physics |
| Sub domain | QCD jets |
| Carrier | particle |
| Problem class | parameter_estimation |
| Solution space | jet_4vector_list |
| Noise model | pileup_detector_gaussian |
| Integration axis | rapidity_phi_plane |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered jet_4vector_list 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 ~= 100); pileup_contamination_residual dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Pileup detector gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | jet_energy_resolution_sigma_E_over_E |
| Secondary | jet_mass_RMSE_GeV |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Pileup mu | — | 50 |
| Jet pt gev | — | 200 |
| Jet radius r | — | 0.4 |
| N particles per event | — | 2000 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Pileup mu | — | 0 – 200 |
| Jet pt gev | — | 30 – 5000 |
| Jet radius r | — | 0.2 – 1.0 |
| N particles per event | — | 100 – 10000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.05 jet_energy_resolution_sigma_E_over_E

| Metric | Range |
|---|---|
| Jet energy resolution sigma e over e | 0.02 – 0.15 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **jet_energy_resolution_sigma_E_over_E**, with κ = `1000.0` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xc80f843b96c36dfcd5bbf210445f7bb5402681f1fbe638f5ba69782ef1eb0166`
- **Chain tx hash:** `0xec250d2cb078e8199e626dd1c0d0033243346ba321cc88deff4da7e3f9e9de48`
- **Chain block:** `41555317`

---

## File Mapping

This bundle consists of: `L1-487.md`, `L1-487.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-487.md` | Source of truth — edit this | Human or LLM |
| `L1-487.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 `L1-487`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._