L1 ⚛ L1-484 ⊙ Testnet

Charged Particle Track Reconstruction

Particle Physics · Tracking detectors

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⬇ L1-484.md

# ⚛ L1 Principle — Charged Particle Track Reconstruction **ID:** `L1-484` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Particle Physics — *Tracking detectors* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** track parameter vector > **📡 Carrier:** particle · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555317 --- ## 🧠 1. Introduction **Charged Particle Track Reconstruction** is a **nonlinear inverse problem** whose unknown lives in **track parameter vector** space, within the **Tracking detectors** sub-domain of **Particle Physics**. Measurements consist of particle interactions in a detector via a **silicon tracker hit pattern** sensing mechanism. The forward operator applies, in order: S · kalman · track filter operator; time evolution of the state; O · chi2 · hit residuals operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered track_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 ~= 200); alignment_uncertainty_um dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → O · chi2 · hit residuals → **y** (detector). ``` y = `O.chi2.hit_residuals` ∂_t x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.chi2.hit_residuals` | O · chi2 · hit residuals operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `S.kalman.track_filter` | S · kalman · track filter operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Particle Physics | | Sub domain | Tracking detectors | | Carrier | particle | | Problem class | nonlinear_inverse | | Solution space | track_parameter_vector | | Noise model | gaussian | | Integration axis | track_helix | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered track_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 ~= 200); alignment_uncertainty_um dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | track_parameter_resolution_sigma_pt_over_pt | | Secondary | tracking_efficiency_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `silicon_tracker_hit_pattern` **Center point:** | Parameter | Unit | Value | |---|---|---| | N layers | — | 10 | | B field t | — | 2 | | Pileup mu | — | 50 | | Material x0 percent | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N layers | — | 4 – 20 | | B field t | — | 0.5 – 4.0 | | Pileup mu | — | 0 – 200 | | Material x0 percent | — | 0.1 – 3.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.001 track_parameter_resolution_sigma_pt_over_pt | Metric | Range | |---|---| | Track parameter resolution sigma pt over pt | 0.0001 – 0.01 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **track_parameter_resolution_sigma_pt_over_pt**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x751db39c2e389f94308495e5a28df961aff9eed62bff526231f292a7ead5f943` - **Chain tx hash:** `0x0a900f5a04283e365f732dcd071354524a5e14b22bd4fec638f3257acdf17f3b` - **Chain block:** `41555317` --- ## File Mapping This bundle consists of: `L1-484.md`, `L1-484.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-484.md` | Source of truth — edit this | Human or LLM | | `L1-484.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 `L1-484`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-484.md).
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L2-484-001 Charged Particle Track Reconstruction — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Particle Physics",
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    "sub_domain": "Tracking detectors",
    "title": "Charged Particle Track Reconstruction"
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  "status": "testnet",
  "sub_domain": "Tracking detectors",
  "title": "Charged Particle Track Reconstruction"
}

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