L1 ⚛ L1-486 ⊙ Testnet

Dark Matter Direct Detection Inversion

Particle Physics · Dark matter search

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⬇ L1-486.md

# ⚛ L1 Principle — Dark Matter Direct Detection Inversion **ID:** `L1-486` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Particle Physics — *Dark matter search* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** WIMP cross section mass > **📡 Carrier:** particle · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41555317 --- ## 🧠 1. Introduction **Dark Matter Direct Detection Inversion** is a **parameter-estimation problem** whose unknown lives in **WIMP cross section mass** space, within the **Dark matter search** sub-domain of **Particle Physics**. Measurements consist of particle interactions in a detector via a **nuclear recoil detection** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · background · rejection signal region operator; O · likelihood · profile operator. Observations are corrupted by Poisson counting noise. Existence of the recovered WIMP_cross_section_mass 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 ~= 1000); halo_model_uncertainty 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** → Pointwise nonlinearity → S · background · rejection signal region → O · likelihood · profile → **y** (detector). ``` y = `O.likelihood.profile` `S.background.rejection_signal_region` f(·) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.background.rejection_signal_region` | S · background · rejection signal region operator | | `O.likelihood.profile` | O · likelihood · profile operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Particle Physics | | Sub domain | Dark matter search | | Carrier | particle | | Problem class | parameter_estimation | | Solution space | WIMP_cross_section_mass | | Noise model | poisson | | Integration axis | recoil_energy | | Difficulty delta | 10 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered WIMP_cross_section_mass 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 ~= 1000); halo_model_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Poisson sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | sigma_SI_upper_limit_log10 | | Secondary | m_DM_exclusion_reach | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `nuclear_recoil_detection` **Center point:** | Parameter | Unit | Value | |---|---|---| | M dm gev | — | 100 | | E threshold kev | — | 1 | | Exposure ton yr | — | 1 | | Background rate evt kev ton yr | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | M dm gev | — | 1 – 10000 | | E threshold kev | — | 0.1 – 10.0 | | Exposure ton yr | — | 0.01 – 10.0 | | Background rate evt kev ton yr | — | 0.001 – 10.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** -47 sigma_SI_upper_limit_log10 | Metric | Range | |---|---| | Sigma si upper limit log10 | -52 – -40 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **sigma_SI_upper_limit_log10**, with κ = `100000.0` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3f20cdba022cf9a4810d377b0e004278643b99d61e2cfc5f8d0c6ed72411d816` - **Chain tx hash:** `0x38b299e2ba2e37fcfb52f9b63b84a2801e73edc113765c61f15828c9f3b40d34` - **Chain block:** `41555317` --- ## File Mapping This bundle consists of: `L1-486.md`, `L1-486.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-486.md` | Source of truth — edit this | Human or LLM | | `L1-486.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 `L1-486`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "sub_domain": "Dark matter search",
  "title": "Dark Matter Direct Detection Inversion"
}

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