L1 ⚛ L1-362 ⊙ Testnet

Nuclear Data — R-matrix resonance evaluation

Nuclear Engineering · Resonance cross-section parameter inference

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⬇ L1-362.md

# ⚛ L1 Principle — Nuclear Data — R-matrix resonance evaluation **ID:** `L1-362` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *Resonance cross-section parameter inference* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** resonance parameter set > **📡 Carrier:** neutron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554106 --- ## 🧠 1. Introduction **Nuclear Data — R-matrix resonance evaluation** is a **nonlinear inverse problem** whose unknown lives in **resonance parameter set** space, within the **Resonance cross-section parameter inference** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **xs measurements** sensing mechanism. The forward operator applies, in order: L · breit wigner operator; L · rmatrix fit operator; L · doppler broaden operator; int · energy operator. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · breit wigner → L · rmatrix fit → L · doppler broaden → int · energy → **y** (detector). ``` y = `int.energy` `L.doppler_broaden` `L.rmatrix_fit` `L.breit_wigner` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.breit_wigner` | L · breit wigner operator | | `L.rmatrix_fit` | L · rmatrix fit operator | | `L.doppler_broaden` | L · doppler broaden operator | | `int.energy` | Int · energy operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | Resonance cross-section parameter inference | | Carrier | neutron | | Problem class | nonlinear_inverse | | Solution space | resonance_parameter_set | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | resonance_param_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `rmatrix` · **Forward operator:** `rmatrix_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | Width error | — | 0 | | N energy pts | — | 5000 | | N resonances | — | 100 | | Peak pos error | — | 0 | | Temp nuc error | — | 0 | | Background error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | Width error | — | 0.0 – 0.1 | | N energy pts | — | 100 – 1000000 | | N resonances | — | 1 – 5000 | | Peak pos error | — | 0.0 – 0.02 | | Temp nuc error | — | 0.0 – 100 | | Background error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 2.0 | Metric | Range | |---|---| | Param rel | 0.2 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **resonance_param_rel_error_percent**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf18afdccdb466faa8458259f883a7439d2fd424b3568bcc1b7893af2d912852a` - **Chain tx hash:** `0x2e703c906d9ccbac6238c63e934269c8d3bfd56c1029d20920dc32019b7a8e78` - **Chain block:** `41554106` --- ## File Mapping This bundle consists of: `L1-362.md`, `L1-362.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-362.md` | Source of truth — edit this | Human or LLM | | `L1-362.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 `L1-362`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-362.md).
Regenerate L1-362.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-362-001 Nuclear Data — R-matrix resonance evaluation Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554106,
  "chain_hash": "0xf18afdccdb466faa8458259f883a7439d2fd424b3568bcc1b7893af2d912852a",
  "chain_tx_hash": "0x2e703c906d9ccbac6238c63e934269c8d3bfd56c1029d20920dc32019b7a8e78",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "resonance_param_rel_error_percent",
    "type": "epsilon_fn"
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  "observable_profile": {
    "metric": "resonance_param_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "neutron",
    "difficulty_delta": 5,
    "domain": "Nuclear Engineering",
    "integration_axis": "energy",
    "noise_model": "gaussian",
    "primitives": [
      "L.breit_wigner",
      "L.rmatrix_fit",
      "L.doppler_broaden",
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    "sensing_mechanism": "xs_measurements",
    "solution_space": "resonance_parameter_set",
    "sub_domain": "Resonance cross-section parameter inference",
    "title": "Nuclear Data \u2014 R-matrix resonance evaluation"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "N_energy_pts",
      "SNR_dB",
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      "background_error",
      "peak_pos_error",
      "width_error",
      "temp_nuc_error",
      "background_error"
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    "center_spec": {
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      "forward_operator": "rmatrix_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_resonances": 100,
        "SNR_dB": 30,
        "background_error": 0.0,
        "peak_pos_error": 0.0,
        "temp_nuc_error": 0.0,
        "width_error": 0.0
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    },
    "epsilon_bounds": {
      "param_rel": [
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        30.0
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    },
    "omega_bounds": {
      "N_energy_pts": [
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      ],
      "N_resonances": [
        1,
        5000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "background_error": [
        0.0,
        0.3
      ],
      "peak_pos_error": [
        0.0,
        0.02
      ],
      "temp_nuc_error": [
        0.0,
        100
      ],
      "width_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Resonance cross-section parameter inference",
  "title": "Nuclear Data \u2014 R-matrix resonance evaluation"
}

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