L1 ⚛ L1-355 ⊙ Testnet

Neutron Diffusion — multi-group diffusion approximation

Nuclear Engineering · Multi-group diffusion (PWR / BWR core physics)

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⬇ L1-355.md

# ⚛ L1 Principle — Neutron Diffusion — multi-group diffusion approximation **ID:** `L1-355` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *Multi-group diffusion (PWR / BWR core physics)* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** core flux map > **📡 Carrier:** neutron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554097 --- ## 🧠 1. Introduction **Neutron Diffusion — multi-group diffusion approximation** is a **linear inverse problem** whose unknown lives in **core flux map** space, within the **Multi-group diffusion (PWR / BWR core physics)** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **flux map incore** sensing mechanism. The forward operator applies, in order: L · diffusion operator; L · group coupling operator; L · fission source operator; int · energy operator. Observations are corrupted by Poisson counting noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · diffusion → L · group coupling → L · fission source → int · energy → **y** (detector). ``` y = `int.energy` `L.fission_source` `L.group_coupling` `L.diffusion` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.diffusion` | L · diffusion operator | | `L.group_coupling` | L · group coupling operator | | `L.fission_source` | L · fission source operator | | `int.energy` | Int · energy operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | Multi-group diffusion (PWR / BWR core physics) | | Carrier | neutron | | Problem class | linear_inverse | | Solution space | core_flux_map | | Noise model | poisson | | Integration axis | energy | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | flux_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `diffusion` · **Forward operator:** `diffusion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 64 | | Snr db | dB | 30 | | N groups | — | 2 | | N detectors | — | 64 | | D coeff error | — | 0 | | Sigma a error | — | 0 | | Nu sigma f error | — | 0 | | Extrapol dist error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 512 | | W | px | 32 – 512 | | Z | — | 32 – 512 | | Snr db | dB | 0 – 40 | | N groups | — | 1 – 10 | | N detectors | — | 8 – 512 | | D coeff error | — | 0.0 – 0.05 | | Sigma a error | — | 0.0 – 0.05 | | Nu sigma f error | — | 0.0 – 0.05 | | Extrapol dist error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 | Metric | Range | |---|---| | Flux rel error | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **flux_rel_error_percent**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x587c24a0168e9b20d41842ecc720aa0f295f759892b564244887143fac66b69e` - **Chain tx hash:** `0x790956123eb436b8e42585bd77ffc50d1b82a741448e167ac12626322c1ef2c4` - **Chain block:** `41554097` --- ## File Mapping This bundle consists of: `L1-355.md`, `L1-355.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-355.md` | Source of truth — edit this | Human or LLM | | `L1-355.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 `L1-355`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Regenerate L1-355.json so every field matches the Markdown.
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L2-355-001 Neutron Diffusion — multi-group diffusion approximation Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554097,
  "chain_hash": "0x587c24a0168e9b20d41842ecc720aa0f295f759892b564244887143fac66b69e",
  "chain_tx_hash": "0x790956123eb436b8e42585bd77ffc50d1b82a741448e167ac12626322c1ef2c4",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "flux_rel_error_percent",
    "type": "epsilon_fn"
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  "observable_profile": {
    "metric": "flux_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "neutron",
    "difficulty_delta": 5,
    "domain": "Nuclear Engineering",
    "integration_axis": "energy",
    "noise_model": "poisson",
    "primitives": [
      "L.diffusion",
      "L.group_coupling",
      "L.fission_source",
      "int.energy"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "flux_map_incore",
    "solution_space": "core_flux_map",
    "sub_domain": "Multi-group diffusion (PWR / BWR core physics)",
    "title": "Neutron Diffusion \u2014 multi-group diffusion approximation"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "N_groups",
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      "SNR_dB",
      "D_coeff_error",
      "sigma_a_error",
      "nu_sigma_f_error",
      "extrapol_dist_error",
      "D_coeff_error",
      "sigma_a_error",
      "nu_sigma_f_error",
      "extrapol_dist_error"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
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      "forward_operator": "diffusion_forward",
      "input_format": "measurement_only",
      "omega": {
        "D_coeff_error": 0.0,
        "H": 128,
        "N_detectors": 64,
        "N_groups": 2,
        "SNR_dB": 30,
        "W": 128,
        "Z": 64,
        "extrapol_dist_error": 0.0,
        "nu_sigma_f_error": 0.0,
        "sigma_a_error": 0.0
      },
      "problem_class": "diffusion"
    },
    "epsilon_bounds": {
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        30.0
      ]
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        0.0,
        0.05
      ],
      "H": [
        32,
        512
      ],
      "N_detectors": [
        8,
        512
      ],
      "N_groups": [
        1,
        10
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        512
      ],
      "Z": [
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      ],
      "extrapol_dist_error": [
        0.0,
        0.1
      ],
      "nu_sigma_f_error": [
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        0.05
      ],
      "sigma_a_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Multi-group diffusion (PWR / BWR core physics)",
  "title": "Neutron Diffusion \u2014 multi-group diffusion approximation"
}

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