L1 ⚛ L1-356 ⊙ Testnet

Criticality Eigenvalue — k-effective calculation

Nuclear Engineering · k-eff generalized eigenvalue

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⬇ L1-356.md

# ⚛ L1 Principle — Criticality Eigenvalue — k-effective calculation **ID:** `L1-356` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *k-eff generalized eigenvalue* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** k eff scalar and fundamental mode > **📡 Carrier:** neutron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554097 --- ## 🧠 1. Introduction **Criticality Eigenvalue — k-effective calculation** is a **linear inverse problem** whose unknown lives in **k eff scalar and fundamental mode** space, within the **k-eff generalized eigenvalue** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **reactivity meter** sensing mechanism. The forward operator applies, in order: L · diffusion or transport operator; L · power iteration operator; L · fission source scale operator; int · eigenvalue operator. Observations are corrupted by Poisson counting noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · diffusion or transport → L · power iteration → L · fission source scale → int · eigenvalue → **y** (detector). ``` y = `int.eigenvalue` `L.fission_source_scale` `L.power_iteration` `L.diffusion_or_transport` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.diffusion_or_transport` | L · diffusion or transport operator | | `L.power_iteration` | L · power iteration operator | | `L.fission_source_scale` | L · fission source scale operator | | `int.eigenvalue` | Int · eigenvalue operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | k-eff generalized eigenvalue | | Carrier | neutron | | Problem class | linear_inverse | | Solution space | k_eff_scalar_and_fundamental_mode | | Noise model | poisson | | Integration axis | eigenvalue | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | k_eff_absolute_error | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `keff` · **Forward operator:** `keff_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 64 | | Snr db | dB | 30 | | N groups | — | 8 | | Xs error | — | 0 | | Burnup error | — | 0 | | Reflector error | — | 0 | | Power shape 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 – 47 | | Xs error | — | 0.0 – 0.02 | | Burnup error | — | 0.0 – 0.2 | | Reflector error | — | 0.0 – 0.05 | | Power shape error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.002 | Metric | Range | |---|---| | K eff delta | 0.0001 – 0.05 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **k_eff_absolute_error**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa1e3a839b544bafd3a5f87d1fe9db23840096cf737ab7035c272670182d75064` - **Chain tx hash:** `0x04d97db02a9cf14c0fb262121fa0cfb014ab1ab4d0b0dc50e11d92a47823877d` - **Chain block:** `41554097` --- ## File Mapping This bundle consists of: `L1-356.md`, `L1-356.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-356.md` | Source of truth — edit this | Human or LLM | | `L1-356.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 `L1-356`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "artifact_id": "L1-356",
  "chain_block": 41554097,
  "chain_hash": "0xa1e3a839b544bafd3a5f87d1fe9db23840096cf737ab7035c272670182d75064",
  "chain_tx_hash": "0x04d97db02a9cf14c0fb262121fa0cfb014ab1ab4d0b0dc50e11d92a47823877d",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
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    "kappa": 500,
    "metric": "k_eff_absolute_error",
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
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  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "neutron",
    "difficulty_delta": 5,
    "domain": "Nuclear Engineering",
    "integration_axis": "eigenvalue",
    "noise_model": "poisson",
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    "problem_class": "linear_inverse",
    "sensing_mechanism": "reactivity_meter",
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    "sub_domain": "k-eff generalized eigenvalue",
    "title": "Criticality Eigenvalue \u2014 k-effective calculation"
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      "burnup_error": [
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      ],
      "power_shape_error": [
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      "reflector_error": [
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      ],
      "xs_error": [
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        0.02
      ]
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "k-eff generalized eigenvalue",
  "title": "Criticality Eigenvalue \u2014 k-effective calculation"
}

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