L1 ⚛ L1-357 ⊙ Testnet

Point Reactor Kinetics — power transient modeling

Nuclear Engineering · Coupled precursor/power ODEs for reactivity insertion

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⬇ L1-357.md

# ⚛ L1 Principle — Point Reactor Kinetics — power transient modeling **ID:** `L1-357` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *Coupled precursor/power ODEs for reactivity insertion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** reactivity time and power > **📡 Carrier:** neutron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554097 --- ## 🧠 1. Introduction **Point Reactor Kinetics — power transient modeling** is a **linear inverse problem** whose unknown lives in **reactivity time and power** space, within the **Coupled precursor/power ODEs for reactivity insertion** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **ex core detectors** sensing mechanism. The forward operator applies, in order: L · precursor balance operator; L · power balance operator; L · delayed neutrons operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · precursor balance → L · power balance → L · delayed neutrons → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.delayed_neutrons` `L.power_balance` `L.precursor_balance` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.precursor_balance` | L · precursor balance operator | | `L.power_balance` | L · power balance operator | | `L.delayed_neutrons` | L · delayed neutrons operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | Coupled precursor/power ODEs for reactivity insertion | | Carrier | neutron | | Problem class | linear_inverse | | Solution space | reactivity_time_and_power | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `pointkinetics` · **Forward operator:** `pointkinetics_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N groups | — | 6 | | N samples | — | 1000 | | Rho error | — | 0 | | Lambda error | — | 0 | | Beta eff error | — | 0 | | Generation time error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N groups | — | 1 – 10 | | N samples | — | 100 – 100000 | | Rho error | — | 0.0 – 0.1 | | Lambda error | — | 0.0 – 0.1 | | Beta eff error | — | 0.0 – 0.1 | | Generation time error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xde713502edc70c8b4e58593b58072e264d5d8bcd263d3449a8321ec13c68adc2` - **Chain tx hash:** `0xf17a2c44dc3a9a54d63ba209c86163bc3105d6f5d5734074b2c67ad6e13ea7aa` - **Chain block:** `41554097` --- ## File Mapping This bundle consists of: `L1-357.md`, `L1-357.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-357.md` | Source of truth — edit this | Human or LLM | | `L1-357.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 `L1-357`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-357.md).
Regenerate L1-357.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-357-001 Point Reactor Kinetics — power transient modeling Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-357",
  "chain_block": 41554097,
  "chain_hash": "0xde713502edc70c8b4e58593b58072e264d5d8bcd263d3449a8321ec13c68adc2",
  "chain_tx_hash": "0xf17a2c44dc3a9a54d63ba209c86163bc3105d6f5d5734074b2c67ad6e13ea7aa",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "neutron",
    "difficulty_delta": 3,
    "domain": "Nuclear Engineering",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.precursor_balance",
      "L.power_balance",
      "L.delayed_neutrons",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "ex_core_detectors",
    "solution_space": "reactivity_time_and_power",
    "sub_domain": "Coupled precursor/power ODEs for reactivity insertion",
    "title": "Point Reactor Kinetics \u2014 power transient modeling"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "pointkinetics_forward"
    ],
    "allowed_omega_dimensions": [
      "N_groups",
      "N_samples",
      "SNR_dB",
      "beta_eff_error",
      "lambda_error",
      "generation_time_error",
      "rho_error",
      "beta_eff_error",
      "lambda_error",
      "generation_time_error",
      "rho_error"
    ],
    "allowed_problem_classes": [
      "pointkinetics"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "pointkinetics_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_groups": 6,
        "N_samples": 1000,
        "SNR_dB": 30,
        "beta_eff_error": 0.0,
        "generation_time_error": 0.0,
        "lambda_error": 0.0,
        "rho_error": 0.0
      },
      "problem_class": "pointkinetics"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_groups": [
        1,
        10
      ],
      "N_samples": [
        100,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "beta_eff_error": [
        0.0,
        0.1
      ],
      "generation_time_error": [
        0.0,
        0.2
      ],
      "lambda_error": [
        0.0,
        0.1
      ],
      "rho_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Coupled precursor/power ODEs for reactivity insertion",
  "title": "Point Reactor Kinetics \u2014 power transient modeling"
}

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