L1 ⚛ L1-360 ⊙ Testnet

Monte Carlo Neutron Transport — stochastic particle tracking

Nuclear Engineering · MCNP / OpenMC continuous-energy MC transport

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⬇ L1-360.md

# ⚛ L1 Principle — Monte Carlo Neutron Transport — stochastic particle tracking **ID:** `L1-360` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *MCNP / OpenMC continuous-energy MC transport* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** tally expected values with variance > **📡 Carrier:** neutron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554098 --- ## 🧠 1. Introduction **Monte Carlo Neutron Transport — stochastic particle tracking** is a **linear inverse problem** whose unknown lives in **tally expected values with variance** space, within the **MCNP / OpenMC continuous-energy MC transport** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **tally scores** sensing mechanism. The forward operator applies, in order: L · sample source operator; L · track particle operator; L · score tally operator; int · stochastic operator. Observations are corrupted by Poisson counting noise. Statistical convergence O(1/sqrt(N_histories)); bias via biased sampling; ill-posed for very deep penetration. ## ⚙ 2. Forward Model Physical chain: **x** → L · sample source → L · track particle → L · score tally → int · stochastic → **y** (detector). ``` y = `int.stochastic` `L.score_tally` `L.track_particle` `L.sample_source` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.sample_source` | L · sample source operator | | `L.track_particle` | L · track particle operator | | `L.score_tally` | L · score tally operator | | `int.stochastic` | Int · stochastic operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | MCNP / OpenMC continuous-energy MC transport | | Carrier | neutron | | Problem class | linear_inverse | | Solution space | tally_expected_values_with_variance | | Noise model | poisson | | Integration axis | stochastic | | Difficulty delta | 10 | | L dag | 3.5 | ## 📡 4. Measurement Model Statistical convergence O(1/sqrt(N_histories)); bias via biased sampling; ill-posed for very deep penetration. | Metric | Value | |---|---| | Metric | tally_rel_uncertainty_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `mc_neutron_transport` · **Forward operator:** `mc_neutron_transport_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N cells | — | 10000 | | N tallies | — | 50 | | N histories | — | 1e+07 | | Ace data error | — | 0 | | Source biasing error | — | 0 | | Variance reduction error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N cells | — | 10 – 1000000 | | N tallies | — | 1 – 10000 | | N histories | — | 10000.0 – 100000000000.0 | | Ace data error | — | 0.0 – 0.05 | | Source biasing error | — | 0.0 – 0.2 | | Variance reduction error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 2.0 | Metric | Range | |---|---| | Tally rel | 0.1 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **tally_rel_uncertainty_percent**, with κ = `800` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xff707605f77f25c0a80b1d2fb42a81948c2d5c44cf6d1236b89f84329fc59e5a` - **Chain tx hash:** `0x64b83291c7ed683e5cfc62f63eda49da55effdd07636ff0bac0131e3f3bb93fd` - **Chain block:** `41554098` --- ## File Mapping This bundle consists of: `L1-360.md`, `L1-360.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-360.md` | Source of truth — edit this | Human or LLM | | `L1-360.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 `L1-360`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-360.md).
Regenerate L1-360.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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L2-360-001 Monte Carlo Neutron Transport — stochastic particle tracking Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-360",
  "chain_block": 41554098,
  "chain_hash": "0xff707605f77f25c0a80b1d2fb42a81948c2d5c44cf6d1236b89f84329fc59e5a",
  "chain_tx_hash": "0x64b83291c7ed683e5cfc62f63eda49da55effdd07636ff0bac0131e3f3bb93fd",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 10,
    "kappa": 800,
    "metric": "tally_rel_uncertainty_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "tally_rel_uncertainty_percent",
    "regime": "Statistical convergence O(1/sqrt(N_histories)); bias via biased sampling; ill-posed for very deep penetration.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "neutron",
    "difficulty_delta": 10,
    "domain": "Nuclear Engineering",
    "integration_axis": "stochastic",
    "noise_model": "poisson",
    "primitives": [
      "L.sample_source",
      "L.track_particle",
      "L.score_tally",
      "int.stochastic"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "tally_scores",
    "solution_space": "tally_expected_values_with_variance",
    "sub_domain": "MCNP / OpenMC continuous-energy MC transport",
    "title": "Monte Carlo Neutron Transport \u2014 stochastic particle tracking"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mc_neutron_transport_forward"
    ],
    "allowed_omega_dimensions": [
      "N_histories",
      "N_tallies",
      "N_cells",
      "SNR_dB",
      "ace_data_error",
      "source_biasing_error",
      "variance_reduction_error",
      "ace_data_error",
      "source_biasing_error",
      "variance_reduction_error"
    ],
    "allowed_problem_classes": [
      "mc_neutron_transport"
    ],
    "center_spec": {
      "epsilon_fn_center": "2.0",
      "forward_operator": "mc_neutron_transport_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_cells": 10000,
        "N_histories": 10000000.0,
        "N_tallies": 50,
        "SNR_dB": 30,
        "ace_data_error": 0.0,
        "source_biasing_error": 0.0,
        "variance_reduction_error": 0.0
      },
      "problem_class": "mc_neutron_transport"
    },
    "epsilon_bounds": {
      "tally_rel": [
        0.1,
        30.0
      ]
    },
    "omega_bounds": {
      "N_cells": [
        10,
        1000000
      ],
      "N_histories": [
        10000.0,
        100000000000.0
      ],
      "N_tallies": [
        1,
        10000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "ace_data_error": [
        0.0,
        0.05
      ],
      "source_biasing_error": [
        0.0,
        0.2
      ],
      "variance_reduction_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "MCNP / OpenMC continuous-energy MC transport",
  "title": "Monte Carlo Neutron Transport \u2014 stochastic particle tracking"
}

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