L1 ⚛ L1-354 ⊙ Testnet

Neutron Transport — linear Boltzmann equation

Nuclear Engineering · Discrete-ordinates / SN neutron transport

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⬇ principle.md ⬇ principle.json

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⬇ L1-354.md ⬇ L1-354.json

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You are helping me submit a MODIFICATION of L1-354 (Neutron Transport — linear Boltzmann equation) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-354.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-354.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `int.angular_energy` `L.source_fission` `L.collision_scatter` `L.streaming` x,    measurements ~ Poisson(αy)

world state x (angular flux phase space)

→

L · streaming `L.streaming`

→

L · collision scatter `L.collision_scatter`

→

L · source fission `L.source_fission`

→

int · angular energy `int.angular_energy`

→

observation y (neutron detector)

Noise: Poisson counting noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-354.md

# ⚛ L1 Principle — Neutron Transport — linear Boltzmann equation **ID:** `L1-354` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *Discrete-ordinates / SN neutron transport* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** angular flux phase space > **📡 Carrier:** neutron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554096 --- ## 🧠 1. Introduction **Neutron Transport — linear Boltzmann equation** is a **linear inverse problem** whose unknown lives in **angular flux phase space** space, within the **Discrete-ordinates / SN neutron transport** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **flux foils detectors** sensing mechanism. The forward operator applies, in order: L · streaming operator; L · collision scatter operator; L · source fission operator; int · angular energy operator. Observations are corrupted by Poisson counting noise. 7D phase space (x, y, z, E, mu, phi, t); curse of dimensionality; ill-posed for sparse detector data. ## ⚙ 2. Forward Model Physical chain: **x** → L · streaming → L · collision scatter → L · source fission → int · angular energy → **y** (detector). ``` y = `int.angular_energy` `L.source_fission` `L.collision_scatter` `L.streaming` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.streaming` | L · streaming operator | | `L.collision_scatter` | L · collision scatter operator | | `L.source_fission` | L · source fission operator | | `int.angular_energy` | Int · angular energy operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | Discrete-ordinates / SN neutron transport | | Carrier | neutron | | Problem class | linear_inverse | | Solution space | angular_flux_phase_space | | Noise model | poisson | | Integration axis | angular_energy | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model 7D phase space (x, y, z, E, mu, phi, t); curse of dimensionality; ill-posed for sparse detector data. | Metric | Value | |---|---| | Metric | flux_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `sn_transport` · **Forward operator:** `sn_transport_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 64 | | W | px | 64 | | Z | — | 64 | | Snr db | dB | 25 | | N detectors | — | 16 | | N angular dir | — | 24 | | Xs data error | — | 0 | | N energy groups | — | 47 | | Material homo error | — | 0 | | Boundary albedo error | — | 0 | | Source spectrum error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 16 – 512 | | W | px | 16 – 512 | | Z | — | 16 – 512 | | Snr db | dB | 0 – 40 | | N detectors | — | 4 – 256 | | N angular dir | — | 4 – 288 | | Xs data error | — | 0.0 – 0.05 | | N energy groups | — | 1 – 500 | | Material homo error | — | 0.0 – 0.1 | | Boundary albedo error | — | 0.0 – 0.2 | | Source spectrum error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 | Metric | Range | |---|---| | Flux rel error | 1.0 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **flux_rel_error_percent**, with κ = `1200` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x06dd2b6aaaea158e4fd9975ba33aca7df674c73ad57dea914026c7adb6dbf8f6` - **Chain tx hash:** `0x9621272528a0152743f7a09dcb16fe3e5da95987b53097e333dcea79764f1867` - **Chain block:** `41554096` --- ## File Mapping This bundle consists of: `L1-354.md`, `L1-354.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-354.md` | Source of truth — edit this | Human or LLM | | `L1-354.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 `L1-354`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-354-001 Neutron Transport — linear Boltzmann equation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-354",
  "chain_block": 41554096,
  "chain_hash": "0x06dd2b6aaaea158e4fd9975ba33aca7df674c73ad57dea914026c7adb6dbf8f6",
  "chain_tx_hash": "0x9621272528a0152743f7a09dcb16fe3e5da95987b53097e333dcea79764f1867",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 10,
    "kappa": 1200,
    "metric": "flux_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
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    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "neutron",
    "difficulty_delta": 10,
    "domain": "Nuclear Engineering",
    "integration_axis": "angular_energy",
    "noise_model": "poisson",
    "primitives": [
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      "L.collision_scatter",
      "L.source_fission",
      "int.angular_energy"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "flux_foils_detectors",
    "solution_space": "angular_flux_phase_space",
    "sub_domain": "Discrete-ordinates / SN neutron transport",
    "title": "Neutron Transport \u2014 linear Boltzmann equation"
  },
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    ],
    "allowed_problem_classes": [
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    "center_spec": {
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        50.0
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      "Z": [
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      "boundary_albedo_error": [
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      "material_homo_error": [
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      ],
      "source_spectrum_error": [
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        0.2
      ],
      "xs_data_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Discrete-ordinates / SN neutron transport",
  "title": "Neutron Transport \u2014 linear Boltzmann equation"
}

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