L1 ⚛ L1-358 ⊙ Testnet

Burnup / Depletion — fuel nuclide evolution

Nuclear Engineering · Bateman nuclide transmutation + flux coupling

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-358

⬇ L1-358.md ⬇ L1-358.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-358 (Burnup / Depletion — fuel nuclide evolution) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-358.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-358.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 = ∫_t dt `L.flux_coupling` `L.cross_section_update` `L.bateman` x + n,    n ~ 𝒩(0, σ²)

world state x (nuclide inventory time)

→

L · bateman `L.bateman`

→

L · cross section update `L.cross_section_update`

→

L · flux coupling `L.flux_coupling`

→

Temporal integration ∫_t dt

→

observation y (neutron detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-358.md

# ⚛ L1 Principle — Burnup / Depletion — fuel nuclide evolution **ID:** `L1-358` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Nuclear Engineering — *Bateman nuclide transmutation + flux coupling* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** nuclide inventory time > **📡 Carrier:** neutron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554097 --- ## 🧠 1. Introduction **Burnup / Depletion — fuel nuclide evolution** is a **nonlinear inverse problem** whose unknown lives in **nuclide inventory time** space, within the **Bateman nuclide transmutation + flux coupling** sub-domain of **Nuclear Engineering**. Measurements consist of neutrons transmitted through the sample via a **spent fuel assay** sensing mechanism. The forward operator applies, in order: L · bateman operator; L · cross section update operator; L · flux coupling 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 · bateman → L · cross section update → L · flux coupling → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.flux_coupling` `L.cross_section_update` `L.bateman` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.bateman` | L · bateman operator | | `L.cross_section_update` | L · cross section update operator | | `L.flux_coupling` | L · flux coupling operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Nuclear Engineering | | Sub domain | Bateman nuclide transmutation + flux coupling | | Carrier | neutron | | Problem class | nonlinear_inverse | | Solution space | nuclide_inventory_time | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | isotope_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `bateman_depletion` · **Forward operator:** `bateman_depletion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | Fy error | — | 0 | | N nuclides | — | 1500 | | N timesteps | — | 50 | | Burnup gwd per tu | — | 40 | | Decay const error | — | 0 | | Flux history error | — | 0 | | Xs microscopic error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | Fy error | — | 0.0 – 0.1 | | N nuclides | — | 10 – 3600 | | N timesteps | — | 5 – 1000 | | Burnup gwd per tu | — | 1 – 120 | | Decay const error | — | 0.0 – 0.02 | | Flux history error | — | 0.0 – 0.1 | | Xs microscopic error | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 | Metric | Range | |---|---| | Isotope rel error | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **isotope_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:** `0x0195a7ec6b535e4cbb029f42da727208f2608d48260c45a981422de28166dbac` - **Chain tx hash:** `0xd0c832b56c37a8962f8dd92ee61ba55da971b5ac3a179658835f148a2a3ee40d` - **Chain block:** `41554097` --- ## File Mapping This bundle consists of: `L1-358.md`, `L1-358.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-358.md` | Source of truth — edit this | Human or LLM | | `L1-358.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 `L1-358`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-358-001 Burnup / Depletion — fuel nuclide evolution Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-358",
  "chain_block": 41554097,
  "chain_hash": "0x0195a7ec6b535e4cbb029f42da727208f2608d48260c45a981422de28166dbac",
  "chain_tx_hash": "0xd0c832b56c37a8962f8dd92ee61ba55da971b5ac3a179658835f148a2a3ee40d",
  "domain": "Nuclear Engineering",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "isotope_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "isotope_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "neutron",
    "difficulty_delta": 5,
    "domain": "Nuclear Engineering",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.bateman",
      "L.cross_section_update",
      "L.flux_coupling",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "spent_fuel_assay",
    "solution_space": "nuclide_inventory_time",
    "sub_domain": "Bateman nuclide transmutation + flux coupling",
    "title": "Burnup / Depletion \u2014 fuel nuclide evolution"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "bateman_depletion_forward"
    ],
    "allowed_omega_dimensions": [
      "N_nuclides",
      "N_timesteps",
      "burnup_GWd_per_tU",
      "SNR_dB",
      "xs_microscopic_error",
      "decay_const_error",
      "flux_history_error",
      "fy_error",
      "xs_microscopic_error",
      "decay_const_error",
      "flux_history_error",
      "fy_error"
    ],
    "allowed_problem_classes": [
      "bateman_depletion"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0",
      "forward_operator": "bateman_depletion_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_nuclides": 1500,
        "N_timesteps": 50,
        "SNR_dB": 30,
        "burnup_GWd_per_tU": 40,
        "decay_const_error": 0.0,
        "flux_history_error": 0.0,
        "fy_error": 0.0,
        "xs_microscopic_error": 0.0
      },
      "problem_class": "bateman_depletion"
    },
    "epsilon_bounds": {
      "isotope_rel_error": [
        0.5,
        30.0
      ]
    },
    "omega_bounds": {
      "N_nuclides": [
        10,
        3600
      ],
      "N_timesteps": [
        5,
        1000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "burnup_GWd_per_tU": [
        1,
        120
      ],
      "decay_const_error": [
        0.0,
        0.02
      ],
      "flux_history_error": [
        0.0,
        0.1
      ],
      "fy_error": [
        0.0,
        0.1
      ],
      "xs_microscopic_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Bateman nuclide transmutation + flux coupling",
  "title": "Burnup / Depletion \u2014 fuel nuclide evolution"
}

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