L1 ⚛ L1-220 ⊙ Testnet

Linear Elastic Fracture Mechanics (LEFM) — K/J evaluation

Structural Mechanics · SIF / J-integral extraction

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⬇ L1-220.md

# ⚛ L1 Principle — Linear Elastic Fracture Mechanics (LEFM) — K/J evaluation **ID:** `L1-220` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *SIF / J-integral extraction* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** sif and J integral > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554012 --- ## 🧠 1. Introduction **Linear Elastic Fracture Mechanics (LEFM) — K/J evaluation** is a **linear inverse problem** whose unknown lives in **sif and J integral** space, within the **SIF / J-integral extraction** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **dic caustics** sensing mechanism. The forward operator applies, in order: L · contour integral operator; L · stress intensity operator; L · williams expansion operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · contour integral → L · stress intensity → L · williams expansion → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.williams_expansion` `L.stress_intensity` `L.contour_integral` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.contour_integral` | L · contour integral operator | | `L.stress_intensity` | L · stress intensity operator | | `L.williams_expansion` | L · williams expansion operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | SIF / J-integral extraction | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | sif_and_J_integral | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | K_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `lefm` · **Forward operator:** `lefm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 50000 | | Snr db | dB | 30 | | N contours | — | 5 | | Material error | — | 0 | | Contour size error | — | 0 | | Crack tip pos error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 1000 – 10000000 | | Snr db | dB | 0 – 40 | | N contours | — | 1 – 50 | | Material error | — | 0.0 – 0.1 | | Contour size error | — | 0.0 – 0.3 | | Crack tip pos error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 4.0 | Metric | Range | |---|---| | K rel | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **K_rel_error_percent**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe0de8a7196bc8d872796501a4d8c417e616148e21a8932b406b40b1d316cfbf1` - **Chain tx hash:** `0xf75f057f4f87ef3fa14ca466d3cba53517724070ad25a959576b83c764b3b639` - **Chain block:** `41554012` --- ## File Mapping This bundle consists of: `L1-220.md`, `L1-220.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-220.md` | Source of truth — edit this | Human or LLM | | `L1-220.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 `L1-220`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-220.md).
Regenerate L1-220.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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L2-220-001 Linear Elastic Fracture Mechanics (LEFM) — K/J evaluation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-220",
  "chain_block": 41554012,
  "chain_hash": "0xe0de8a7196bc8d872796501a4d8c417e616148e21a8932b406b40b1d316cfbf1",
  "chain_tx_hash": "0xf75f057f4f87ef3fa14ca466d3cba53517724070ad25a959576b83c764b3b639",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "K_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "K_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.contour_integral",
      "L.stress_intensity",
      "L.williams_expansion",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "dic_caustics",
    "solution_space": "sif_and_J_integral",
    "sub_domain": "SIF / J-integral extraction",
    "title": "Linear Elastic Fracture Mechanics (LEFM) \u2014 K/J evaluation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "lefm_forward"
    ],
    "allowed_omega_dimensions": [
      "N_DOF",
      "N_contours",
      "SNR_dB",
      "crack_tip_pos_error",
      "contour_size_error",
      "material_error",
      "crack_tip_pos_error",
      "contour_size_error",
      "material_error"
    ],
    "allowed_problem_classes": [
      "lefm"
    ],
    "center_spec": {
      "epsilon_fn_center": "4.0",
      "forward_operator": "lefm_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_DOF": 50000,
        "N_contours": 5,
        "SNR_dB": 30,
        "contour_size_error": 0.0,
        "crack_tip_pos_error": 0.0,
        "material_error": 0.0
      },
      "problem_class": "lefm"
    },
    "epsilon_bounds": {
      "K_rel": [
        0.5,
        30.0
      ]
    },
    "omega_bounds": {
      "N_DOF": [
        1000,
        10000000
      ],
      "N_contours": [
        1,
        50
      ],
      "SNR_dB": [
        0,
        40
      ],
      "contour_size_error": [
        0.0,
        0.3
      ],
      "crack_tip_pos_error": [
        0.0,
        0.1
      ],
      "material_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "SIF / J-integral extraction",
  "title": "Linear Elastic Fracture Mechanics (LEFM) \u2014 K/J evaluation"
}

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