L1 ⚛ L1-224 ⊙ Testnet

Fatigue — Paris law crack growth

Structural Mechanics · da/dN = C * (delta K)^m crack growth

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⬇ L1-224.md

# ⚛ L1 Principle — Fatigue — Paris law crack growth **ID:** `L1-224` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *da/dN = C * (delta K)^m crack growth* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** fatigue life curve > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554022 --- ## 🧠 1. Introduction **Fatigue — Paris law crack growth** is a **linear inverse problem** whose unknown lives in **fatigue life curve** space, within the **da/dN = C * (delta K)^m crack growth** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **crack meter** sensing mechanism. The forward operator applies, in order: L · stress intensity operator; L · paris growth operator; L · life integrate 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 · stress intensity → L · paris growth → L · life integrate → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.life_integrate` `L.paris_growth` `L.stress_intensity` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.stress_intensity` | L · stress intensity operator | | `L.paris_growth` | L · paris growth operator | | `L.life_integrate` | L · life integrate operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | da/dN = C * (delta K)^m crack growth | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | fatigue_life_curve | | 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:** `fatigue` · **Forward operator:** `fatigue_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | C error | — | 0 | | M error | — | 0 | | N cycles | — | 1e+06 | | Threshold delta k error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | C error | — | 0.0 – 0.3 | | M error | — | 0.0 – 0.1 | | N cycles | — | 1000.0 – 10000000000.0 | | Threshold delta k error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x969e957ac50eb55f7380f414d3295308937461f41c624dc9cbd9f6e4f627ada2` - **Chain tx hash:** `0xa7dff094fe129c92f135d32a2babff54699ec670145e8b8dc4646dbb673a80a8` - **Chain block:** `41554022` --- ## File Mapping This bundle consists of: `L1-224.md`, `L1-224.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-224.md` | Source of truth — edit this | Human or LLM | | `L1-224.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 `L1-224`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-224.md).
Regenerate L1-224.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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L2-224-001 Fatigue — Paris law crack growth Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-224",
  "chain_block": 41554022,
  "chain_hash": "0x969e957ac50eb55f7380f414d3295308937461f41c624dc9cbd9f6e4f627ada2",
  "chain_tx_hash": "0xa7dff094fe129c92f135d32a2babff54699ec670145e8b8dc4646dbb673a80a8",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "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": "mechanical",
    "difficulty_delta": 3,
    "domain": "Structural Mechanics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.stress_intensity",
      "L.paris_growth",
      "L.life_integrate",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "crack_meter",
    "solution_space": "fatigue_life_curve",
    "sub_domain": "da/dN = C * (delta K)^m crack growth",
    "title": "Fatigue \u2014 Paris law crack growth"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fatigue_forward"
    ],
    "allowed_omega_dimensions": [
      "N_cycles",
      "SNR_dB",
      "C_error",
      "m_error",
      "threshold_delta_K_error",
      "C_error",
      "m_error",
      "threshold_delta_K_error"
    ],
    "allowed_problem_classes": [
      "fatigue"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "fatigue_forward",
      "input_format": "measurement_only",
      "omega": {
        "C_error": 0.0,
        "N_cycles": 1000000.0,
        "SNR_dB": 30,
        "m_error": 0.0,
        "threshold_delta_K_error": 0.0
      },
      "problem_class": "fatigue"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "C_error": [
        0.0,
        0.3
      ],
      "N_cycles": [
        1000.0,
        10000000000.0
      ],
      "SNR_dB": [
        0,
        40
      ],
      "m_error": [
        0.0,
        0.1
      ],
      "threshold_delta_K_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "da/dN = C * (delta K)^m crack growth",
  "title": "Fatigue \u2014 Paris law crack growth"
}

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