L1 ⚛ L1-211 ⊙ Testnet

Mindlin-Reissner Plate — thick-plate with shear

Structural Mechanics · Shear-deformable plate theory

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⬇ L1-211.md

# ⚛ L1 Principle — Mindlin-Reissner Plate — thick-plate with shear **ID:** `L1-211` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Shear-deformable plate theory* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** plate w phi 2D > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554010 --- ## 🧠 1. Introduction **Mindlin-Reissner Plate — thick-plate with shear** is a **linear inverse problem** whose unknown lives in **plate w phi 2D** space, within the **Shear-deformable plate theory** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **dic strain** sensing mechanism. The forward operator applies, in order: L · shear factor operator; L · bending operator; L · coupled w phi 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 · shear factor → L · bending → L · coupled w phi → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.coupled_w_phi` `L.bending` `L.shear_factor` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.shear_factor` | L · shear factor operator | | `L.bending` | L · bending operator | | `L.coupled_w_phi` | L · coupled w phi operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Shear-deformable plate theory | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | plate_w_phi_2D | | Noise model | gaussian | | Integration axis | spatial | | 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:** `mindlin` · **Forward operator:** `mindlin_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 64 | | W | px | 64 | | Snr db | dB | 30 | | D error | — | 0 | | G error | — | 0 | | Bc error | — | 0 | | N sensors | — | 64 | | K shear error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 16 – 1024 | | W | px | 16 – 1024 | | Snr db | dB | 0 – 40 | | D error | — | 0.0 – 0.1 | | G error | — | 0.0 – 0.1 | | Bc error | — | 0.0 – 0.2 | | N sensors | — | 4 – 10000 | | K shear error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.5 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xefe8cb830821341fb6412a505f5009b67474b3739db5b4b8815207cb017345dd` - **Chain tx hash:** `0x31126860980e316071a885dd06778e1dd61c14d412c1468819f991d19ed8dac8` - **Chain block:** `41554010` --- ## File Mapping This bundle consists of: `L1-211.md`, `L1-211.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-211.md` | Source of truth — edit this | Human or LLM | | `L1-211.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 `L1-211`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-211.md).
Regenerate L1-211.json so every field matches the Markdown.
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L2-211-001 Mindlin-Reissner Plate — thick-plate with shear Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-211",
  "chain_block": 41554010,
  "chain_hash": "0xefe8cb830821341fb6412a505f5009b67474b3739db5b4b8815207cb017345dd",
  "chain_tx_hash": "0x31126860980e316071a885dd06778e1dd61c14d412c1468819f991d19ed8dac8",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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      "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": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.shear_factor",
      "L.bending",
      "L.coupled_w_phi",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "dic_strain",
    "solution_space": "plate_w_phi_2D",
    "sub_domain": "Shear-deformable plate theory",
    "title": "Mindlin-Reissner Plate \u2014 thick-plate with shear"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "W",
      "N_sensors",
      "SNR_dB",
      "k_shear_error",
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      "G_error",
      "bc_error",
      "k_shear_error",
      "D_error",
      "G_error",
      "bc_error"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "26.5",
      "forward_operator": "mindlin_forward",
      "input_format": "measurement_only",
      "omega": {
        "D_error": 0.0,
        "G_error": 0.0,
        "H": 64,
        "N_sensors": 64,
        "SNR_dB": 30,
        "W": 64,
        "bc_error": 0.0,
        "k_shear_error": 0.0
      },
      "problem_class": "mindlin"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "D_error": [
        0.0,
        0.1
      ],
      "G_error": [
        0.0,
        0.1
      ],
      "H": [
        16,
        1024
      ],
      "N_sensors": [
        4,
        10000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        16,
        1024
      ],
      "bc_error": [
        0.0,
        0.2
      ],
      "k_shear_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Shear-deformable plate theory",
  "title": "Mindlin-Reissner Plate \u2014 thick-plate with shear"
}

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