L1 ⚛ L1-225 ⊙ Testnet

Hertzian Contact — elastic sphere/cylinder contact

Structural Mechanics · Classical Hertz elastic contact

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⬇ L1-225.md

# ⚛ L1 Principle — Hertzian Contact — elastic sphere/cylinder contact **ID:** `L1-225` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Classical Hertz elastic contact* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** contact pressure area > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554022 --- ## 🧠 1. Introduction **Hertzian Contact — elastic sphere/cylinder contact** is a **linear inverse problem** whose unknown lives in **contact pressure area** space, within the **Classical Hertz elastic contact** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **pressure sensor** sensing mechanism. The forward operator applies, in order: L · hertz theory operator; L · contact pressure operator; L · elastic deformation 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 · hertz theory → L · contact pressure → L · elastic deformation → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.elastic_deformation` `L.contact_pressure` `L.hertz_theory` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.hertz_theory` | L · hertz theory operator | | `L.contact_pressure` | L · contact pressure operator | | `L.elastic_deformation` | L · elastic deformation operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Classical Hertz elastic contact | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | contact_pressure_area | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 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:** `hertz_contact` · **Forward operator:** `hertz_contact_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | F n | N | 100 | | R m | m | 0.01 | | Snr db | dB | 30 | | E error | — | 0 | | Radius error | — | 0 | | Friction error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | F n | N | 0.1 – 10000000.0 | | R m | m | 1e-05 – 10 | | Snr db | dB | 0 – 40 | | E error | — | 0.0 – 0.1 | | Radius error | — | 0.0 – 0.05 | | Friction error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 | 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:** `0xaed109ce04833bd3110a8d40475aec5b928dc1483badc7f8c4a9a3fab57490e6` - **Chain tx hash:** `0xc1bcd2acd904e7843b6cae1d49a2c792ff0664cdd2f6f72fa99b69d1b4e8965f` - **Chain block:** `41554022` --- ## File Mapping This bundle consists of: `L1-225.md`, `L1-225.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-225.md` | Source of truth — edit this | Human or LLM | | `L1-225.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 `L1-225`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-225.md).
Regenerate L1-225.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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L2-225-001 Hertzian Contact — elastic sphere/cylinder contact Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-225",
  "chain_block": 41554022,
  "chain_hash": "0xaed109ce04833bd3110a8d40475aec5b928dc1483badc7f8c4a9a3fab57490e6",
  "chain_tx_hash": "0xc1bcd2acd904e7843b6cae1d49a2c792ff0664cdd2f6f72fa99b69d1b4e8965f",
  "domain": "Structural Mechanics",
  "hardness_fn": {
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    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.hertz_theory",
      "L.contact_pressure",
      "L.elastic_deformation",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "pressure_sensor",
    "solution_space": "contact_pressure_area",
    "sub_domain": "Classical Hertz elastic contact",
    "title": "Hertzian Contact \u2014 elastic sphere/cylinder contact"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "hertz_contact_forward"
    ],
    "allowed_omega_dimensions": [
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      "F_N",
      "SNR_dB",
      "radius_error",
      "E_error",
      "friction_error",
      "radius_error",
      "E_error",
      "friction_error"
    ],
    "allowed_problem_classes": [
      "hertz_contact"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0",
      "forward_operator": "hertz_contact_forward",
      "input_format": "measurement_only",
      "omega": {
        "E_error": 0.0,
        "F_N": 100,
        "R_m": 0.01,
        "SNR_dB": 30,
        "friction_error": 0.0,
        "radius_error": 0.0
      },
      "problem_class": "hertz_contact"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "E_error": [
        0.0,
        0.1
      ],
      "F_N": [
        0.1,
        10000000.0
      ],
      "R_m": [
        1e-05,
        10
      ],
      "SNR_dB": [
        0,
        40
      ],
      "friction_error": [
        0.0,
        0.2
      ],
      "radius_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Classical Hertz elastic contact",
  "title": "Hertzian Contact \u2014 elastic sphere/cylinder contact"
}

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