L1 ⚛ L1-457 ⊙ Testnet

Hydrodynamic Lubrication (Reynolds Equation)

Robotics · Tribology

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⬇ L1-457.md

# ⚛ L1 Principle — Hydrodynamic Lubrication (Reynolds Equation) **ID:** `L1-457` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Robotics — *Tribology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** pressure film field > **📡 Carrier:** N/A · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555279 --- ## 🧠 1. Introduction **Hydrodynamic Lubrication (Reynolds Equation)** is a **parameter-estimation problem** whose unknown lives in **pressure film field** space, within the **Tribology** sub-domain of **Robotics**. Measurements consist of N/A via a **pressure film measurement** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · fdm · cavitation constraint operator; O · least squares · bearing operator. Observations are corrupted by measurement gaussian. Existence of the recovered pressure_film_field is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); viscosity_temperature_dependence dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → S · fdm · cavitation constraint → O · least squares · bearing → **y** (detector). ``` y = `O.least_squares.bearing` `S.fdm.cavitation_constraint` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.fdm.cavitation_constraint` | S · fdm · cavitation constraint operator | | `O.least_squares.bearing` | O · least squares · bearing operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Robotics | | Sub domain | Tribology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | pressure_film_field | | Noise model | measurement_gaussian | | Integration axis | thin_film_domain | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered pressure_film_field is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); viscosity_temperature_dependence dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | pressure_field_RMSE_MPa | | Secondary | load_capacity_RMSE_N | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `pressure_film_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N grid x | — | 50 | | Speed rpm | — | 3000 | | Viscosity pa s | s | 0.05 | | Eccentricity ratio e | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N grid x | — | 10 – 200 | | Speed rpm | — | 100 – 100000 | | Viscosity pa s | s | 0.001 – 1.0 | | Eccentricity ratio e | — | 0.0 – 0.9 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 pressure_field_RMSE_MPa | Metric | Range | |---|---| | Pressure field rmse mpa | 0.05 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **pressure_field_RMSE_MPa**, with κ = `3000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb43e3e0cba2d00b611e1a7d0ecd8b06fc0cd15de90bf464ef107101558111107` - **Chain tx hash:** `0xad3ae721d03843349c39bc7d9e55bdc04ba5a468d2c574a76f6c675e2cb6fde1` - **Chain block:** `41555279` --- ## File Mapping This bundle consists of: `L1-457.md`, `L1-457.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-457.md` | Source of truth — edit this | Human or LLM | | `L1-457.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 `L1-457`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-457-001 Hydrodynamic Lubrication (Reynolds Equation) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555279,
  "chain_hash": "0xb43e3e0cba2d00b611e1a7d0ecd8b06fc0cd15de90bf464ef107101558111107",
  "chain_tx_hash": "0xad3ae721d03843349c39bc7d9e55bdc04ba5a468d2c574a76f6c675e2cb6fde1",
  "domain": "Robotics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 3000,
    "metric": "pressure_field_RMSE_MPa",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "pressure_field_RMSE_MPa",
    "regime": "Existence of the recovered pressure_film_field is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); viscosity_temperature_dependence dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "load_capacity_RMSE_N"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Robotics",
    "integration_axis": "thin_film_domain",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.space",
      "S.fdm.cavitation_constraint",
      "O.least_squares.bearing"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "pressure_film_measurement",
    "solution_space": "pressure_film_field",
    "sub_domain": "Tribology",
    "title": "Hydrodynamic Lubrication (Reynolds Equation)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "pressure_film_measurement"
    ],
    "allowed_omega_dimensions": [
      "N_grid_x",
      "eccentricity_ratio_e",
      "speed_RPM",
      "viscosity_Pa_s"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.5 pressure_field_RMSE_MPa",
      "forward_operator": "pressure_film_measurement",
      "input_format": "measurement_only",
      "omega": {
        "N_grid_x": 50,
        "eccentricity_ratio_e": 0.5,
        "speed_RPM": 3000,
        "viscosity_Pa_s": 0.05
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "pressure_field_RMSE_MPa": [
        0.05,
        5.0
      ]
    },
    "omega_bounds": {
      "N_grid_x": [
        10,
        200
      ],
      "eccentricity_ratio_e": [
        0.0,
        0.9
      ],
      "speed_RPM": [
        100,
        100000
      ],
      "viscosity_Pa_s": [
        0.001,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Tribology",
  "title": "Hydrodynamic Lubrication (Reynolds Equation)"
}

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