L1 ⚛ L1-469 ⊙ Testnet

LiDAR Point Cloud 3D Mapping

Geodesy · Airborne laser scanning

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⬇ L1-469.md

# ⚛ L1 Principle — LiDAR Point Cloud 3D Mapping **ID:** `L1-469` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Airborne laser scanning* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 3D point cloud > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555299 --- ## 🧠 1. Introduction **LiDAR Point Cloud 3D Mapping** is a **parameter-estimation problem** whose unknown lives in **3D point cloud** space, within the **Airborne laser scanning** sub-domain of **Geodesy**. Measurements consist of photons collected by an optical detector via a **time of flight lidar** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · boresight · calibration operator; O · icp · registration operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D_point_cloud 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 ~= 20); IMU_drift_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → S · boresight · calibration → O · icp · registration → **y** (detector). ``` y = `O.icp.registration` `S.boresight.calibration` f(·) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.boresight.calibration` | S · boresight · calibration operator | | `O.icp.registration` | O · icp · registration operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Airborne laser scanning | | Carrier | photon | | Problem class | parameter_estimation | | Solution space | 3D_point_cloud | | Noise model | gaussian | | Integration axis | 3d_scan_volume | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered 3D_point_cloud 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 ~= 20); IMU_drift_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | vertical_accuracy_RMSE_cm | | Secondary | horizontal_accuracy_RMSE_cm | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `time_of_flight_lidar` **Center point:** | Parameter | Unit | Value | |---|---|---| | Imu drift deg hr | — | 0.01 | | N points million | — | 10 | | Point density m2 | — | 10 | | Flight altitude m | m | 1000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Imu drift deg hr | — | 0.001 – 0.1 | | N points million | — | 0.1 – 1000 | | Point density m2 | — | 1 – 100 | | Flight altitude m | m | 100 – 5000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 vertical_accuracy_RMSE_cm | Metric | Range | |---|---| | Vertical accuracy rmse cm | 1.0 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **vertical_accuracy_RMSE_cm**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4a56d139c601d19f8f5b054ca578dfe5c874dee2d1d26a5842b34f646d6b5bd7` - **Chain tx hash:** `0xb92b44160887511e8460cb43316b5cc1b043725cfe5fdd67e1386876f19d120d` - **Chain block:** `41555299` --- ## File Mapping This bundle consists of: `L1-469.md`, `L1-469.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-469.md` | Source of truth — edit this | Human or LLM | | `L1-469.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 `L1-469`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-469.md).
Regenerate L1-469.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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L2-469-001 LiDAR Point Cloud 3D Mapping — Nominal + Mismatch Specs

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📋 JSON metadata

{
  "artifact_id": "L1-469",
  "chain_block": 41555299,
  "chain_hash": "0x4a56d139c601d19f8f5b054ca578dfe5c874dee2d1d26a5842b34f646d6b5bd7",
  "chain_tx_hash": "0xb92b44160887511e8460cb43316b5cc1b043725cfe5fdd67e1386876f19d120d",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "vertical_accuracy_RMSE_cm",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "vertical_accuracy_RMSE_cm",
    "regime": "Existence of the recovered 3D_point_cloud 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 ~= 20); IMU_drift_deg dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "horizontal_accuracy_RMSE_cm"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "3d_scan_volume",
    "noise_model": "gaussian",
    "primitives": [
      "N.pointwise",
      "S.boresight.calibration",
      "O.icp.registration"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "time_of_flight_lidar",
    "solution_space": "3D_point_cloud",
    "sub_domain": "Airborne laser scanning",
    "title": "LiDAR Point Cloud 3D Mapping"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "time_of_flight_lidar"
    ],
    "allowed_omega_dimensions": [
      "N_points_million",
      "flight_altitude_m",
      "point_density_m2",
      "IMU_drift_deg_hr"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "5.0 vertical_accuracy_RMSE_cm",
      "forward_operator": "time_of_flight_lidar",
      "input_format": "measurement_only",
      "omega": {
        "IMU_drift_deg_hr": 0.01,
        "N_points_million": 10,
        "flight_altitude_m": 1000,
        "point_density_m2": 10
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "vertical_accuracy_RMSE_cm": [
        1.0,
        50.0
      ]
    },
    "omega_bounds": {
      "IMU_drift_deg_hr": [
        0.001,
        0.1
      ],
      "N_points_million": [
        0.1,
        1000
      ],
      "flight_altitude_m": [
        100,
        5000
      ],
      "point_density_m2": [
        1,
        100
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Airborne laser scanning",
  "title": "LiDAR Point Cloud 3D Mapping"
}

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