L1 ⚛ L1-467 ⊙ Testnet

Satellite Orbit Determination

Geodesy · Orbital mechanics

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-467.md

# ⚛ L1 Principle — Satellite Orbit Determination **ID:** `L1-467` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Orbital mechanics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 6D orbital state vector > **📡 Carrier:** RF · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555298 --- ## 🧠 1. Introduction **Satellite Orbit Determination** is a **parameter-estimation problem** whose unknown lives in **6D orbital state vector** space, within the **Orbital mechanics** sub-domain of **Geodesy**. Measurements consist of RF coil signals (typical of MRI) via a **range range rate tracking** sensing mechanism. The forward operator applies, in order: time evolution of the state; S · kalman · orbit filter operator; O · least squares · batch operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered 6D_orbital_state_vector 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 ~= 200); atmospheric_drag_uncertainty 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** → Time derivative → O · least squares · batch → **y** (detector). ``` y = `O.least_squares.batch` ∂_t x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.least_squares.batch` | O · least squares · batch operator | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `S.kalman.orbit_filter` | S · kalman · orbit filter operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Orbital mechanics | | Carrier | RF | | Problem class | parameter_estimation | | Solution space | 6D_orbital_state_vector | | Noise model | gaussian | | Integration axis | orbital_arc | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Existence of the recovered 6D_orbital_state_vector 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 ~= 200); atmospheric_drag_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | position_prediction_error_km | | Secondary | velocity_error_m_s | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `range_range_rate_tracking` **Center point:** | Parameter | Unit | Value | |---|---|---| | Altitude km | km | 500 | | N observations | — | 1000 | | Arc length days | — | 3 | | Drag cd uncertainty | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Altitude km | km | 200 – 36000 | | N observations | — | 50 – 10000 | | Arc length days | — | 0.5 – 10.0 | | Drag cd uncertainty | — | 0.01 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.1 position_prediction_error_km | Metric | Range | |---|---| | Position prediction error km | 0.01 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **position_prediction_error_km**, with κ = `5000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x86246f83246228f4bb276e90e41f317760dc9848e2085c2f9f0c7ffaedca22dd` - **Chain tx hash:** `0x803c02ae02ab4e8f9645574a3ef360e4e99f8dda68d669ed1002fb880a8a2c72` - **Chain block:** `41555298` --- ## File Mapping This bundle consists of: `L1-467.md`, `L1-467.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-467.md` | Source of truth — edit this | Human or LLM | | `L1-467.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 `L1-467`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-467.md).
Regenerate L1-467.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-467-001 Satellite Orbit Determination — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-467",
  "chain_block": 41555298,
  "chain_hash": "0x86246f83246228f4bb276e90e41f317760dc9848e2085c2f9f0c7ffaedca22dd",
  "chain_tx_hash": "0x803c02ae02ab4e8f9645574a3ef360e4e99f8dda68d669ed1002fb880a8a2c72",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 5000,
    "metric": "position_prediction_error_km",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "position_prediction_error_km",
    "regime": "Existence of the recovered 6D_orbital_state_vector 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 ~= 200); atmospheric_drag_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "velocity_error_m_s"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "RF",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "orbital_arc",
    "noise_model": "gaussian",
    "primitives": [
      "D.time",
      "S.kalman.orbit_filter",
      "O.least_squares.batch"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "range_range_rate_tracking",
    "solution_space": "6D_orbital_state_vector",
    "sub_domain": "Orbital mechanics",
    "title": "Satellite Orbit Determination"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "range_range_rate_tracking"
    ],
    "allowed_omega_dimensions": [
      "N_observations",
      "arc_length_days",
      "drag_Cd_uncertainty",
      "altitude_km"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.1 position_prediction_error_km",
      "forward_operator": "range_range_rate_tracking",
      "input_format": "measurement_only",
      "omega": {
        "N_observations": 1000,
        "altitude_km": 500,
        "arc_length_days": 3.0,
        "drag_Cd_uncertainty": 0.1
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "position_prediction_error_km": [
        0.01,
        5.0
      ]
    },
    "omega_bounds": {
      "N_observations": [
        50,
        10000
      ],
      "altitude_km": [
        200,
        36000
      ],
      "arc_length_days": [
        0.5,
        10.0
      ],
      "drag_Cd_uncertainty": [
        0.01,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Orbital mechanics",
  "title": "Satellite Orbit Determination"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.