L1 ⚛ L1-100 ⊙ Testnet

Synthetic Aperture Radar (SAR) — range-Doppler coherent imaging

Remote Sensing · Microwave coherent imaging

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-100.md

# ⚛ L1 Principle — Synthetic Aperture Radar (SAR) — range-Doppler coherent imaging **ID:** `L1-100` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Microwave coherent imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D complex scattering > **📡 Carrier:** radio_wave · **🌫 Noise:** speckle > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554185 --- ## 🧠 1. Introduction **Synthetic Aperture Radar (SAR) — range-Doppler coherent imaging** is a **nonlinear inverse problem** whose unknown lives in **2D complex scattering** space, within the **Microwave coherent imaging** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **sar coherent imaging** sensing mechanism. The forward operator applies, in order: L · emit · chirp operator; S · scan · platform operator; L · pulse compression operator; L · range doppler operator; pixel-level spatial averaging on the detector. Observations are corrupted by multiplicative speckle from coherent imaging. Existence of the recovered 2D complex scattering is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 20); platform_motion_error dominates the stability cliff; ionospheric_phase and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → L · emit · chirp → S · scan · platform → L · pulse compression → L · range doppler → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.range_doppler` `L.pulse_compression` `S.scan.platform` `L.emit.chirp` x · η, η ~ speckle (multiplicative) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.chirp` | L · emit · chirp operator | | `S.scan.platform` | S · scan · platform operator | | `L.pulse_compression` | L · pulse compression operator | | `L.range_doppler` | L · range doppler operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Microwave coherent imaging | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_complex_scattering | | Noise model | speckle | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 2D complex scattering is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 20); platform_motion_error dominates the stability cliff; ionospheric_phase and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `sar_range_doppler` · **Forward operator:** `sar_range_doppler_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 8192 | | W | px | 8192 | | Snr db | dB | 15 | | Pixel m | m | 3 | | N pulses | — | 2048 | | Lambda cm | — | 5.6 | | Ionospheric phase | — | 0 | | Platform motion error | — | 0 | | Speckle coherence loss | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 32768 | | W | px | 1024 – 32768 | | Snr db | dB | 0.0 – 30.0 | | Pixel m | m | 0.3 – 30 | | N pulses | — | 256 – 16384 | | Lambda cm | — | 0.5 – 30 | | Layover shadow | — | 0.0 – 0.3 | | Ionospheric phase | — | 0.0 – 2.0 | | Platform motion error | — | 0.0 – 1.0 | | Speckle coherence loss | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x59a24287101a429839669a5b318a683ffd8aaf242c7128db57f8c0bf18118353` - **Chain tx hash:** `0xffd9dd8d05128c88c52d826e619483f4783881ab8ce004299ff20012cc655259` - **Chain block:** `41554185` --- ## File Mapping This bundle consists of: `L1-100.md`, `L1-100.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-100.md` | Source of truth — edit this | Human or LLM | | `L1-100.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 `L1-100`._ _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 (L1-100.md).
Regenerate L1-100.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 ▾

L2-100-001 Synthetic Aperture Radar (SAR) — range-Doppler coherent imaging Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-100",
  "chain_block": 41554185,
  "chain_hash": "0x59a24287101a429839669a5b318a683ffd8aaf242c7128db57f8c0bf18118353",
  "chain_tx_hash": "0xffd9dd8d05128c88c52d826e619483f4783881ab8ce004299ff20012cc655259",
  "domain": "Remote Sensing",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D complex scattering is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 20); platform_motion_error dominates the stability cliff; ionospheric_phase and the remaining mismatch parameters contribute higher-order bias terms. Multiplicative speckle (rayleigh amplitude / exponential intensity) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Remote Sensing",
    "integration_axis": "angular",
    "noise_model": "speckle",
    "primitives": [
      "L.emit.chirp",
      "S.scan.platform",
      "L.pulse_compression",
      "L.range_doppler",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "sar_coherent_imaging",
    "solution_space": "2D_complex_scattering",
    "sub_domain": "Microwave coherent imaging",
    "title": "Synthetic Aperture Radar (SAR) \u2014 range-Doppler coherent imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "sar_range_doppler_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_m",
      "lambda_cm",
      "N_pulses",
      "platform_motion_error",
      "ionospheric_phase",
      "speckle_coherence_loss",
      "SNR_dB",
      "platform_motion_error",
      "ionospheric_phase",
      "speckle_coherence_loss",
      "layover_shadow"
    ],
    "allowed_problem_classes": [
      "sar_range_doppler"
    ],
    "center_spec": {
      "epsilon_fn_center": "18.0",
      "forward_operator": "sar_range_doppler_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 8192,
        "N_pulses": 2048,
        "SNR_dB": 15.0,
        "W": 8192,
        "ionospheric_phase": 0.0,
        "lambda_cm": 5.6,
        "pixel_m": 3.0,
        "platform_motion_error": 0.0,
        "speckle_coherence_loss": 0.0
      },
      "problem_class": "sar_range_doppler"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        1024,
        32768
      ],
      "N_pulses": [
        256,
        16384
      ],
      "SNR_dB": [
        0.0,
        30.0
      ],
      "W": [
        1024,
        32768
      ],
      "ionospheric_phase": [
        0.0,
        2.0
      ],
      "lambda_cm": [
        0.5,
        30
      ],
      "layover_shadow": [
        0.0,
        0.3
      ],
      "pixel_m": [
        0.3,
        30
      ],
      "platform_motion_error": [
        0.0,
        1.0
      ],
      "speckle_coherence_loss": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Microwave coherent imaging",
  "title": "Synthetic Aperture Radar (SAR) \u2014 range-Doppler coherent imaging"
}

🎁

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.