L1 ⚛ L1-109 ⊙ Testnet

Polarimetric SAR (PolSAR) — full-polarimetric decomposition

Remote Sensing · Polarimetric scattering analysis

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

🎁 Contribute & earn PWM

Improve L1-109 — submit with or without uploading. Accepted submissions earn the 1/16 modify share of A(t).

✨ Submit without uploading free check · 1×

One click — no files, no typing. We submit a check of L1-109 for you; it goes through review and earns the 1/16 share once. One free no-upload Principle per account.

You'll be asked to log in first — then it's one click, no files.

⬆ Or submit by uploading your files

Upload your .md + .json as a modification of L1-109. Unlimited.

🛠 Helper: build your files in ChatGPT / Gemini / Claude

Layer template

⬇ principle.md ⬇ principle.json

Fork L1-109

⬇ L1-109.md ⬇ L1-109.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-109 (Polarimetric SAR (PolSAR) — full-polarimetric decomposition) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-109.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-109.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_A dA `L.polarimetric_decompose` `L.scattering_matrix` `L.emit.polarized_chirp` x · η,    η ~ speckle (multiplicative)

world state x (polarization decomposition map)

→

L · emit · polarized chirp `L.emit.polarized_chirp`

→

L · scattering matrix `L.scattering_matrix`

→

L · polarimetric decompose `L.polarimetric_decompose`

→

Spatial integration ∫_A dA

→

observation y (radio wave detector)

Noise: multiplicative speckle from coherent imaging

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-109.md

# ⚛ L1 Principle — Polarimetric SAR (PolSAR) — full-polarimetric decomposition **ID:** `L1-109` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Polarimetric scattering analysis* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** polarization decomposition map > **📡 Carrier:** radio_wave · **🌫 Noise:** speckle > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Polarimetric SAR (PolSAR) — full-polarimetric decomposition** is a **linear inverse problem** whose unknown lives in **polarization decomposition map** space, within the **Polarimetric scattering analysis** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **polarimetric sar** sensing mechanism. The forward operator applies, in order: L · emit · polarized chirp operator; L · scattering matrix operator; L · polarimetric decompose operator; pixel-level spatial averaging on the detector. Observations are corrupted by multiplicative speckle from coherent imaging. Existence of the recovered polarization decomposition map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 16); polarization_crosstalk dominates the stability cliff; calibration_drift 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 · polarized chirp → L · scattering matrix → L · polarimetric decompose → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.polarimetric_decompose` `L.scattering_matrix` `L.emit.polarized_chirp` x · η, η ~ speckle (multiplicative) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.polarized_chirp` | L · emit · polarized chirp operator | | `L.scattering_matrix` | L · scattering matrix operator | | `L.polarimetric_decompose` | L · polarimetric decompose operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Polarimetric scattering analysis | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | polarization_decomposition_map | | Noise model | speckle | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered polarization decomposition map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 16); polarization_crosstalk dominates the stability cliff; calibration_drift 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:** `polsar` · **Forward operator:** `polsar_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 4096 | | W | px | 4096 | | Snr db | dB | 18 | | Pixel m | m | 5 | | Lambda cm | — | 5.6 | | Faraday rotation | — | 0 | | Calibration drift | — | 0 | | Polarization crosstalk | — | -30 | | Speckle coherence loss | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 16384 | | W | px | 1024 – 16384 | | Snr db | dB | 0.0 – 30.0 | | Pixel m | m | 0.5 – 30 | | Lambda cm | — | 0.5 – 30 | | Faraday rotation | — | 0.0 – 30.0 | | Calibration drift | — | 0.0 – 2.0 | | Polarization crosstalk | — | -40 – -15 | | Speckle coherence loss | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `320` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x48a5b959081504d2b4e5055db65c316af4b9c1244080a512937aff843a755ab3` - **Chain tx hash:** `0x8de4592585236f7b32462e51fd40c9cbb1cae1fbcc27bdba779c34898aae9af3` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-109.md`, `L1-109.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-109.md` | Source of truth — edit this | Human or LLM | | `L1-109.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 `L1-109`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

💬

Ask the PWM AI agent AI

Ask about this Polarimetric SAR (PolSAR) — full-polarimetric decomposition — or how to improve it & earn PWM

Free to search; log in to chat with the agent & earn PWM. How it works ↗

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Digital Twin 1 child ▾

L2-109-001 Polarimetric SAR (PolSAR) — full-polarimetric decomposition Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-109",
  "chain_block": 41554198,
  "chain_hash": "0x48a5b959081504d2b4e5055db65c316af4b9c1244080a512937aff843a755ab3",
  "chain_tx_hash": "0x8de4592585236f7b32462e51fd40c9cbb1cae1fbcc27bdba779c34898aae9af3",
  "domain": "Remote Sensing",
  "hardness_fn": {
    "delta": 5,
    "kappa": 320,
    "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 polarization decomposition map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 16); polarization_crosstalk dominates the stability cliff; calibration_drift 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": 3.8,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Remote Sensing",
    "integration_axis": "spatial",
    "noise_model": "speckle",
    "primitives": [
      "L.emit.polarized_chirp",
      "L.scattering_matrix",
      "L.polarimetric_decompose",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "polarimetric_sar",
    "solution_space": "polarization_decomposition_map",
    "sub_domain": "Polarimetric scattering analysis",
    "title": "Polarimetric SAR (PolSAR) \u2014 full-polarimetric decomposition"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "polsar_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_m",
      "lambda_cm",
      "polarization_crosstalk",
      "calibration_drift",
      "speckle_coherence_loss",
      "faraday_rotation",
      "SNR_dB",
      "polarization_crosstalk",
      "calibration_drift",
      "speckle_coherence_loss",
      "faraday_rotation"
    ],
    "allowed_problem_classes": [
      "polsar"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "polsar_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 4096,
        "SNR_dB": 18.0,
        "W": 4096,
        "calibration_drift": 0.0,
        "faraday_rotation": 0.0,
        "lambda_cm": 5.6,
        "pixel_m": 5,
        "polarization_crosstalk": -30,
        "speckle_coherence_loss": 0.0
      },
      "problem_class": "polsar"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        1024,
        16384
      ],
      "SNR_dB": [
        0.0,
        30.0
      ],
      "W": [
        1024,
        16384
      ],
      "calibration_drift": [
        0.0,
        2.0
      ],
      "faraday_rotation": [
        0.0,
        30.0
      ],
      "lambda_cm": [
        0.5,
        30
      ],
      "pixel_m": [
        0.5,
        30
      ],
      "polarization_crosstalk": [
        -40,
        -15
      ],
      "speckle_coherence_loss": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Polarimetric scattering analysis",
  "title": "Polarimetric SAR (PolSAR) \u2014 full-polarimetric decomposition"
}

🎁

Earn PWM by promoting this to mainnet

• PWM emission on accept — your share of A(t) (1/16 modify · 3/16 new)
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Go to submit ↑

How: use the “Contribute & earn PWM” panel at the top — either Submit without uploading (one click) or upload your files. Then the review runs and, on accept, it’s promoted to mainnet.