L1 ⚛ L1-237 ⊙ Testnet

Radar Cross-Section — backscatter reconstruction

Electromagnetics · Monostatic / bistatic RCS

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-237

⬇ L1-237.md ⬇ L1-237.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-237 (Radar Cross-Section — backscatter reconstruction) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-237.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-237.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.coherent_sum` `L.scatter_target` `L.incident_pw` x + n,    n ~ 𝒩(0, σ²)

world state x (rcs vs aspect)

→

L · incident pw `L.incident_pw`

→

L · scatter target `L.scatter_target`

→

L · coherent sum `L.coherent_sum`

→

Spatial integration ∫_A dA

→

observation y (em detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-237.md

# ⚛ L1 Principle — Radar Cross-Section — backscatter reconstruction **ID:** `L1-237` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Monostatic / bistatic RCS* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** rcs vs aspect > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553987 --- ## 🧠 1. Introduction **Radar Cross-Section — backscatter reconstruction** is a **linear inverse problem** whose unknown lives in **rcs vs aspect** space, within the **Monostatic / bistatic RCS** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **radar echo** sensing mechanism. The forward operator applies, in order: L · incident pw operator; L · scatter target operator; L · coherent sum operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · incident pw → L · scatter target → L · coherent sum → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.coherent_sum` `L.scatter_target` `L.incident_pw` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.incident_pw` | L · incident pw operator | | `L.scatter_target` | L · scatter target operator | | `L.coherent_sum` | L · coherent sum operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Monostatic / bistatic RCS | | Carrier | em | | Problem class | linear_inverse | | Solution space | rcs_vs_aspect | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | RCS_error_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `rcs` · **Forward operator:** `rcs_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N freqs | — | 32 | | N angles | — | 361 | | Freq ghz | GHz | 10 | | Freq error | — | 0 | | Range error | — | 0 | | Material error | — | 0 | | Target orientation error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | -5 – 40 | | N freqs | — | 1 – 512 | | N angles | — | 36 – 36000 | | Freq ghz | GHz | 0.1 – 300 | | Freq error | — | 0.0 – 0.02 | | Range error | — | 0.0 – 1.0 | | Material error | — | 0.0 – 0.1 | | Target orientation error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 | Metric | Range | |---|---| | Rcs db | 0.3 – 20.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **RCS_error_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe27c89cd980325966a1b34e66546f563006d702fcf8000f6274d633214802bb5` - **Chain tx hash:** `0xb6f0e14d2e34e9d8d1c99a022751d39066da9b5ae0ab908c916b2b178ec40fea` - **Chain block:** `41553987` --- ## File Mapping This bundle consists of: `L1-237.md`, `L1-237.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-237.md` | Source of truth — edit this | Human or LLM | | `L1-237.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 `L1-237`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-237-001 Radar Cross-Section — backscatter reconstruction Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-237",
  "chain_block": 41553987,
  "chain_hash": "0xe27c89cd980325966a1b34e66546f563006d702fcf8000f6274d633214802bb5",
  "chain_tx_hash": "0xb6f0e14d2e34e9d8d1c99a022751d39066da9b5ae0ab908c916b2b178ec40fea",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "RCS_error_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "RCS_error_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.incident_pw",
      "L.scatter_target",
      "L.coherent_sum",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "radar_echo",
    "solution_space": "rcs_vs_aspect",
    "sub_domain": "Monostatic / bistatic RCS",
    "title": "Radar Cross-Section \u2014 backscatter reconstruction"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "rcs_forward"
    ],
    "allowed_omega_dimensions": [
      "N_freqs",
      "N_angles",
      "freq_GHz",
      "SNR_dB",
      "target_orientation_error",
      "material_error",
      "freq_error",
      "range_error",
      "target_orientation_error",
      "material_error",
      "freq_error",
      "range_error"
    ],
    "allowed_problem_classes": [
      "rcs"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0",
      "forward_operator": "rcs_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_angles": 361,
        "N_freqs": 32,
        "SNR_dB": 25,
        "freq_GHz": 10,
        "freq_error": 0.0,
        "material_error": 0.0,
        "range_error": 0.0,
        "target_orientation_error": 0.0
      },
      "problem_class": "rcs"
    },
    "epsilon_bounds": {
      "RCS_dB": [
        0.3,
        20.0
      ]
    },
    "omega_bounds": {
      "N_angles": [
        36,
        36000
      ],
      "N_freqs": [
        1,
        512
      ],
      "SNR_dB": [
        -5,
        40
      ],
      "freq_GHz": [
        0.1,
        300
      ],
      "freq_error": [
        0.0,
        0.02
      ],
      "material_error": [
        0.0,
        0.1
      ],
      "range_error": [
        0.0,
        1.0
      ],
      "target_orientation_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Monostatic / bistatic RCS",
  "title": "Radar Cross-Section \u2014 backscatter reconstruction"
}

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