L1 ⚛ L1-247 ⊙ Testnet

Phase Retrieval — Gerchberg-Saxton / hybrid input-output

Electromagnetics · Non-convex phase recovery from intensity

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⬇ L1-247.md

# ⚛ L1 Principle — Phase Retrieval — Gerchberg-Saxton / hybrid input-output **ID:** `L1-247` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Non-convex phase recovery from intensity* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** complex 2D field > **📡 Carrier:** em · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553989 --- ## 🧠 1. Introduction **Phase Retrieval — Gerchberg-Saxton / hybrid input-output** is a **nonlinear inverse problem** whose unknown lives in **complex 2D field** space, within the **Non-convex phase recovery from intensity** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **intensity camera** sensing mechanism. The forward operator applies, in order: L · fourier transform operator; L · modulus projection operator; L · support projection operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson counting noise. Non-convex; stagnation in local minima common without good initialization. ## ⚙ 2. Forward Model Physical chain: **x** → L · fourier transform → L · modulus projection → L · support projection → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.support_projection` `L.modulus_projection` `L.fourier_transform` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fourier_transform` | L · fourier transform operator | | `L.modulus_projection` | L · modulus projection operator | | `L.support_projection` | L · support projection operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Non-convex phase recovery from intensity | | Carrier | em | | Problem class | nonlinear_inverse | | Solution space | complex_2D_field | | Noise model | poisson | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Non-convex; stagnation in local minima common without good initialization. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `phase_retrieval` · **Forward operator:** `phase_retrieval_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 30 | | Oversampling | — | 2 | | Support error | — | 0 | | Stagnation risk | — | 0 | | Oversampling error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 4096 | | W | px | 64 – 4096 | | Snr db | dB | 0 – 40 | | Oversampling | — | 1.0 – 10.0 | | Support error | — | 0.0 – 0.2 | | Stagnation risk | — | 0.0 – 0.5 | | Oversampling error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x763aebc50168130e949c69ebf43055e392f7ea049eaacffe9bafe59af2172e88` - **Chain tx hash:** `0x634bc618203f2e3950ccfcb55061edf2d86608416da69a5022e39e62d0bfc318` - **Chain block:** `41553989` --- ## File Mapping This bundle consists of: `L1-247.md`, `L1-247.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-247.md` | Source of truth — edit this | Human or LLM | | `L1-247.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 `L1-247`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-247.md).
Regenerate L1-247.json so every field matches the Markdown.
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L2-247-001 Phase Retrieval — Gerchberg-Saxton / hybrid input-output Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553989,
  "chain_hash": "0x763aebc50168130e949c69ebf43055e392f7ea049eaacffe9bafe59af2172e88",
  "chain_tx_hash": "0x634bc618203f2e3950ccfcb55061edf2d86608416da69a5022e39e62d0bfc318",
  "domain": "Electromagnetics",
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  "physics_fingerprint": {
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    "integration_axis": "spatial",
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    "sub_domain": "Non-convex phase recovery from intensity",
    "title": "Phase Retrieval \u2014 Gerchberg-Saxton / hybrid input-output"
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      "SNR_dB": [
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      "support_error": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Non-convex phase recovery from intensity",
  "title": "Phase Retrieval \u2014 Gerchberg-Saxton / hybrid input-output"
}

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