L1 ⚛ L1-026 ⊙ Testnet

Single-Pixel Imaging (random basis compressive sensing)

Compressive Imaging · Single-pixel / single-detector imaging

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⬇ principle.md ⬇ principle.json

Fork L1-026

⬇ L1-026.md ⬇ L1-026.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-026 (Single-Pixel Imaging (random basis compressive sensing)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-026.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-026.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 = `D.scalar` ∫_A dA `L.inner_product` `S.pattern.random` x + n,    n ~ 𝒩(0, σ²)

world state x (2D spatial)

→

S · pattern · random `S.pattern.random`

→

L · inner product `L.inner_product`

→

Spatial integration ∫_A dA

→

D · scalar `D.scalar`

→

observation y (photon detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-026.md

# ⚛ L1 Principle — Single-Pixel Imaging (random basis compressive sensing) **ID:** `L1-026` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Compressive Imaging — *Single-pixel / single-detector imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547811 --- ## 🧠 1. Introduction **Single-Pixel Imaging (random basis compressive sensing)** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Single-pixel / single-detector imaging** sub-domain of **Compressive Imaging**. Measurements consist of photons collected by an optical detector via a **structured illumination** sensing mechanism. The forward operator applies, in order: S · pattern · random operator; L · inner product operator; pixel-level spatial averaging on the detector; D · scalar operator. Observations are corrupted by additive Gaussian noise. Underdetermined (m << n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m >= C * s * log(n/s) for s-sparse signals in a known basis. ## ⚙ 2. Forward Model Physical chain: **x** → S · pattern · random → L · inner product → Spatial integration → D · scalar → **y** (detector). ``` y = `D.scalar` ∫_A dA `L.inner_product` `S.pattern.random` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.pattern.random` | S · pattern · random operator | | `L.inner_product` | L · inner product operator | | `int.spatial` | Pixel-level spatial averaging on the detector | | `D.scalar` | D · scalar operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Compressive Imaging | | Sub domain | Single-pixel / single-detector imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_spatial | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Underdetermined (m << n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m >= C * s * log(n/s) for s-sparse signals in a known basis. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `compressed_sensing_recovery` · **Forward operator:** `random_projection` **Center point:** | Parameter | Unit | Value | |---|---|---| | N pixels | — | 4096 | | Gain alpha | — | 0 | | Illum sigma | — | 0 | | Noise level | — | 0.01 | | Sampling ratio | — | 0.25 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N pixels | — | 1024 – 65536 | | Gain alpha | — | 0.0 – 0.003 | | Dark offset | — | 0.0 – 0.02 | | Illum sigma | — | 0.0 – 15.0 | | Noise level | — | 0.001 – 0.05 | | Sampling ratio | — | 0.05 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `4000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9530ddad080c15de3e2194d2487f390339dd06a6f57560f5c6196e85c3c655cb` - **Chain tx hash:** `0xdb29b0671dfe88bafb7b42624f90e28dd67bf064cd72ced85046d7feea520814` - **Chain block:** `41547811` --- ## File Mapping This bundle consists of: `L1-026.md`, `L1-026.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-026.md` | Source of truth — edit this | Human or LLM | | `L1-026.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 `L1-026`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-026-001 Single-Pixel Imaging Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-026",
  "chain_block": 41547811,
  "chain_hash": "0x9530ddad080c15de3e2194d2487f390339dd06a6f57560f5c6196e85c3c655cb",
  "chain_tx_hash": "0xdb29b0671dfe88bafb7b42624f90e28dd67bf064cd72ced85046d7feea520814",
  "domain": "Compressive Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 4000,
    "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": "Underdetermined (m \u003c\u003c n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m \u003e= C * s * log(n/s) for s-sparse signals in a known basis.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Compressive Imaging",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "S.pattern.random",
      "L.inner_product",
      "int.spatial",
      "D.scalar"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "structured_illumination",
    "solution_space": "2D_spatial",
    "sub_domain": "Single-pixel / single-detector imaging",
    "title": "Single-Pixel Imaging (random basis compressive sensing)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "random_projection",
      "hadamard",
      "noiselet",
      "gaussian_sensing"
    ],
    "allowed_omega_dimensions": [
      "n_pixels",
      "sampling_ratio",
      "noise_level",
      "gain_alpha",
      "illum_sigma",
      "dark_offset"
    ],
    "allowed_problem_classes": [
      "compressed_sensing_recovery",
      "sparse_recovery",
      "basis_pursuit"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0 dB PSNR",
      "forward_operator": "random_projection",
      "input_format": "measurement_plus_pattern_matrix",
      "omega": {
        "gain_alpha": 0.0,
        "illum_sigma": 0.0,
        "n_pixels": 4096,
        "noise_level": 0.01,
        "sampling_ratio": 0.25
      },
      "problem_class": "compressed_sensing_recovery"
    },
    "epsilon_bounds": {
      "psnr_db": [
        18.0,
        40.0
      ]
    },
    "omega_bounds": {
      "dark_offset": [
        0.0,
        0.02
      ],
      "gain_alpha": [
        0.0,
        0.003
      ],
      "illum_sigma": [
        0.0,
        15.0
      ],
      "n_pixels": [
        1024,
        65536
      ],
      "noise_level": [
        0.001,
        0.05
      ],
      "sampling_ratio": [
        0.05,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Single-pixel / single-detector imaging",
  "title": "Single-Pixel Imaging (random basis compressive sensing)"
}

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