L1 ⚛ L1-070 ⊙ Testnet

Ptychography (scanning coherent diffraction with probe overlap)

Coherent Imaging · Scanning coherent diffraction

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-070.md

# ⚛ L1 Principle — Ptychography (scanning coherent diffraction with probe overlap) **ID:** `L1-070` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Coherent Imaging — *Scanning coherent diffraction* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554169 --- ## 🧠 1. Introduction **Ptychography (scanning coherent diffraction with probe overlap)** is a **nonlinear inverse problem** whose unknown lives in **complex 2D** space, within the **Scanning coherent diffraction** sub-domain of **Coherent Imaging**. Measurements consist of photons collected by an optical detector via a **coherent diffraction scanning** sensing mechanism. The forward operator applies, in order: S · scan · grid operator; L · hadamard · complex operator; F · fourier operator; phase is lost; only intensity is measured; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Non-convex phaseless recovery; Hayes ambiguity (global phase, conjugate flip, constant offset) resolved by overlap redundancy and probe structure. Oversampling sigma >= 2 per dim combined with overlap >= 0.6 guarantees local-minimum convergence for iterative projection solvers. ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · grid → L · hadamard · complex → F · fourier → Magnitude-squared → Spatial integration → **y** (detector). ``` y = ∫_A dA |·|² `F.fourier` `L.hadamard.complex` `S.scan.grid` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.grid` | S · scan · grid operator | | `L.hadamard.complex` | L · hadamard · complex operator | | `F.fourier` | F · fourier operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Coherent Imaging | | Sub domain | Scanning coherent diffraction | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4.5 | ## 📡 4. Measurement Model Non-convex phaseless recovery; Hayes ambiguity (global phase, conjugate flip, constant offset) resolved by overlap redundancy and probe structure. Oversampling sigma >= 2 per dim combined with overlap >= 0.6 guarantees local-minimum convergence for iterative projection solvers. | Metric | Value | |---|---| | Metric | FRC_half_bit_resolution | | Secondary | PSNR_dB | ## 📏 5. Operating Range (Ω) **Center problem class:** `ptychographic_recovery` · **Forward operator:** `ptychographic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | J scan | — | 400 | | Probe size | — | 128 | | Photon count | — | 1000 | | Overlap fraction | — | 0.7 | | Partial coherence | — | 1 | | Probe position error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | J scan | — | 50 – 10000 | | Probe size | — | 32 – 512 | | Photon count | — | 10 – 100000 | | Overlap fraction | — | 0.3 – 0.85 | | Partial coherence | — | 0.7 – 1.0 | | Probe shape drift | — | 0.0 – 0.2 | | Background scatter | — | 0.0 – 0.1 | | Probe position error | — | 0.0 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB PSNR at center probe | Metric | Range | |---|---| | Psnr db | 15.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **FRC_half_bit_resolution**, with κ = `8000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf373831010f2638f47561ccac9b634dad334d4ada252d5202810cbc0b5a866c5` - **Chain tx hash:** `0x61ced87669952be19bd10e361dac7046fea3cfec96ce40fab72d9843da129b83` - **Chain block:** `41554169` --- ## File Mapping This bundle consists of: `L1-070.md`, `L1-070.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-070.md` | Source of truth — edit this | Human or LLM | | `L1-070.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 `L1-070`._ _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 (L1-070.md).
Regenerate L1-070.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 ▾

L2-070-001 Ptychography Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-070",
  "chain_block": 41554169,
  "chain_hash": "0xf373831010f2638f47561ccac9b634dad334d4ada252d5202810cbc0b5a866c5",
  "chain_tx_hash": "0x61ced87669952be19bd10e361dac7046fea3cfec96ce40fab72d9843da129b83",
  "domain": "Coherent Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 8000,
    "metric": "FRC_half_bit_resolution",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "FRC_half_bit_resolution",
    "regime": "Non-convex phaseless recovery; Hayes ambiguity (global phase, conjugate flip, constant offset) resolved by overlap redundancy and probe structure. Oversampling sigma \u003e= 2 per dim combined with overlap \u003e= 0.6 guarantees local-minimum convergence for iterative projection solvers.",
    "secondary": "PSNR_dB"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Coherent Imaging",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
      "S.scan.grid",
      "L.hadamard.complex",
      "F.fourier",
      "L.modulus_squared",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "coherent_diffraction_scanning",
    "solution_space": "complex_2D",
    "sub_domain": "Scanning coherent diffraction",
    "title": "Ptychography (scanning coherent diffraction with probe overlap)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ptychographic_forward",
      "fourier_ptychography",
      "bragg_ptychography"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "probe_size",
      "J_scan",
      "overlap_fraction",
      "photon_count",
      "probe_position_error",
      "probe_shape_drift",
      "partial_coherence",
      "background_scatter"
    ],
    "allowed_problem_classes": [
      "ptychographic_recovery",
      "fourier_ptychography"
    ],
    "center_spec": {
      "epsilon_fn_center": "30.0 dB PSNR at center probe",
      "forward_operator": "ptychographic_forward",
      "input_format": "diffraction_patterns_plus_scan_positions",
      "omega": {
        "H": 512,
        "J_scan": 400,
        "W": 512,
        "overlap_fraction": 0.7,
        "partial_coherence": 1.0,
        "photon_count": 1000,
        "probe_position_error": 0.0,
        "probe_size": 128
      },
      "problem_class": "ptychographic_recovery"
    },
    "epsilon_bounds": {
      "psnr_db": [
        15.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        4096
      ],
      "J_scan": [
        50,
        10000
      ],
      "W": [
        128,
        4096
      ],
      "background_scatter": [
        0.0,
        0.1
      ],
      "overlap_fraction": [
        0.3,
        0.85
      ],
      "partial_coherence": [
        0.7,
        1.0
      ],
      "photon_count": [
        10,
        100000
      ],
      "probe_position_error": [
        0.0,
        2.0
      ],
      "probe_shape_drift": [
        0.0,
        0.2
      ],
      "probe_size": [
        32,
        512
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Scanning coherent diffraction",
  "title": "Ptychography (scanning coherent diffraction with probe overlap)"
}

🎁

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.