L1 ⚛ L1-091 ⊙ Testnet

Off-Axis Electron Holography — nanoscale phase imaging

Electron Microscopy · Electron-beam interferometric phase imaging

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-091.md

# ⚛ L1 Principle — Off-Axis Electron Holography — nanoscale phase imaging **ID:** `L1-091` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Electron-beam interferometric phase imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554184 --- ## 🧠 1. Introduction **Off-Axis Electron Holography — nanoscale phase imaging** is a **linear inverse problem** whose unknown lives in **complex 2D** space, within the **Electron-beam interferometric phase imaging** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **electron interferometry** sensing mechanism. The forward operator applies, in order: L · biprism operator; L · add coherent operator; phase is lost; only intensity is measured; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered complex 2D 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 ~= 12); biprism_stability dominates the stability cliff; fringe_contrast_loss and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · biprism → L · add coherent → Magnitude-squared → Temporal integration → **y** (detector). ``` y = ∫_t dt |·|² `L.add_coherent` `L.biprism` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.biprism` | L · biprism operator | | `L.add_coherent` | L · add coherent operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Electron-beam interferometric phase imaging | | Carrier | electron | | Problem class | linear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered complex 2D 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 ~= 12); biprism_stability dominates the stability cliff; fringe_contrast_loss and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `electron_holography` · **Forward operator:** `electron_holography_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Kv | — | 300 | | Pixel a | — | 0.5 | | Peak electrons | — | 100 | | Biprism stability | — | 1 | | Fringe spacing nm | nm | 2 | | Fringe contrast loss | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 4096 | | W | px | 512 – 4096 | | Kv | — | 200 – 300 | | Pixel a | — | 0.1 – 5.0 | | Peak electrons | — | 10 – 5000 | | Reference drift | — | 0.0 – 0.01 | | Biprism stability | — | 0.5 – 1.0 | | Fringe spacing nm | nm | 0.5 – 10 | | Fringe contrast loss | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8b5044ed6a60c71fe13ac4f0879738b6293f975fbbb8c59f6e933b12c27e6704` - **Chain tx hash:** `0x41d4cc43ad38afa1c67f7b86bf36e66b8411fe7fcaecfb5218e561045df6ee45` - **Chain block:** `41554184` --- ## File Mapping This bundle consists of: `L1-091.md`, `L1-091.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-091.md` | Source of truth — edit this | Human or LLM | | `L1-091.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 `L1-091`._ _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 (L1-091.md).
Regenerate L1-091.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 ▾

L2-091-001 Off-Axis Electron Holography — nanoscale phase imaging Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-091",
  "chain_block": 41554184,
  "chain_hash": "0x8b5044ed6a60c71fe13ac4f0879738b6293f975fbbb8c59f6e933b12c27e6704",
  "chain_tx_hash": "0x41d4cc43ad38afa1c67f7b86bf36e66b8411fe7fcaecfb5218e561045df6ee45",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 240,
    "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 complex 2D 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 ~= 12); biprism_stability dominates the stability cliff; fringe_contrast_loss and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Electron Microscopy",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.biprism",
      "L.add_coherent",
      "L.modulus_squared",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "electron_interferometry",
    "solution_space": "complex_2D",
    "sub_domain": "Electron-beam interferometric phase imaging",
    "title": "Off-Axis Electron Holography \u2014 nanoscale phase imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "electron_holography_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_A",
      "fringe_spacing_nm",
      "kV",
      "peak_electrons",
      "biprism_stability",
      "fringe_contrast_loss",
      "biprism_stability",
      "fringe_contrast_loss",
      "reference_drift"
    ],
    "allowed_problem_classes": [
      "electron_holography"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "electron_holography_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 2048,
        "W": 2048,
        "biprism_stability": 1.0,
        "fringe_contrast_loss": 0.0,
        "fringe_spacing_nm": 2,
        "kV": 300,
        "peak_electrons": 100,
        "pixel_A": 0.5
      },
      "problem_class": "electron_holography"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        512,
        4096
      ],
      "W": [
        512,
        4096
      ],
      "biprism_stability": [
        0.5,
        1.0
      ],
      "fringe_contrast_loss": [
        0.0,
        0.5
      ],
      "fringe_spacing_nm": [
        0.5,
        10
      ],
      "kV": [
        200,
        300
      ],
      "peak_electrons": [
        10,
        5000
      ],
      "pixel_A": [
        0.1,
        5.0
      ],
      "reference_drift": [
        0.0,
        0.01
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Electron-beam interferometric phase imaging",
  "title": "Off-Axis Electron Holography \u2014 nanoscale phase imaging"
}

🎁

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.