L1 ⚛ L1-014 ⊙ Testnet

Expansion Microscopy (ExM) — physical hydrogel expansion

Microscopy · Sample-side super-resolution via isotropic swelling

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-014.md

# ⚛ L1 Principle — Expansion Microscopy (ExM) — physical hydrogel expansion **ID:** `L1-014` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Sample-side super-resolution via isotropic swelling* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554155 --- ## 🧠 1. Introduction **Expansion Microscopy (ExM) — physical hydrogel expansion** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Sample-side super-resolution via isotropic swelling** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **fluorescence widefield** sensing mechanism. The forward operator applies, in order: L · sample expansion operator; convolution with the Airy disk of a circular aperture; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 2D intensity 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 well-conditioned (kappa_eff ~= 9); expansion_anisotropy dominates the stability cliff; expansion_factor_drift and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise 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 · sample expansion → Airy PSF convolution → Temporal integration → **y** (detector). ``` y = ∫_t dt K_Airy * `L.sample_expansion` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.sample_expansion` | L · sample expansion operator | | `K.psf.airy` | Convolution with the airy disk of a circular aperture | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Sample-side super-resolution via isotropic swelling | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | poisson_gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered 2D intensity 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 well-conditioned (kappa_eff ~= 9); expansion_anisotropy dominates the stability cliff; expansion_factor_drift and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise 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:** `exm` · **Forward operator:** `exm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Na | — | 1.4 | | F expand | — | 4 | | Pixel nm | nm | 65 | | Peak photons | photons | 500 | | Expansion anisotropy | — | 0.01 | | Expansion factor drift | — | 0.01 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Na | — | 1.0 – 1.49 | | F expand | — | 2.0 – 20.0 | | Pixel nm | nm | 30 – 200 | | Peak photons | photons | 50 – 5000 | | Labeling loss | — | 0.0 – 0.3 | | Expansion anisotropy | — | 0.0 – 0.1 | | Expansion factor drift | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 29.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `180` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x58199cb8a72dcc774e6eb7374523c69ff971193ff50bef3f32a33ecc70dd08ec` - **Chain tx hash:** `0xb92916a6b1edab33ba8493d43604696f92b49a5ce5efd0b938503ff0532b707d` - **Chain block:** `41554155` --- ## File Mapping This bundle consists of: `L1-014.md`, `L1-014.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-014.md` | Source of truth — edit this | Human or LLM | | `L1-014.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 `L1-014`._ _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 (L1-014.md).
Regenerate L1-014.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 ▾

L2-014-001 Expansion Microscopy (ExM) — physical hydrogel expansion Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-014",
  "chain_block": 41554155,
  "chain_hash": "0x58199cb8a72dcc774e6eb7374523c69ff971193ff50bef3f32a33ecc70dd08ec",
  "chain_tx_hash": "0xb92916a6b1edab33ba8493d43604696f92b49a5ce5efd0b938503ff0532b707d",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 180,
    "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 2D intensity 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 well-conditioned (kappa_eff ~= 9); expansion_anisotropy dominates the stability cliff; expansion_factor_drift and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise 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": 2.5,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "poisson_gaussian",
    "primitives": [
      "L.sample_expansion",
      "K.psf.airy",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "fluorescence_widefield",
    "solution_space": "2D_intensity",
    "sub_domain": "Sample-side super-resolution via isotropic swelling",
    "title": "Expansion Microscopy (ExM) \u2014 physical hydrogel expansion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "exm_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_nm",
      "NA",
      "F_expand",
      "peak_photons",
      "expansion_anisotropy",
      "expansion_factor_drift",
      "expansion_anisotropy",
      "expansion_factor_drift",
      "labeling_loss"
    ],
    "allowed_problem_classes": [
      "exm"
    ],
    "center_spec": {
      "epsilon_fn_center": "29.0",
      "forward_operator": "exm_forward",
      "input_format": "measurement_only",
      "omega": {
        "F_expand": 4.0,
        "H": 1024,
        "NA": 1.4,
        "W": 1024,
        "expansion_anisotropy": 0.01,
        "expansion_factor_drift": 0.01,
        "peak_photons": 500,
        "pixel_nm": 65
      },
      "problem_class": "exm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "F_expand": [
        2.0,
        20.0
      ],
      "H": [
        256,
        4096
      ],
      "NA": [
        1.0,
        1.49
      ],
      "W": [
        256,
        4096
      ],
      "expansion_anisotropy": [
        0.0,
        0.1
      ],
      "expansion_factor_drift": [
        0.0,
        0.1
      ],
      "labeling_loss": [
        0.0,
        0.3
      ],
      "peak_photons": [
        50,
        5000
      ],
      "pixel_nm": [
        30,
        200
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sample-side super-resolution via isotropic swelling",
  "title": "Expansion Microscopy (ExM) \u2014 physical hydrogel expansion"
}

🎁

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.