L1 ⚛ L1-048 ⊙ Testnet

Fiber-Optic Endoscopy

Medical Imaging · Flexible multimode / coherent bundle endoscopy

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-048.md

# ⚛ L1 Principle — Fiber-Optic Endoscopy **ID:** `L1-048` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Flexible multimode / coherent bundle endoscopy* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553385 --- ## 🧠 1. Introduction **Fiber-Optic Endoscopy** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Flexible multimode / coherent bundle endoscopy** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **fiber endoscopy** sensing mechanism. The forward operator applies, in order: L · fiber illumination operator; L · fiber transmission operator; K · psf · bundle operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian 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 moderately conditioned (kappa_eff ~= 12); fiber_bending dominates the stability cliff; pixelation_comb and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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 · fiber illumination → L · fiber transmission → K · psf · bundle → Spatial integration → **y** (detector). ``` y = ∫_A dA `K.psf.bundle` `L.fiber_transmission` `L.fiber_illumination` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fiber_illumination` | L · fiber illumination operator | | `L.fiber_transmission` | L · fiber transmission operator | | `K.psf.bundle` | K · psf · bundle operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Flexible multimode / coherent bundle endoscopy | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 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 moderately conditioned (kappa_eff ~= 12); fiber_bending dominates the stability cliff; pixelation_comb and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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:** `fiber_endoscopy` · **Forward operator:** `fiber_endoscopy_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 25 | | N fibers | — | 30000 | | Pixel um | µm | 10 | | Fiber bending | — | 0 | | Pixelation comb | — | 0 | | Dynamic range compression | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Snr db | dB | 0.0 – 40.0 | | N fibers | — | 1000 – 100000 | | Pixel um | µm | 2 – 50 | | Fiber bending | — | 0.0 – 0.3 | | Pixelation comb | — | 0.0 – 0.5 | | Fiber attenuation | — | 0.0 – 0.3 | | Dynamic range compression | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xd65f0cf17fa140d2c9ee3b820458f3cae872f36d852f163a54f80b0c3d105808` - **Chain tx hash:** `0xa5305802da32e43968dcdbb8c29d907ea028bbe6475edd9167237feaac4214b6` - **Chain block:** `41553385` --- ## File Mapping This bundle consists of: `L1-048.md`, `L1-048.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-048.md` | Source of truth — edit this | Human or LLM | | `L1-048.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 `L1-048`._ _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 (L1-048.md).
Regenerate L1-048.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 ▾

L2-048-001 Fiber-Optic Endoscopy Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-048",
  "chain_block": 41553385,
  "chain_hash": "0xd65f0cf17fa140d2c9ee3b820458f3cae872f36d852f163a54f80b0c3d105808",
  "chain_tx_hash": "0xa5305802da32e43968dcdbb8c29d907ea028bbe6475edd9167237feaac4214b6",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "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 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 moderately conditioned (kappa_eff ~= 12); fiber_bending dominates the stability cliff; pixelation_comb and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.fiber_illumination",
      "L.fiber_transmission",
      "K.psf.bundle",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "fiber_endoscopy",
    "solution_space": "2D_intensity",
    "sub_domain": "Flexible multimode / coherent bundle endoscopy",
    "title": "Fiber-Optic Endoscopy"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fiber_endoscopy_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_fibers",
      "pixel_um",
      "SNR_dB",
      "fiber_bending",
      "pixelation_comb",
      "dynamic_range_compression",
      "fiber_bending",
      "pixelation_comb",
      "dynamic_range_compression",
      "fiber_attenuation"
    ],
    "allowed_problem_classes": [
      "fiber_endoscopy"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "fiber_endoscopy_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "N_fibers": 30000,
        "SNR_dB": 25,
        "W": 512,
        "dynamic_range_compression": 0.0,
        "fiber_bending": 0.0,
        "pixel_um": 10,
        "pixelation_comb": 0.0
      },
      "problem_class": "fiber_endoscopy"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": 128,
      "N_fibers": [
        1000,
        100000
      ],
      "SNR_dB": [
        0.0,
        40.0
      ],
      "W": 128,
      "dynamic_range_compression": [
        0.0,
        0.3
      ],
      "fiber_attenuation": [
        0.0,
        0.3
      ],
      "fiber_bending": [
        0.0,
        0.3
      ],
      "pixel_um": [
        2,
        50
      ],
      "pixelation_comb": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Flexible multimode / coherent bundle endoscopy",
  "title": "Fiber-Optic Endoscopy"
}

🎁

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.