L1 ⚛ L1-009 ⊙ Testnet

Two-Photon Microscopy (chi-3 NLO excitation)

Microscopy · Non-linear optical deep tissue imaging

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

🎁 Contribute & earn PWM

Improve L1-009 — submit with or without uploading. Accepted submissions earn the 1/16 modify share of A(t).

✨ Submit without uploading free check · 1×

One click — no files, no typing. We submit a check of L1-009 for you; it goes through review and earns the 1/16 share once. One free no-upload Principle per account.

You'll be asked to log in first — then it's one click, no files.

⬆ Or submit by uploading your files

Upload your .md + .json as a modification of L1-009. Unlimited.

🛠 Helper: build your files in ChatGPT / Gemini / Claude

Layer template

⬇ principle.md ⬇ principle.json

Fork L1-009

⬇ L1-009.md ⬇ L1-009.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-009 (Two-Photon Microscopy (chi-3 NLO excitation)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-009.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-009.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 = ∫_t dt S_raster `L.excitation.nonlinear_chi3` x,    measurements ~ Poisson(αy)

world state x (3D intensity)

→

L · excitation · nonlinear chi3 `L.excitation.nonlinear_chi3`

→

Raster scan S_raster

→

Temporal integration ∫_t dt

→

observation y (photon detector)

Noise: Poisson shot noise from quantum-limited detection

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-009.md

# ⚛ L1 Principle — Two-Photon Microscopy (chi-3 NLO excitation) **ID:** `L1-009` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Non-linear optical deep tissue imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D intensity > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554154 --- ## 🧠 1. Introduction **Two-Photon Microscopy (chi-3 NLO excitation)** is a **nonlinear inverse problem** whose unknown lives in **3D intensity** space, within the **Non-linear optical deep tissue imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **two photon nlo** sensing mechanism. The forward operator applies, in order: L · excitation · nonlinear chi3 operator; ordered pixel-by-pixel sampling; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); pulse_compression_drift dominates the stability cliff; sample_scattering 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 · excitation · nonlinear chi3 → Raster scan → Temporal integration → **y** (detector). ``` y = ∫_t dt S_raster `L.excitation.nonlinear_chi3` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.nonlinear_chi3` | L · excitation · nonlinear chi3 operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Non-linear optical deep tissue imaging | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); pulse_compression_drift dominates the stability cliff; sample_scattering 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:** `twophoton` · **Forward operator:** `twophoton_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 100 | | Na | — | 1 | | Pixel nm | nm | 400 | | Lambda ex nm | nm | 920 | | Peak photons | photons | 200 | | Pulse width fs | — | 150 | | Sample scattering | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Z | — | 16 – 512 | | Na | — | 0.6 – 1.1 | | Pixel nm | nm | 200 – 1000 | | Lambda ex nm | nm | 800 – 1060 | | Peak photons | photons | 20 – 2000 | | Pulse width fs | — | 50 – 500 | | Sample scattering | — | 0.0 – 0.5 | | Laser pointing jitter | — | 0.0 – 0.02 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x435c478b52cf1037fadff4c7b460c6bab0766e1d7f546f116ba5292006bd69fb` - **Chain tx hash:** `0x97c63d098b3b153461432279e78ea19fc3313dc98b4d2a1ce1b77fb99c46fdb8` - **Chain block:** `41554154` --- ## File Mapping This bundle consists of: `L1-009.md`, `L1-009.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-009.md` | Source of truth — edit this | Human or LLM | | `L1-009.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 `L1-009`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

💬

Ask the PWM AI agent AI

Ask about this Two-Photon Microscopy (chi-3 NLO excitation) — or how to improve it & earn PWM

Free to search; log in to chat with the agent & earn PWM. How it works ↗

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Digital Twin 1 child ▾

L2-009-001 Two-Photon Microscopy (chi-3 NLO excitation) Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-009",
  "chain_block": 41554154,
  "chain_hash": "0x435c478b52cf1037fadff4c7b460c6bab0766e1d7f546f116ba5292006bd69fb",
  "chain_tx_hash": "0x97c63d098b3b153461432279e78ea19fc3313dc98b4d2a1ce1b77fb99c46fdb8",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "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 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); pulse_compression_drift dominates the stability cliff; sample_scattering 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": "photon",
    "difficulty_delta": 5,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.excitation.nonlinear_chi3",
      "S.scan.raster",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "two_photon_nlo",
    "solution_space": "3D_intensity",
    "sub_domain": "Non-linear optical deep tissue imaging",
    "title": "Two-Photon Microscopy (chi-3 NLO excitation)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "twophoton_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "pixel_nm",
      "NA",
      "lambda_ex_nm",
      "peak_photons",
      "pulse_width_fs",
      "sample_scattering",
      "pulse_compression_drift",
      "sample_scattering",
      "laser_pointing_jitter"
    ],
    "allowed_problem_classes": [
      "twophoton"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "twophoton_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "NA": 1.0,
        "W": 512,
        "Z": 100,
        "lambda_ex_nm": 920,
        "peak_photons": 200,
        "pixel_nm": 400,
        "pulse_width_fs": 150,
        "sample_scattering": 0.0
      },
      "problem_class": "twophoton"
    },
    "epsilon_bounds": {
      "psnr_db": [
        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        2048
      ],
      "NA": [
        0.6,
        1.1
      ],
      "W": [
        128,
        2048
      ],
      "Z": [
        16,
        512
      ],
      "lambda_ex_nm": [
        800,
        1060
      ],
      "laser_pointing_jitter": [
        0.0,
        0.02
      ],
      "peak_photons": [
        20,
        2000
      ],
      "pixel_nm": [
        200,
        1000
      ],
      "pulse_width_fs": [
        50,
        500
      ],
      "sample_scattering": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Non-linear optical deep tissue imaging",
  "title": "Two-Photon Microscopy (chi-3 NLO excitation)"
}

🎁

Earn PWM by promoting this to mainnet

• PWM emission on accept — your share of A(t) (1/16 modify · 3/16 new)
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Go to submit ↑

How: use the “Contribute & earn PWM” panel at the top — either Submit without uploading (one click) or upload your files. Then the review runs and, on accept, it’s promoted to mainnet.