L1 ⚛ L1-151 ⊙ Testnet

Compressed Ultrafast Photography (CUP) — trillion fps imaging

Ultrafast Imaging · Coded-aperture + streak camera 1 Tfps imaging

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-151.md

# ⚛ L1 Principle — Compressed Ultrafast Photography (CUP) — trillion fps imaging **ID:** `L1-151` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Ultrafast Imaging — *Coded-aperture + streak camera 1 Tfps imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D xyt video > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554229 --- ## 🧠 1. Introduction **Compressed Ultrafast Photography (CUP) — trillion fps imaging** is a **linear inverse problem** whose unknown lives in **3D xyt video** space, within the **Coded-aperture + streak camera 1 Tfps imaging** sub-domain of **Ultrafast Imaging**. Measurements consist of photons collected by an optical detector via a **compressed ultrafast** sensing mechanism. The forward operator applies, in order: element-wise multiplication by a binary mask; S · temporal · coded operator; L · streak sweep 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 3D xyt video 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 ~= 28); dmd_mask_drift dominates the stability cliff; streak_nonlinearity and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → Binary coded aperture → S · temporal · coded → L · streak sweep → Magnitude-squared → Temporal integration → **y** (detector). ``` y = ∫_t dt |·|² `L.streak_sweep` `S.temporal.coded` M ⊙ x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.diag.binary` | Element-wise multiplication by a binary mask | | `S.temporal.coded` | S · temporal · coded operator | | `L.streak_sweep` | L · streak sweep 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 | Ultrafast Imaging | | Sub domain | Coded-aperture + streak camera 1 Tfps imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_xyt_video | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered 3D xyt video 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 ~= 28); dmd_mask_drift dominates the stability cliff; streak_nonlinearity and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `cup` · **Forward operator:** `cup_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | N frames | — | 100 | | Cross talk | — | 0 | | Photon count | — | 200 | | Dmd mask drift | — | 0 | | Low photon regime | — | 0 | | Streak nonlinearity | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | N frames | — | 20 – 500 | | Cross talk | — | 0.0 – 0.3 | | Photon count | — | 10 – 5000 | | Dmd mask drift | — | 0.0 – 0.3 | | Low photon regime | — | 0.0 – 1.0 | | Streak nonlinearity | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `560` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe4a745062413162527d0bf4d3f2652023b62cf6fb94ef132d303fc7767462e9a` - **Chain tx hash:** `0x1c8081115525d0fec2c04ea5317cc8d3b1bc761180cd3234c0bfb841218f29f5` - **Chain block:** `41554229` --- ## File Mapping This bundle consists of: `L1-151.md`, `L1-151.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-151.md` | Source of truth — edit this | Human or LLM | | `L1-151.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 `L1-151`._ _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 (L1-151.md).
Regenerate L1-151.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 ▾

L2-151-001 Compressed Ultrafast Photography (CUP) — trillion fps imaging Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-151",
  "chain_block": 41554229,
  "chain_hash": "0xe4a745062413162527d0bf4d3f2652023b62cf6fb94ef132d303fc7767462e9a",
  "chain_tx_hash": "0x1c8081115525d0fec2c04ea5317cc8d3b1bc761180cd3234c0bfb841218f29f5",
  "domain": "Ultrafast Imaging",
  "hardness_fn": {
    "delta": 10,
    "kappa": 560,
    "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 xyt video 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 ~= 28); dmd_mask_drift dominates the stability cliff; streak_nonlinearity and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "photon",
    "difficulty_delta": 10,
    "domain": "Ultrafast Imaging",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.diag.binary",
      "S.temporal.coded",
      "L.streak_sweep",
      "L.modulus_squared",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "compressed_ultrafast",
    "solution_space": "3D_xyt_video",
    "sub_domain": "Coded-aperture + streak camera 1 Tfps imaging",
    "title": "Compressed Ultrafast Photography (CUP) \u2014 trillion fps imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "cup_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_frames",
      "photon_count",
      "dmd_mask_drift",
      "streak_nonlinearity",
      "cross_talk",
      "low_photon_regime",
      "dmd_mask_drift",
      "streak_nonlinearity",
      "cross_talk",
      "low_photon_regime"
    ],
    "allowed_problem_classes": [
      "cup"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "cup_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_frames": 100,
        "W": 128,
        "cross_talk": 0.0,
        "dmd_mask_drift": 0.0,
        "low_photon_regime": 0.0,
        "photon_count": 200,
        "streak_nonlinearity": 0.0
      },
      "problem_class": "cup"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": 64,
      "N_frames": [
        20,
        500
      ],
      "W": 64,
      "cross_talk": [
        0.0,
        0.3
      ],
      "dmd_mask_drift": [
        0.0,
        0.3
      ],
      "low_photon_regime": [
        0.0,
        1.0
      ],
      "photon_count": [
        10,
        5000
      ],
      "streak_nonlinearity": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Coded-aperture + streak camera 1 Tfps imaging",
  "title": "Compressed Ultrafast Photography (CUP) \u2014 trillion fps 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.