# ⚛  L1 Principle — Coded Aperture Compressive Temporal Imaging (CACTI)

**ID:** `L1-004` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Compressive Imaging — *Video snapshot compressive sensing*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D temporal
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** — · **⛓ Block:** 41421560

---

## 🧠 1. Introduction

**Coded Aperture Compressive Temporal Imaging (CACTI)** is a **linear inverse problem** whose unknown lives in **3D temporal** space, within the **Video snapshot compressive sensing** sub-domain of **Compressive Imaging**.

Measurements consist of photons collected by an optical detector via a **coded aperture temporal** sensing mechanism.

The forward operator applies, in order: S · temporal · coded operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. underdetermined B:1 compressive video recovery; binary random temporally-varying masks satisfy RIP-like conditions; sub-pixel mask mismatch is dominant stability risk (10.4x residual ratio observed, EfficientSCI drops 20.58 dB under severe mismatch).

## ⚙ 2. Forward Model

Physical chain: **x** → S · temporal · coded → Temporal integration → **y** (detector).

```
y(i,j) = sum_{b=1}^{B} C_b(i,j) * x(i,j,b) + n(i,j)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.temporal.coded` | S · temporal · coded operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Compressive Imaging |
| Sub domain | Video snapshot compressive sensing |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 3D_temporal |
| Noise model | shot_poisson |
| Integration axis | temporal |
| L dag | 1.4 |

## 📡 4. Measurement Model

underdetermined B:1 compressive video recovery; binary random temporally-varying masks satisfy RIP-like conditions; sub-pixel mask mismatch is dominant stability risk (10.4x residual ratio observed, EfficientSCI drops 20.58 dB under severe mismatch).

| Metric | Value |
|---|---|
| Metric | PSNR_dB |

## ⚖ 6. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `2500`.

## 💾 7. Reference Dataset

- **KAIST-30** · weight 0.5 · IPFS _(not pinned yet)_
- **CAVE multispectral** · weight 0.3 · IPFS _(not pinned yet)_
- **ICVL hyperspectral** · weight 0.2 · IPFS _(not pinned yet)_

## 8. On-chain Registration

- **Chain hash:** `0xa2ae37946ef2822a308a4e60245dd2655070190cf8f3913559ae36286b26a56b`
- **Chain tx hash:** `0xe7c1a57e92d7a901179131ad60b0262564b63ac5aeab565ae481d52a57540ace`
- **Chain block:** `41421560`

**Staked PWM:** 5000.0

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## File Mapping

This bundle consists of: `L1-004.md`, `L1-004.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-004.md` | Source of truth — edit this | Human or LLM |
| `L1-004.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 `L1-004`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._