{
  "artifact_id": "L1-004",
  "layer": "L1",
  "registration_tier": "founder_vetted",
  "principle_number": "004",
  "title": "Coded Aperture Compressive Temporal Imaging (CACTI)",
  "domain": "Compressive Imaging",
  "sub_domain": "Video snapshot compressive sensing",
  "source_file": "B_compressive_imaging/027_cacti.md",
  "E": {
    "description": "Single-shot compressive video forward model: a temporally varying binary coded mask gates photons per-pixel for each sub-frame, and the detector integrates all B masked sub-frames into a single 2D snapshot exposure.",
    "forward_model": "y(i,j) = sum_{b=1}^{B} C_b(i,j) * x(i,j,b) + n(i,j)",
    "world_state_x": "3D video cube x in R^{H x W x B}, non-negative, compressible in spatio-temporal basis (e.g., 3D wavelet, sparse optical flow)",
    "observation_y": "2D sensor snapshot y in R^{H x W} at effective frame rate 1/B of the sub-frame rate (Poisson+Gaussian noise)",
    "physical_parameters_theta": [
      "C_b: binary coded mask per sub-frame b in {0,1}^{H x W}",
      "B: compression ratio (sub-frames per snapshot)",
      "detector exposure time T, sensor gain gamma, offset o",
      "mask duty cycle eta, clock offset dt",
      "sub-pixel registration (dx, dy) and rotation theta",
      "read noise sigma_n"
    ]
  },
  "G": {
    "dag": "S.temporal.coded -> int.temporal",
    "vertices": [
      "S.temporal.coded",
      "int.temporal"
    ],
    "arcs": [
      "S.temporal.coded -> int.temporal"
    ],
    "L_DAG": 1.4,
    "n_c": 0,
    "_L_DAG_derivation": "(|V|-1) + log10(kappa_sys/kappa_0) + n_c = 1 + log10(2500/1000) + 0 = 1 + 0.398 = 1.398 (rounded to 1.4). kappa_0=1000 is the registry-wide convention (established by CASSI #25); CACTI satisfies kappa_sys >= kappa_0 so no max(0, .) clamp applies."
  },
  "W": {
    "existence": true,
    "uniqueness": true,
    "stability": "conditional",
    "condition_number_kappa": 2500,
    "condition_number_effective": 30,
    "condition_number_mismatched": 300,
    "regime": "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)."
  },
  "C": {
    "solver_class": "iterative_proximal (GAP-TV, DeSCI) or plug-and-play (PnP-FFDNet) or learned unrolling (EfficientSCI, BIRNAT)",
    "convergence_rate_q": 2.0,
    "error_bound": "||x_hat - x||_2 <= C1 * sigma_noise / sqrt(m) + C2 * ||x - x_s||_1; per-frame PSNR recovery ratio = 1.00 with GAP-TV at 60s calibration.",
    "complexity": "O(H * W * B * log(H*W*B)) per iteration for FFT-based proximal steps; O(H*W*B) for denoising priors."
  },
  "physics_fingerprint": {
    "carrier": "photon",
    "sensing_mechanism": "coded_aperture_temporal",
    "integration_axis": "temporal",
    "problem_class": "linear_inverse",
    "noise_model": "shot_poisson",
    "solution_space": "3D_temporal",
    "primitives": [
      "S.temporal.coded",
      "int.temporal"
    ]
  },
  "difficulty_delta": 3,
  "difficulty_tier": "standard",
  "mismatch_parameters": [
    "dx",
    "dy",
    "theta",
    "dt",
    "eta",
    "gamma",
    "offset",
    "sigma_n"
  ],
  "error_metric": "PSNR_dB",
  "error_metric_secondary": "SSIM",
  "error_metric_tertiary": "temporal_consistency",
  "spec_range": {
    "center_spec": {
      "problem_class": "temporal_video_reconstruction",
      "forward_operator": "cacti_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "W": 256,
        "B": 8,
        "noise_level": 0.01,
        "dx": 0.0,
        "dy": 0.0,
        "theta": 0.0,
        "dt": 0.0,
        "eta": 1.0,
        "gamma": 1.0,
        "offset": 0.0,
        "sigma_n": 1.0
      },
      "epsilon_fn_center": "26.0 dB PSNR"
    },
    "allowed_forward_operators": [
      "cacti_forward",
      "cacti_forward_oracle"
    ],
    "allowed_problem_classes": [
      "temporal_video_reconstruction",
      "high_speed_video_sci"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "B",
      "noise_level",
      "dx",
      "dy",
      "theta",
      "dt",
      "eta",
      "gamma",
      "offset",
      "sigma_n"
    ],
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "W": [
        32,
        1024
      ],
      "B": [
        4,
        32
      ],
      "noise_level": [
        0.001,
        0.1
      ],
      "dx": [
        0.0,
        1.0
      ],
      "dy": [
        0.0,
        1.0
      ],
      "theta": [
        0.0,
        0.15
      ],
      "dt": [
        0.0,
        0.1
      ],
      "eta": [
        0.9,
        1.0
      ],
      "gamma": [
        0.95,
        1.05
      ],
      "offset": [
        0.0,
        0.01
      ],
      "sigma_n": [
        0.5,
        2.0
      ]
    },
    "epsilon_bounds": {
      "psnr_db": [
        20.0,
        40.0
      ]
    }
  },
  "p1_p10_tests": [
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS",
    "PASS"
  ],
  "s1_s4_gates": [
    "PASS",
    "PASS",
    "PASS",
    "PASS"
  ],
  "ipfs_cid": null,
  "verification_status": "triple-verified",
  "verified_by": [
    "agent-physics-verifier",
    "agent-numerics-verifier",
    "agent-cross-domain-verifier"
  ],
  "verification_date": "2026-04-21",
  "display_slug": "cacti"
}