L1 ⚛ L1-086 ⊙ Testnet

Electron Tomography — tilt-series 3D reconstruction

Electron Microscopy · Tilt-series TEM for 3D cellular structure

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⬇ L1-086.md

# ⚛ L1 Principle — Electron Tomography — tilt-series 3D reconstruction **ID:** `L1-086` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Tilt-series TEM for 3D cellular structure* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D density > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554184 --- ## 🧠 1. Introduction **Electron Tomography — tilt-series 3D reconstruction** is a **linear inverse problem** whose unknown lives in **3D density** space, within the **Tilt-series TEM for 3D cellular structure** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **electron transmission** sensing mechanism. The forward operator applies, in order: L · transmit sample operator; rotates source / detector to acquire different projections; spreads measurements back along source rays (adjoint operator); integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D density 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 ~= 20); tilt_angle_error dominates the stability cliff; missing_wedge 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** → L · transmit sample → Angular scan → Angular integration → **y** (detector). ``` y = ∫dΩ R(θ) `L.transmit_sample` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.transmit_sample` | L · transmit sample operator | | `S.scan.angular` | Rotates source / detector to acquire different projections | | `int.angular` | Integration over the solid angle of incidence/emission | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `L.backproject` | Spreads measurements back along source rays (adjoint operator) | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Tilt-series TEM for 3D cellular structure | | Carrier | electron | | Problem class | linear_inverse | | Solution space | 3D_density | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D density 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 ~= 20); tilt_angle_error dominates the stability cliff; missing_wedge 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:** `etomo_tilt_series` · **Forward operator:** `etomo_tilt_series_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Z | — | 128 | | Kv | — | 300 | | N tilts | — | 61 | | Missing wedge | — | 0.33 | | Peak electrons | — | 30 | | Tilt range deg | deg | 60 | | Tilt angle error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 4096 | | W | px | 512 – 4096 | | Z | — | 32 – 512 | | Kv | — | 200 – 300 | | N tilts | — | 20 – 200 | | Beam damage | — | 0.0 – 0.5 | | Missing wedge | — | 0.1 – 0.6 | | Peak electrons | — | 1 – 500 | | Tilt range deg | deg | 40 – 80 | | Alignment error | — | 0.0 – 5.0 | | Tilt angle error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xfb181034b956374646ef8727ee21d10ec1b88668f4aa5156494b5c8dcc3a17a7` - **Chain tx hash:** `0xd4f0c4fe89f7a6aad1b0a7286d708e7f7fa7159edfcd30bec2178532f034bdcf` - **Chain block:** `41554184` --- ## File Mapping This bundle consists of: `L1-086.md`, `L1-086.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-086.md` | Source of truth — edit this | Human or LLM | | `L1-086.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 `L1-086`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-086-001 Electron Tomography — tilt-series 3D reconstruction Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0xd4f0c4fe89f7a6aad1b0a7286d708e7f7fa7159edfcd30bec2178532f034bdcf",
  "domain": "Electron Microscopy",
  "hardness_fn": {
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    "kappa": 400,
    "metric": "PSNR_dB",
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Electron Microscopy",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
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      "S.scan.angular",
      "L.backproject",
      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "electron_transmission",
    "solution_space": "3D_density",
    "sub_domain": "Tilt-series TEM for 3D cellular structure",
    "title": "Electron Tomography \u2014 tilt-series 3D reconstruction"
  },
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      "missing_wedge",
      "tilt_angle_error",
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      "alignment_error"
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        "peak_electrons": 30,
        "tilt_angle_error": 0.0,
        "tilt_range_deg": 60
      },
      "problem_class": "etomo_tilt_series"
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        40.0
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        4096
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      "N_tilts": [
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      "Z": [
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      "alignment_error": [
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      ],
      "beam_damage": [
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        0.5
      ],
      "kV": [
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        300
      ],
      "missing_wedge": [
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        0.6
      ],
      "peak_electrons": [
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      ],
      "tilt_angle_error": [
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        0.5
      ],
      "tilt_range_deg": [
        40,
        80
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Tilt-series TEM for 3D cellular structure",
  "title": "Electron Tomography \u2014 tilt-series 3D reconstruction"
}

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