L1 ⚛ L1-280 ⊙ Testnet

Magnetic Field Inversion — susceptibility imaging

Geophysics · 3D magnetic susceptibility inversion

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-280.md

# ⚛ L1 Principle — Magnetic Field Inversion — susceptibility imaging **ID:** `L1-280` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *3D magnetic susceptibility inversion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D susceptibility distribution > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554064 --- ## 🧠 1. Introduction **Magnetic Field Inversion — susceptibility imaging** is a **linear inverse problem** whose unknown lives in **3D susceptibility distribution** space, within the **3D magnetic susceptibility inversion** sub-domain of **Geophysics**. Measurements consist of electromagnetic field measurements via a **magnetometer** sensing mechanism. The forward operator applies, in order: L · dipole field operator; L · linear forward operator; L · regularize operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Ill-posed similar to gravity; non-unique without priors. ## ⚙ 2. Forward Model Physical chain: **x** → L · dipole field → L · linear forward → L · regularize → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.regularize` `L.linear_forward` `L.dipole_field` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.dipole_field` | L · dipole field operator | | `L.linear_forward` | L · linear forward operator | | `L.regularize` | L · regularize operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | 3D magnetic susceptibility inversion | | Carrier | em | | Problem class | linear_inverse | | Solution space | 3D_susceptibility_distribution | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Ill-posed similar to gravity; non-unique without priors. | Metric | Value | |---|---| | Metric | chi_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `magnetic_inversion` · **Forward operator:** `magnetic_inversion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 64 | | Snr db | dB | 30 | | Terrain error | — | 0 | | N observations | — | 1024 | | Declination error | — | 0 | | Remanence unmodelled | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Z | — | 8 – 512 | | Snr db | dB | 0 – 40 | | Terrain error | — | 0.0 – 0.2 | | N observations | — | 64 – 100000 | | Declination error | — | 0.0 – 0.1 | | Remanence unmodelled | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 | Metric | Range | |---|---| | Chi rel | 0.5 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **chi_rel_error_percent**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4f03aa4981f6f2d48c503815cfec0c096d2d91a46de95aa8c37e12f319528e18` - **Chain tx hash:** `0x1a529955d6b572b91840b3909465e713bddb68e653559e49485b503c6d03bc21` - **Chain block:** `41554064` --- ## File Mapping This bundle consists of: `L1-280.md`, `L1-280.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-280.md` | Source of truth — edit this | Human or LLM | | `L1-280.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 `L1-280`._ _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 (L1-280.md).
Regenerate L1-280.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 ▾

L2-280-001 Magnetic Field Inversion — susceptibility imaging Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-280",
  "chain_block": 41554064,
  "chain_hash": "0x4f03aa4981f6f2d48c503815cfec0c096d2d91a46de95aa8c37e12f319528e18",
  "chain_tx_hash": "0x1a529955d6b572b91840b3909465e713bddb68e653559e49485b503c6d03bc21",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "chi_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "chi_rel_error_percent",
    "regime": "Ill-posed similar to gravity; non-unique without priors.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.dipole_field",
      "L.linear_forward",
      "L.regularize",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "magnetometer",
    "solution_space": "3D_susceptibility_distribution",
    "sub_domain": "3D magnetic susceptibility inversion",
    "title": "Magnetic Field Inversion \u2014 susceptibility imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "magnetic_inversion_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_observations",
      "SNR_dB",
      "remanence_unmodelled",
      "declination_error",
      "terrain_error",
      "remanence_unmodelled",
      "declination_error",
      "terrain_error"
    ],
    "allowed_problem_classes": [
      "magnetic_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "5.0",
      "forward_operator": "magnetic_inversion_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_observations": 1024,
        "SNR_dB": 30,
        "W": 256,
        "Z": 64,
        "declination_error": 0.0,
        "remanence_unmodelled": 0.0,
        "terrain_error": 0.0
      },
      "problem_class": "magnetic_inversion"
    },
    "epsilon_bounds": {
      "chi_rel": [
        0.5,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        2048
      ],
      "N_observations": [
        64,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "Z": [
        8,
        512
      ],
      "declination_error": [
        0.0,
        0.1
      ],
      "remanence_unmodelled": [
        0.0,
        0.3
      ],
      "terrain_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "3D magnetic susceptibility inversion",
  "title": "Magnetic Field Inversion \u2014 susceptibility 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.