L1 ⚛ L1-472 ⊙ Testnet

Hyperspectral Spectral Unmixing

Geodesy · Remote sensing spectroscopy

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⬇ L1-472.md

# ⚛ L1 Principle — Hyperspectral Spectral Unmixing **ID:** `L1-472` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geodesy — *Remote sensing spectroscopy* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** abundance map > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555299 --- ## 🧠 1. Introduction **Hyperspectral Spectral Unmixing** is a **linear inverse problem** whose unknown lives in **abundance map** space, within the **Remote sensing spectroscopy** sub-domain of **Geodesy**. Measurements consist of photons collected by an optical detector via a **hyperspectral reflectance unmixing** sensing mechanism. The forward operator applies, in order: an unspecified linear measurement operator; O · nonneg ls · fcls operator; S · endmember · extraction operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered abundance_map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); endmember_variability dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Generic linear operator → O · nonneg ls · fcls → S · endmember · extraction → **y** (detector). ``` y = `S.endmember.extraction` `O.nonneg_ls.fcls` A x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.linear_op` | An unspecified linear measurement operator | | `O.nonneg_ls.fcls` | O · nonneg ls · fcls operator | | `S.endmember.extraction` | S · endmember · extraction operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geodesy | | Sub domain | Remote sensing spectroscopy | | Carrier | photon | | Problem class | linear_inverse | | Solution space | abundance_map | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Existence of the recovered abundance_map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); endmember_variability dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | abundance_RMSE | | Secondary | endmember_SAM_deg | ## 📏 5. Operating Range (Ω) **Center problem class:** `linear_inverse` · **Forward operator:** `hyperspectral_reflectance_unmixing` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 100 | | W | px | 100 | | Snr db | dB | 30 | | K endmembers | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 20 – 500 | | W | px | 20 – 500 | | Snr db | dB | 10 – 60 | | K endmembers | — | 2 – 20 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.05 abundance_RMSE | Metric | Range | |---|---| | Abundance rmse | 0.01 – 0.2 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **abundance_RMSE**, with κ = `1000.0` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xecf047403de0792a114aee70830d2d3023179f19ea9ed1d1f12c55d780fef091` - **Chain tx hash:** `0xf8363ef360ceda918f16cd61a16901ce95b84aaae4cc9fb2349880f29440510f` - **Chain block:** `41555299` --- ## File Mapping This bundle consists of: `L1-472.md`, `L1-472.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-472.md` | Source of truth — edit this | Human or LLM | | `L1-472.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 `L1-472`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-472.md).
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L2-472-001 Hyperspectral Spectral Unmixing — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555299,
  "chain_hash": "0xecf047403de0792a114aee70830d2d3023179f19ea9ed1d1f12c55d780fef091",
  "chain_tx_hash": "0xf8363ef360ceda918f16cd61a16901ce95b84aaae4cc9fb2349880f29440510f",
  "domain": "Geodesy",
  "hardness_fn": {
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    "kappa": 1000.0,
    "metric": "abundance_RMSE",
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      "name": "primary",
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  "observable_profile": {
    "metric": "abundance_RMSE",
    "regime": "Existence of the recovered abundance_map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); endmember_variability dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "endmember_SAM_deg"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
      "L.linear_op",
      "O.nonneg_ls.fcls",
      "S.endmember.extraction"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "hyperspectral_reflectance_unmixing",
    "solution_space": "abundance_map",
    "sub_domain": "Remote sensing spectroscopy",
    "title": "Hyperspectral Spectral Unmixing"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "W",
      "K_endmembers",
      "SNR_dB"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "0.05 abundance_RMSE",
      "forward_operator": "hyperspectral_reflectance_unmixing",
      "input_format": "measurement_only",
      "omega": {
        "H": 100,
        "K_endmembers": 5,
        "SNR_dB": 30,
        "W": 100
      },
      "problem_class": "linear_inverse"
    },
    "epsilon_bounds": {
      "abundance_RMSE": [
        0.01,
        0.2
      ]
    },
    "omega_bounds": {
      "H": [
        20,
        500
      ],
      "K_endmembers": [
        2,
        20
      ],
      "SNR_dB": [
        10,
        60
      ],
      "W": [
        20,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Remote sensing spectroscopy",
  "title": "Hyperspectral Spectral Unmixing"
}

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