L1 ⚛ L1-371 ⊙ Testnet

Stellar Atmosphere Spectral Inversion

Astrophysics · Stellar spectroscopy

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⬇ L1-371.md

# ⚛ L1 Principle — Stellar Atmosphere Spectral Inversion **ID:** `L1-371` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Stellar spectroscopy* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 1D atmospheric profile > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555177 --- ## 🧠 1. Introduction **Stellar Atmosphere Spectral Inversion** is a **nonlinear inverse problem** whose unknown lives in **1D atmospheric profile** space, within the **Stellar spectroscopy** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **radiative transfer spectral** sensing mechanism. The forward operator applies, in order: S · radiative · transfer lte operator; operator inherits structure from a graph (mesh, network); O · chi2 · spectral lines operator. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 1D_atmospheric_profile 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 ~= 500); continuum_normalization_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · radiative · transfer lte → Structured graph operator → O · chi2 · spectral lines → **y** (detector). ``` y = `O.chi2.spectral_lines` G `S.radiative.transfer_lte` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.radiative.transfer_lte` | S · radiative · transfer lte operator | | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `O.chi2.spectral_lines` | O · chi2 · spectral lines operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Stellar spectroscopy | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 1D_atmospheric_profile | | Noise model | shot_poisson | | Integration axis | optical_depth | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 1D_atmospheric_profile 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 ~= 500); continuum_normalization_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | spectral_chi2_reduced | | Secondary | T_eff_RMSE_K | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `radiative_transfer_spectral` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr | — | 100 | | T eff k | — | 5500 | | N lambda | — | 5000 | | Log g cgs | — | 4 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr | — | 10 – 500 | | T eff k | — | 3500 – 7500 | | N lambda | — | 1000 – 50000 | | Log g cgs | — | 1.0 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.15 spectral_chi2_reduced | Metric | Range | |---|---| | Spectral chi2 reduced | 0.8 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **spectral_chi2_reduced**, with κ = `50000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5fb66349c542ef26e19324c512acc166e8899083bdfe422729638d56682f845c` - **Chain tx hash:** `0x07de7824abdecdaadb29394b675b2c80f0de7f152526d1cca6f6443dc1f6cb15` - **Chain block:** `41555177` --- ## File Mapping This bundle consists of: `L1-371.md`, `L1-371.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-371.md` | Source of truth — edit this | Human or LLM | | `L1-371.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 `L1-371`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-371.md).
Regenerate L1-371.json so every field matches the Markdown.
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L2-371-001 Stellar Atmosphere Spectral Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555177,
  "chain_hash": "0x5fb66349c542ef26e19324c512acc166e8899083bdfe422729638d56682f845c",
  "chain_tx_hash": "0x07de7824abdecdaadb29394b675b2c80f0de7f152526d1cca6f6443dc1f6cb15",
  "domain": "Astrophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 50000.0,
    "metric": "spectral_chi2_reduced",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "spectral_chi2_reduced",
    "regime": "Existence of the recovered 1D_atmospheric_profile 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 ~= 500); continuum_normalization_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.",
    "secondary": "T_eff_RMSE_K"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Astrophysics",
    "integration_axis": "optical_depth",
    "noise_model": "shot_poisson",
    "primitives": [
      "S.radiative.transfer_lte",
      "G.structured",
      "O.chi2.spectral_lines"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "radiative_transfer_spectral",
    "solution_space": "1D_atmospheric_profile",
    "sub_domain": "Stellar spectroscopy",
    "title": "Stellar Atmosphere Spectral Inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "radiative_transfer_spectral"
    ],
    "allowed_omega_dimensions": [
      "N_lambda",
      "T_eff_K",
      "log_g_cgs",
      "SNR"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.15 spectral_chi2_reduced",
      "forward_operator": "radiative_transfer_spectral",
      "input_format": "measurement_only",
      "omega": {
        "N_lambda": 5000,
        "SNR": 100,
        "T_eff_K": 5500,
        "log_g_cgs": 4.0
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "spectral_chi2_reduced": [
        0.8,
        5.0
      ]
    },
    "omega_bounds": {
      "N_lambda": [
        1000,
        50000
      ],
      "SNR": [
        10,
        500
      ],
      "T_eff_K": [
        3500,
        7500
      ],
      "log_g_cgs": [
        1.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Stellar spectroscopy",
  "title": "Stellar Atmosphere Spectral Inversion"
}

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