L1 ⚛ L1-370 ⊙ Testnet

Stellar Structure Inverse Problem

Astrophysics · Stellar physics

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⬇ L1-370.md

# ⚛ L1 Principle — Stellar Structure Inverse Problem **ID:** `L1-370` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Stellar physics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 1D stellar profile > **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555177 --- ## 🧠 1. Introduction **Stellar Structure Inverse Problem** is a **parameter-estimation problem** whose unknown lives in **1D stellar profile** space, within the **Stellar physics** sub-domain of **Astrophysics**. Measurements consist of N/A via a **stellar oscillation inversion** sensing mechanism. The forward operator applies, in order: S · helioseismic · kernel operator; O · rnla · inversion operator; time evolution of the state. Observations are corrupted by observation gaussian. Existence of the recovered 1D_stellar_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 ~= 50); surface_term_offset dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · helioseismic · kernel → O · rnla · inversion → Time derivative → **y** (detector). ``` y = ∂_t `O.rnla.inversion` `S.helioseismic.kernel` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.helioseismic.kernel` | S · helioseismic · kernel operator | | `O.rnla.inversion` | O · rnla · inversion operator | | `D.time` | Time evolution of the state | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Stellar physics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | 1D_stellar_profile | | Noise model | observation_gaussian | | Integration axis | radial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered 1D_stellar_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 ~= 50); surface_term_offset dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | sound_speed_inversion_chi2 | | Secondary | density_profile_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `stellar_oscillation_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | N modes | — | 200 | | Mass msun | — | 1 | | Metallicity z | — | 0.02 | | Noise sigma microhz | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N modes | — | 20 – 1000 | | Mass msun | — | 0.5 – 2.0 | | Metallicity z | — | 0.001 – 0.05 | | Noise sigma microhz | — | 0.01 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.2 sound_speed_inversion_chi2 | Metric | Range | |---|---| | Sound speed inversion chi2 | 0.8 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **sound_speed_inversion_chi2**, with κ = `1000.0` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xffd57bfc88bee31c965a9647a73d78e9ebbf054029f9b88c52055e1e9d941207` - **Chain tx hash:** `0xe71800b693887c668fa41382d57492941a4b92db66fefb2c231e6145aab73f9d` - **Chain block:** `41555177` --- ## File Mapping This bundle consists of: `L1-370.md`, `L1-370.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-370.md` | Source of truth — edit this | Human or LLM | | `L1-370.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 `L1-370`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-370.md).
Regenerate L1-370.json so every field matches the Markdown.
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L2-370-001 Stellar Structure Inverse Problem — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-370",
  "chain_block": 41555177,
  "chain_hash": "0xffd57bfc88bee31c965a9647a73d78e9ebbf054029f9b88c52055e1e9d941207",
  "chain_tx_hash": "0xe71800b693887c668fa41382d57492941a4b92db66fefb2c231e6145aab73f9d",
  "domain": "Astrophysics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 1000.0,
    "metric": "sound_speed_inversion_chi2",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
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    "regime": "Existence of the recovered 1D_stellar_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 ~= 50); surface_term_offset dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "density_profile_RMSE"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Astrophysics",
    "integration_axis": "radial",
    "noise_model": "observation_gaussian",
    "primitives": [
      "S.helioseismic.kernel",
      "O.rnla.inversion",
      "D.time"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "stellar_oscillation_inversion",
    "solution_space": "1D_stellar_profile",
    "sub_domain": "Stellar physics",
    "title": "Stellar Structure Inverse Problem"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "stellar_oscillation_inversion"
    ],
    "allowed_omega_dimensions": [
      "N_modes",
      "mass_Msun",
      "metallicity_Z",
      "noise_sigma_microHz"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.2 sound_speed_inversion_chi2",
      "forward_operator": "stellar_oscillation_inversion",
      "input_format": "measurement_only",
      "omega": {
        "N_modes": 200,
        "mass_Msun": 1.0,
        "metallicity_Z": 0.02,
        "noise_sigma_microHz": 0.1
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "sound_speed_inversion_chi2": [
        0.8,
        3.0
      ]
    },
    "omega_bounds": {
      "N_modes": [
        20,
        1000
      ],
      "mass_Msun": [
        0.5,
        2.0
      ],
      "metallicity_Z": [
        0.001,
        0.05
      ],
      "noise_sigma_microHz": [
        0.01,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Stellar physics",
  "title": "Stellar Structure Inverse Problem"
}

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