L1 ⚛ L1-375 ⊙ Testnet

Accretion Disk Structure Inversion

Astrophysics · Accretion physics

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⬇ L1-375.md

# ⚛ L1 Principle — Accretion Disk Structure Inversion **ID:** `L1-375` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Accretion physics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 1D disk emissivity profile > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555178 --- ## 🧠 1. Introduction **Accretion Disk Structure Inversion** is a **nonlinear inverse problem** whose unknown lives in **1D disk emissivity profile** space, within the **Accretion physics** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **x ray spectral timing** sensing mechanism. The forward operator applies, in order: S · disk · relxill reflection operator; F · fourier · power spectrum operator; O · chi2 · x ray spectrum operator. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 1D_disk_emissivity_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); pile_up_contamination 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 · disk · relxill reflection → F · fourier · power spectrum → O · chi2 · x ray spectrum → **y** (detector). ``` y = `O.chi2.x_ray_spectrum` `F.fourier.power_spectrum` `S.disk.relxill_reflection` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.disk.relxill_reflection` | S · disk · relxill reflection operator | | `F.fourier.power_spectrum` | F · fourier · power spectrum operator | | `O.chi2.x_ray_spectrum` | O · chi2 · x ray spectrum operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Accretion physics | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 1D_disk_emissivity_profile | | Noise model | shot_poisson | | Integration axis | radial_disk | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 1D_disk_emissivity_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); pile_up_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | spin_constraint_sigma | | Secondary | spectral_chi2_reduced | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `x_ray_spectral_timing` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr per bin | — | 20 | | Spin a star | — | 0.7 | | N counts total | — | 1e+06 | | Inclination deg | deg | 40 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr per bin | — | 5 – 100 | | Spin a star | — | 0.0 – 0.998 | | N counts total | — | 10000.0 – 100000000.0 | | Inclination deg | deg | 5 – 80 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.1 spectral_chi2_reduced | Metric | Range | |---|---| | Spectral chi2 reduced | 0.8 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **spin_constraint_sigma**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xda64759d65ad666578c30849ca0830255f49522683040122a3dd95cdff3ba7cd` - **Chain tx hash:** `0xf0cbfede7c123078bbf410e26c6cbbfa5aa4997af7e4567074cd08595556984c` - **Chain block:** `41555178` --- ## File Mapping This bundle consists of: `L1-375.md`, `L1-375.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-375.md` | Source of truth — edit this | Human or LLM | | `L1-375.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 `L1-375`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-375-001 Accretion Disk Structure Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_hash": "0xda64759d65ad666578c30849ca0830255f49522683040122a3dd95cdff3ba7cd",
  "chain_tx_hash": "0xf0cbfede7c123078bbf410e26c6cbbfa5aa4997af7e4567074cd08595556984c",
  "domain": "Astrophysics",
  "hardness_fn": {
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  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Astrophysics",
    "integration_axis": "radial_disk",
    "noise_model": "shot_poisson",
    "primitives": [
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      "F.fourier.power_spectrum",
      "O.chi2.x_ray_spectrum"
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    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "x_ray_spectral_timing",
    "solution_space": "1D_disk_emissivity_profile",
    "sub_domain": "Accretion physics",
    "title": "Accretion Disk Structure Inversion"
  },
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    "allowed_omega_dimensions": [
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    "allowed_problem_classes": [
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    ],
    "center_spec": {
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      "forward_operator": "x_ray_spectral_timing",
      "input_format": "measurement_only",
      "omega": {
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        "SNR_per_bin": 20,
        "inclination_deg": 40,
        "spin_a_star": 0.7
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      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
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        0.8,
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    },
    "omega_bounds": {
      "N_counts_total": [
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      ],
      "SNR_per_bin": [
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        100
      ],
      "inclination_deg": [
        5,
        80
      ],
      "spin_a_star": [
        0.0,
        0.998
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Accretion physics",
  "title": "Accretion Disk Structure Inversion"
}

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