L1 ⚛ L1-379 ⊙ Testnet

Baryon Acoustic Oscillation (BAO) Fitting

Astrophysics · Large-scale structure

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⬇ L1-379.md

# ⚛ L1 Principle — Baryon Acoustic Oscillation (BAO) Fitting **ID:** `L1-379` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Large-scale structure* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** cosmological distance ratios > **📡 Carrier:** N/A · **🌫 Noise:** cosmic variance gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555179 --- ## 🧠 1. Introduction **Baryon Acoustic Oscillation (BAO) Fitting** is a **parameter-estimation problem** whose unknown lives in **cosmological distance ratios** space, within the **Large-scale structure** sub-domain of **Astrophysics**. Measurements consist of N/A via a **two point correlation function** sensing mechanism. The forward operator applies, in order: F · fourier · power spectrum operator; S · bao · peak fitting operator; O · chi2 · dv rd operator. Observations are corrupted by cosmic variance gaussian. Existence of the recovered cosmological_distance_ratios 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 ~= 30); galaxy_bias_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → F · fourier · power spectrum → S · bao · peak fitting → O · chi2 · dv rd → **y** (detector). ``` y = `O.chi2.dv_rd` `S.bao.peak_fitting` `F.fourier.power_spectrum` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.fourier.power_spectrum` | F · fourier · power spectrum operator | | `S.bao.peak_fitting` | S · bao · peak fitting operator | | `O.chi2.dv_rd` | O · chi2 · dv rd operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Large-scale structure | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | cosmological_distance_ratios | | Noise model | cosmic_variance_gaussian | | Integration axis | comoving_separation | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered cosmological_distance_ratios 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 ~= 30); galaxy_bias_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | D_V_rd_sigma_percent | | Secondary | chi2_reduced_BAO | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `two_point_correlation_function` **Center point:** | Parameter | Unit | Value | |---|---|---| | Z eff | — | 0.5 | | N gal million | — | 1 | | Sigma v fog kms | — | 400 | | Survey volume gpc3 h | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Z eff | — | 0.1 – 2.0 | | N gal million | — | 0.1 – 50.0 | | Sigma v fog kms | — | 100 – 1000 | | Survey volume gpc3 h | — | 0.5 – 50.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.0 D_V_rd_sigma_percent | Metric | Range | |---|---| | D v rd sigma percent | 0.2 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **D_V_rd_sigma_percent**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x54d5c4986c82178bde140866b70cf9a8a814f8ea0c8401ad1090574d1a23355d` - **Chain tx hash:** `0x5de8e7f922b44181ffe3356362a7da94c0b9bf6e21e4f9ce3a53469432f9618f` - **Chain block:** `41555179` --- ## File Mapping This bundle consists of: `L1-379.md`, `L1-379.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-379.md` | Source of truth — edit this | Human or LLM | | `L1-379.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 `L1-379`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "domain": "Astrophysics",
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    "regime": "Existence of the recovered cosmological_distance_ratios 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 ~= 30); galaxy_bias_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance gaussian sets the irreducible data-fidelity floor.",
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    "integration_axis": "comoving_separation",
    "noise_model": "cosmic_variance_gaussian",
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      "S.bao.peak_fitting",
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    "sensing_mechanism": "two_point_correlation_function",
    "solution_space": "cosmological_distance_ratios",
    "sub_domain": "Large-scale structure",
    "title": "Baryon Acoustic Oscillation (BAO) Fitting"
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    "center_spec": {
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      "sigma_v_FoG_kms": [
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      ],
      "z_eff": [
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        2.0
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    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Large-scale structure",
  "title": "Baryon Acoustic Oscillation (BAO) Fitting"
}

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