L1 ⚛ L1-366 ⊙ Testnet

CMB Power Spectrum Parameter Estimation

Astrophysics · CMB cosmology

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⬇ L1-366.md

# ⚛ L1 Principle — CMB Power Spectrum Parameter Estimation **ID:** `L1-366` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *CMB cosmology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** cosmological parameter vector > **📡 Carrier:** photon · **🌫 Noise:** thermal gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555176 --- ## 🧠 1. Introduction **CMB Power Spectrum Parameter Estimation** is a **parameter-estimation problem** whose unknown lives in **cosmological parameter vector** space, within the **CMB cosmology** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **boltzmann cmb transfer** sensing mechanism. The forward operator applies, in order: S · boltzmann · transfer operator; adds a prior term that biases the solution toward smoothness/sparsity; O · mcmc · sampler operator. Observations are corrupted by thermally-driven Gaussian fluctuations. Existence of the recovered cosmological_parameter_vector 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 ~= 200); foreground_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · boltzmann · transfer → O · mcmc · sampler → **y** (detector). ``` y = `O.mcmc.sampler` `S.boltzmann.transfer` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.boltzmann.transfer` | S · boltzmann · transfer operator | | `O.mcmc.sampler` | O · mcmc · sampler operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | CMB cosmology | | Carrier | photon | | Problem class | parameter_estimation | | Solution space | cosmological_parameter_vector | | Noise model | thermal_gaussian | | Integration axis | multipole_l | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered cosmological_parameter_vector 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 ~= 200); foreground_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | parameter_constraint_sigma_Omega | | Secondary | chi2_reduced | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `boltzmann_cmb_transfer` **Center point:** | Parameter | Unit | Value | |---|---|---| | L max | — | 2500 | | N ell bins | — | 40 | | Noise uk arcmin | — | 10 | | Beam fwhm arcmin | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | L max | — | 100 – 5000 | | N ell bins | — | 10 – 100 | | Noise uk arcmin | — | 1.0 – 100.0 | | Beam fwhm arcmin | — | 1.0 – 30.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.01 parameter_constraint_sigma_Omega | Metric | Range | |---|---| | Parameter constraint sigma omega | 0.001 – 0.1 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **parameter_constraint_sigma_Omega**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xba42fa11c01ed1157eb4da90a48d20a94ecd876663add1063bfcf00f82e27d05` - **Chain tx hash:** `0xfbacf8043b26b06897549f8ce65a5a24cc538e57feb41b0429437815397811ba` - **Chain block:** `41555176` --- ## File Mapping This bundle consists of: `L1-366.md`, `L1-366.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-366.md` | Source of truth — edit this | Human or LLM | | `L1-366.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 `L1-366`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "status": "testnet",
  "sub_domain": "CMB cosmology",
  "title": "CMB Power Spectrum Parameter Estimation"
}

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