L1 ⚛ L1-377 ⊙ Testnet

Galaxy SED Fitting

Astrophysics · Galaxy properties

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Introduction

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Galaxy SED Fitting (Galaxy properties) is a parameter estimation in Astrophysics. The forward model maps the hidden galaxy parameter vector to a measurement, corrupted by observation gaussian. The inverse goal is to recover the galaxy parameter vector from the observed data.

Governing Equation

y = T_chi2 S_dust G x

parameter estimation Astrophysics L_DAG 3.0 δ = 3 SFR log RMSE

L1 Primitives — forward-model DAG nodes

G.structured → S.dust.attenuation_calzetti → O.chi2.photometric

L2 Ω Dimensions — parameters each benchmark instance fixes

N_filters redshift_z SNR_per_band A_V_mag

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Digital Twins

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Each digital twin (L2) is a concrete instantiation of this principle's forward operator with a specific Ω parameter space. Benchmarks (L3) are seeded from each twin.

#	Digital Twin	ID
1	Galaxy SED Fitting — Nominal + Mismatch Specs	L2-377-001

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Principle — Galaxy SED Fitting L1-377 Testnet

TX: 0x824b97c247312d5ca6… block 41,555,178

sha256: 0xf8e3e00e1cc0411d28bd55c61d6adb81a9a8ea4f0115d558874f4c077531f6bb

PWM Registry — Principle #377

Galaxy SED Fitting · P = (E, G, W, C)

Forward Model

y = T_chi2 S_dust G x

Sensing: broadband_photometric_sed

Carrier: photon

Problem class: parameter estimation

Recover: galaxy_parameter_vector

Noise model: observation_gaussian

Forward operator: broadband_photometric_sed

Nominal Ω

A_V_mag=0.5 N_filters=10 redshift_z=0.5 SNR_per_band=10

ε (nominal): 0.25 SFR_log_RMSE

Ω bounds (4 dims)

A_V_mag: 0.0–3.0N_filters: 3–30redshift_z: 0.0–6.0SNR_per_band: 3–100

DAG Decomposition — G = (V, A)

G.structured → S.dust.attenuation_calzetti → O.chi2.photometric

L_DAG: 3.0

δ: 3

Integration axis: spectral_energy_distribution

Problem classes: parameter_estimation

Operators: broadband_photometric_sed

Well-Posedness Certificate

Existence

YES

galaxy_parameter_vector is guaranteed within the declared Omega bounds

Uniqueness

YES

holds on the measurement-supported subspace

Stability

CONDITIONAL

κ_eff ≈ 80

Dominant instability: AGN_contamination

Data-fidelity floor: Observation gaussian

Full regime certificate

Existence of the recovered galaxy_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 ~= 80); AGN_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

Error-Bounding Methodology

Primary: SFR log RMSE Secondary: stellar_mass_log_RMSE κ = 2000 δ = 3

ε bounds

SFR_log_RMSE: 0.05 – 0.8

Hardness function: epsilon_fn

📝 Markdown source — L1-377.md

# ⚛ L1 Principle — Galaxy SED Fitting **ID:** `L1-377` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Galaxy properties* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** galaxy parameter vector > **📡 Carrier:** photon · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555178 --- ## 🧠 1. Introduction **Galaxy SED Fitting** is a **parameter-estimation problem** whose unknown lives in **galaxy parameter vector** space, within the **Galaxy properties** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **broadband photometric sed** sensing mechanism. The forward operator applies, in order: operator inherits structure from a graph (mesh, network); S · dust · attenuation calzetti operator; O · chi2 · photometric operator. Observations are corrupted by observation gaussian. Existence of the recovered galaxy_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 ~= 80); AGN_contamination 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** → Structured graph operator → S · dust · attenuation calzetti → O · chi2 · photometric → **y** (detector). ``` y = T_chi2 S_dust G x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `S.dust.attenuation_calzetti` | S · dust · attenuation calzetti operator | | `O.chi2.photometric` | O · chi2 · photometric operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Galaxy properties | | Carrier | photon | | Problem class | parameter_estimation | | Solution space | galaxy_parameter_vector | | Noise model | observation_gaussian | | Integration axis | spectral_energy_distribution | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered galaxy_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 ~= 80); AGN_contamination dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | SFR_log_RMSE | | Secondary | stellar_mass_log_RMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `broadband_photometric_sed` **Center point:** | Parameter | Unit | Value | |---|---|---| | A v mag | — | 0.5 | | N filters | — | 10 | | Redshift z | — | 0.5 | | Snr per band | — | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | A v mag | — | 0.0 – 3.0 | | N filters | — | 3 – 30 | | Redshift z | — | 0.0 – 6.0 | | Snr per band | — | 3 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.25 SFR_log_RMSE | Metric | Range | |---|---| | Sfr log rmse | 0.05 – 0.8 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **SFR_log_RMSE**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf8e3e00e1cc0411d28bd55c61d6adb81a9a8ea4f0115d558874f4c077531f6bb` - **Chain tx hash:** `0x824b97c247312d5ca6d0c13ccc8c2b6db28f86ef8b339727234aea29c549a239` - **Chain block:** `41555178` --- ## File Mapping This bundle consists of: `L1-377.md`, `L1-377.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-377.md` | Source of truth — edit this | Human or LLM | | `L1-377.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 `L1-377`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Galaxy SED Fitting

Introduction

Digital Twins

Contents

Galaxy SED Fitting · P = (E, G, W, C)

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