L1 ⚛ L1-376 ⊙ Testnet

Cosmic Ray Propagation Inversion

Astrophysics · Cosmic rays

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⬇ L1-376.md

# ⚛ L1 Principle — Cosmic Ray Propagation Inversion **ID:** `L1-376` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Cosmic rays* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** CR spectral source distribution > **📡 Carrier:** particle · **🌫 Noise:** observation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555178 --- ## 🧠 1. Introduction **Cosmic Ray Propagation Inversion** is a **parameter-estimation problem** whose unknown lives in **CR spectral source distribution** space, within the **Cosmic rays** sub-domain of **Astrophysics**. Measurements consist of particle interactions in a detector via a **diffusion loss transport** sensing mechanism. The forward operator applies, in order: S · diffusion · galactic operator; operator inherits structure from a graph (mesh, network); O · chi2 · cr ratios operator. Observations are corrupted by observation gaussian. Existence of the recovered CR_spectral_source_distribution 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); solar_modulation_uncertainty 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 · diffusion · galactic → Structured graph operator → O · chi2 · cr ratios → **y** (detector). ``` y = `O.chi2.cr_ratios` G `S.diffusion.galactic` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.diffusion.galactic` | S · diffusion · galactic operator | | `G.structured` | Operator inherits structure from a graph (mesh, network) | | `O.chi2.cr_ratios` | O · chi2 · cr ratios operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Cosmic rays | | Carrier | particle | | Problem class | parameter_estimation | | Solution space | CR_spectral_source_distribution | | Noise model | observation_gaussian | | Integration axis | galactic_volume | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Existence of the recovered CR_spectral_source_distribution 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); solar_modulation_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | B_over_C_chi2 | | Secondary | positron_fraction_chi2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `diffusion_loss_transport` **Center point:** | Parameter | Unit | Value | |---|---|---| | D 0 cm2 s | s | 30000000000000000000000000000 | | Z halo kpc | — | 4 | | Solar phi gv | — | 0.5 | | Delta diffusion | — | 0.35 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | D 0 cm2 s | s | 10000000000000000000000000000 – 100000000000000000000000000000 | | Z halo kpc | — | 2.0 – 8.0 | | Solar phi gv | — | 0.3 – 1.5 | | Delta diffusion | — | 0.2 – 0.6 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.3 B_over_C_chi2 | Metric | Range | |---|---| | B over c chi2 | 0.8 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **B_over_C_chi2**, with κ = `1000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x58d9b143d8d8ae3812b97c7640829efa78025eade0df37cbe9857437fa8c026c` - **Chain tx hash:** `0xf6dc5c68c3e2e1c4e463c6d2434cd78b52f5036f66f2c9601423f5280ed3827d` - **Chain block:** `41555178` --- ## File Mapping This bundle consists of: `L1-376.md`, `L1-376.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-376.md` | Source of truth — edit this | Human or LLM | | `L1-376.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 `L1-376`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-376.md).
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📋 JSON metadata

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  "chain_hash": "0x58d9b143d8d8ae3812b97c7640829efa78025eade0df37cbe9857437fa8c026c",
  "chain_tx_hash": "0xf6dc5c68c3e2e1c4e463c6d2434cd78b52f5036f66f2c9601423f5280ed3827d",
  "domain": "Astrophysics",
  "hardness_fn": {
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    "regime": "Existence of the recovered CR_spectral_source_distribution 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); solar_modulation_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.",
    "secondary": "positron_fraction_chi2"
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  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "particle",
    "difficulty_delta": 3,
    "domain": "Astrophysics",
    "integration_axis": "galactic_volume",
    "noise_model": "observation_gaussian",
    "primitives": [
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      "G.structured",
      "O.chi2.cr_ratios"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "diffusion_loss_transport",
    "solution_space": "CR_spectral_source_distribution",
    "sub_domain": "Cosmic rays",
    "title": "Cosmic Ray Propagation Inversion"
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  "size_tiers": {
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    "allowed_omega_dimensions": [
      "D_0_cm2_s",
      "delta_diffusion",
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      "solar_phi_GV"
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    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "1.3 B_over_C_chi2",
      "forward_operator": "diffusion_loss_transport",
      "input_format": "measurement_only",
      "omega": {
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        "delta_diffusion": 0.35,
        "solar_phi_GV": 0.5,
        "z_halo_kpc": 4.0
      },
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    },
    "epsilon_bounds": {
      "B_over_C_chi2": [
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        3.0
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    },
    "omega_bounds": {
      "D_0_cm2_s": [
        10000000000000000000000000000,
        100000000000000000000000000000
      ],
      "delta_diffusion": [
        0.2,
        0.6
      ],
      "solar_phi_GV": [
        0.3,
        1.5
      ],
      "z_halo_kpc": [
        2.0,
        8.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cosmic rays",
  "title": "Cosmic Ray Propagation Inversion"
}

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