L1 ⚛ L1-365 ⊙ Testnet

Cosmological N-body (Large-Scale Structure)

Astrophysics · Cosmological simulation

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⬇ L1-365.md

# ⚛ L1 Principle — Cosmological N-body (Large-Scale Structure) **ID:** `L1-365` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Cosmological simulation* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 3D dark matter density > **📡 Carrier:** N/A · **🌫 Noise:** cosmic variance > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555176 --- ## 🧠 1. Introduction **Cosmological N-body (Large-Scale Structure)** is a **parameter-estimation problem** whose unknown lives in **3D dark matter density** space, within the **Cosmological simulation** sub-domain of **Astrophysics**. Measurements consist of N/A via a **pm tree gravity** sensing mechanism. The forward operator applies, in order: F · fourier · pm gravity operator; S · tree · force softening operator; O · leapfrog · comoving operator. Observations are corrupted by cosmic variance. Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → F · fourier · pm gravity → S · tree · force softening → O · leapfrog · comoving → **y** (detector). ``` y = `O.leapfrog.comoving` `S.tree.force_softening` `F.fourier.pm_gravity` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.fourier.pm_gravity` | F · fourier · pm gravity operator | | `S.tree.force_softening` | S · tree · force softening operator | | `O.leapfrog.comoving` | O · leapfrog · comoving operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Cosmological simulation | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | 3D_dark_matter_density | | Noise model | cosmic_variance | | Integration axis | comoving_time | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | matter_power_spectrum_P_k_chi2 | | Secondary | halo_mass_function_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `pm_tree_gravity` **Center point:** | Parameter | Unit | Value | |---|---|---| | Omega m | m | 0.3 | | Sigma 8 | — | 0.8 | | N particles | — | 134217728 | | Box size mpc h | — | 250 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Omega m | m | 0.2 – 0.5 | | Sigma 8 | — | 0.6 – 1.0 | | N particles | — | 262144 – 8589934592 | | Box size mpc h | — | 50 – 2000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.02 matter_power_spectrum_P_k_chi2 | Metric | Range | |---|---| | Matter power spectrum p k chi2 | 0.9 – 1.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **matter_power_spectrum_P_k_chi2**, with κ = `100000000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5eaf872422d70c8c95f19857af65a6a30c2ca15580c7ffbe8f8e2fd5740a8e78` - **Chain tx hash:** `0x287c23d7c0934b4ae7f925e4e0ad660ae6ca5ba15542041f1afd30a62d551832` - **Chain block:** `41555176` --- ## File Mapping This bundle consists of: `L1-365.md`, `L1-365.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-365.md` | Source of truth — edit this | Human or LLM | | `L1-365.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 `L1-365`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-365.md).
Regenerate L1-365.json so every field matches the Markdown.
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L2-365-001 Cosmological N-body (Large-Scale Structure) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555176,
  "chain_hash": "0x5eaf872422d70c8c95f19857af65a6a30c2ca15580c7ffbe8f8e2fd5740a8e78",
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  "domain": "Astrophysics",
  "hardness_fn": {
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    "regime": "Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor.",
    "secondary": "halo_mass_function_error"
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  "physics_fingerprint": {
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    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Astrophysics",
    "integration_axis": "comoving_time",
    "noise_model": "cosmic_variance",
    "primitives": [
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      "S.tree.force_softening",
      "O.leapfrog.comoving"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "pm_tree_gravity",
    "solution_space": "3D_dark_matter_density",
    "sub_domain": "Cosmological simulation",
    "title": "Cosmological N-body (Large-Scale Structure)"
  },
  "size_tiers": {
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      "pm_tree_gravity"
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    "allowed_omega_dimensions": [
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      "sigma_8"
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    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
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      "forward_operator": "pm_tree_gravity",
      "input_format": "measurement_only",
      "omega": {
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        "box_size_Mpc_h": 250.0,
        "sigma_8": 0.8
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    "epsilon_bounds": {
      "matter_power_spectrum_P_k_chi2": [
        0.9,
        1.5
      ]
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    "omega_bounds": {
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        262144,
        8589934592
      ],
      "Omega_m": [
        0.2,
        0.5
      ],
      "box_size_Mpc_h": [
        50,
        2000
      ],
      "sigma_8": [
        0.6,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cosmological simulation",
  "title": "Cosmological N-body (Large-Scale Structure)"
}

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