L1 ⚛ L1-373 ⊙ Testnet

Pulsar Timing Array GW Background

Astrophysics · Gravitational wave astronomy

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⬇ L1-373.md

# ⚛ L1 Principle — Pulsar Timing Array GW Background **ID:** `L1-373` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Gravitational wave astronomy* > **🎯 Problem class:** statistical inverse · **🧮 Solution space:** GW background spectrum > **📡 Carrier:** radio_wave · **🌫 Noise:** timing noise red white > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555177 --- ## 🧠 1. Introduction **Pulsar Timing Array GW Background** is a **statistical inverse problem** whose unknown lives in **GW background spectrum** space, within the **Gravitational wave astronomy** sub-domain of **Astrophysics**. Measurements consist of radio-frequency electromagnetic waves via a **pulsar timing residuals** sensing mechanism. The forward operator applies, in order: S · pulsar · timing residuals operator; F · fourier · spectral density operator; O · entropy · bayesian operator. Observations are corrupted by timing noise red white. Existence of the recovered GW_background_spectrum 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 ~= 1000); solar_system_ephemeris_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Timing noise red white sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · pulsar · timing residuals → F · fourier · spectral density → O · entropy · bayesian → **y** (detector). ``` y = `O.entropy.bayesian` `F.fourier.spectral_density` `S.pulsar.timing_residuals` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.pulsar.timing_residuals` | S · pulsar · timing residuals operator | | `F.fourier.spectral_density` | F · fourier · spectral density operator | | `O.entropy.bayesian` | O · entropy · bayesian operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Gravitational wave astronomy | | Carrier | radio_wave | | Problem class | statistical_inverse | | Solution space | GW_background_spectrum | | Noise model | timing_noise_red_white | | Integration axis | temporal_timing | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered GW_background_spectrum 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 ~= 1000); solar_system_ephemeris_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Timing noise red white sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | GWB_Bayes_factor_log10 | | Secondary | A_15_constraint_sigma | ## 📏 5. Operating Range (Ω) **Center problem class:** `statistical_inverse` · **Forward operator:** `pulsar_timing_residuals` **Center point:** | Parameter | Unit | Value | |---|---|---| | N psr | — | 25 | | T obs yr | — | 15 | | Cadence yr | — | 0.04 | | Noise rms ns | ns | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N psr | — | 10 – 100 | | T obs yr | — | 5 – 25 | | Cadence yr | — | 0.01 – 0.1 | | Noise rms ns | ns | 10 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 GWB_Bayes_factor_log10 | Metric | Range | |---|---| | Gwb bayes factor log10 | 0.5 – 6.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **GWB_Bayes_factor_log10**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe0534c020796d29359f451a6360471ab64d3af89284fc8c7b563e6774a3b3f05` - **Chain tx hash:** `0x9df456984c82fa2d5356189cade6f2d81c182a6e4844c914e3ae93f23ecad579` - **Chain block:** `41555177` --- ## File Mapping This bundle consists of: `L1-373.md`, `L1-373.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-373.md` | Source of truth — edit this | Human or LLM | | `L1-373.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 `L1-373`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-373-001 Pulsar Timing Array GW Background — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555177,
  "chain_hash": "0xe0534c020796d29359f451a6360471ab64d3af89284fc8c7b563e6774a3b3f05",
  "chain_tx_hash": "0x9df456984c82fa2d5356189cade6f2d81c182a6e4844c914e3ae93f23ecad579",
  "domain": "Astrophysics",
  "hardness_fn": {
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    "kappa": 100000.0,
    "metric": "GWB_Bayes_factor_log10",
    "type": "epsilon_fn"
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  "observable_profile": {
    "metric": "GWB_Bayes_factor_log10",
    "regime": "Existence of the recovered GW_background_spectrum 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 ~= 1000); solar_system_ephemeris_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Timing noise red white sets the irreducible data-fidelity floor.",
    "secondary": "A_15_constraint_sigma"
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  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Astrophysics",
    "integration_axis": "temporal_timing",
    "noise_model": "timing_noise_red_white",
    "primitives": [
      "S.pulsar.timing_residuals",
      "F.fourier.spectral_density",
      "O.entropy.bayesian"
    ],
    "problem_class": "statistical_inverse",
    "sensing_mechanism": "pulsar_timing_residuals",
    "solution_space": "GW_background_spectrum",
    "sub_domain": "Gravitational wave astronomy",
    "title": "Pulsar Timing Array GW Background"
  },
  "size_tiers": {
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      "pulsar_timing_residuals"
    ],
    "allowed_omega_dimensions": [
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      "T_obs_yr",
      "cadence_yr",
      "noise_rms_ns"
    ],
    "allowed_problem_classes": [
      "statistical_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0 GWB_Bayes_factor_log10",
      "forward_operator": "pulsar_timing_residuals",
      "input_format": "measurement_only",
      "omega": {
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        "T_obs_yr": 15,
        "cadence_yr": 0.04,
        "noise_rms_ns": 100
      },
      "problem_class": "statistical_inverse"
    },
    "epsilon_bounds": {
      "GWB_Bayes_factor_log10": [
        0.5,
        6.0
      ]
    },
    "omega_bounds": {
      "N_psr": [
        10,
        100
      ],
      "T_obs_yr": [
        5,
        25
      ],
      "cadence_yr": [
        0.01,
        0.1
      ],
      "noise_rms_ns": [
        10,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Gravitational wave astronomy",
  "title": "Pulsar Timing Array GW Background"
}

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