L1 ⚛ L1-430 ⊙ Testnet

Particle Filter (Sequential Monte Carlo)

Control Theory · Particle filtering

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⬇ L1-430.md

# ⚛ L1 Principle — Particle Filter (Sequential Monte Carlo) **ID:** `L1-430` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Control Theory — *Particle filtering* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** particle distribution > **📡 Carrier:** N/A · **🌫 Noise:** non gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555240 --- ## 🧠 1. Introduction **Particle Filter (Sequential Monte Carlo)** is a **nonlinear inverse problem** whose unknown lives in **particle distribution** space, within the **Particle filtering** sub-domain of **Control Theory**. Measurements consist of N/A via a **sequential monte carlo estimation** sensing mechanism. The forward operator applies, in order: S · pf · importance sampling operator; adds a prior term that biases the solution toward smoothness/sparsity; O · ess · effective sample size operator. Observations are corrupted by non gaussian. Existence of the recovered particle_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 ~= 200); particle_impoverishment dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Non gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · pf · importance sampling → O · ess · effective sample size → **y** (detector). ``` y = `O.ess.effective_sample_size` `S.pf.importance_sampling` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.pf.importance_sampling` | S · pf · importance sampling operator | | `O.ess.effective_sample_size` | O · ess · effective sample size 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 | Control Theory | | Sub domain | Particle filtering | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | particle_distribution | | Noise model | non_gaussian | | Integration axis | discrete_time | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered particle_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 ~= 200); particle_impoverishment dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Non gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | RMSE_state_particle_filter | | Secondary | effective_sample_size_ESS | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `sequential_monte_carlo_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N particles | — | 1000 | | N state dim | — | 4 | | N time steps | — | 100 | | Nonlinearity degree | — | 1.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N particles | — | 100 – 100000 | | N state dim | — | 1 – 20 | | N time steps | — | 10 – 1000 | | Nonlinearity degree | — | 0.5 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.15 RMSE_state_particle_filter | Metric | Range | |---|---| | Rmse state particle filter | 0.02 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **RMSE_state_particle_filter**, with κ = `5000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x337199767be602e792232154c65bbdb7fd49cfa09311d427d20322790539e8e5` - **Chain tx hash:** `0x6093ffa085a046fed0a4b9b7d2b99ff23c5144cb3aaa2dd2c9fdfdaf670c39ff` - **Chain block:** `41555240` --- ## File Mapping This bundle consists of: `L1-430.md`, `L1-430.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-430.md` | Source of truth — edit this | Human or LLM | | `L1-430.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 `L1-430`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-430.md).
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L2-430-001 Particle Filter (Sequential Monte Carlo) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_hash": "0x337199767be602e792232154c65bbdb7fd49cfa09311d427d20322790539e8e5",
  "chain_tx_hash": "0x6093ffa085a046fed0a4b9b7d2b99ff23c5144cb3aaa2dd2c9fdfdaf670c39ff",
  "domain": "Control Theory",
  "hardness_fn": {
    "delta": 5,
    "kappa": 5000,
    "metric": "RMSE_state_particle_filter",
    "type": "epsilon_fn"
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      "name": "primary",
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    "regime": "Existence of the recovered particle_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 ~= 200); particle_impoverishment dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Non gaussian sets the irreducible data-fidelity floor.",
    "secondary": "effective_sample_size_ESS"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Control Theory",
    "integration_axis": "discrete_time",
    "noise_model": "non_gaussian",
    "primitives": [
      "S.pf.importance_sampling",
      "O.regularize",
      "O.ess.effective_sample_size"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "sequential_monte_carlo_estimation",
    "solution_space": "particle_distribution",
    "sub_domain": "Particle filtering",
    "title": "Particle Filter (Sequential Monte Carlo)"
  },
  "size_tiers": {
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      "sequential_monte_carlo_estimation"
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    "allowed_omega_dimensions": [
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      "n_state_dim",
      "nonlinearity_degree",
      "N_time_steps"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.15 RMSE_state_particle_filter",
      "forward_operator": "sequential_monte_carlo_estimation",
      "input_format": "measurement_only",
      "omega": {
        "N_particles": 1000,
        "N_time_steps": 100,
        "n_state_dim": 4,
        "nonlinearity_degree": 1.5
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "RMSE_state_particle_filter": [
        0.02,
        0.5
      ]
    },
    "omega_bounds": {
      "N_particles": [
        100,
        100000
      ],
      "N_time_steps": [
        10,
        1000
      ],
      "n_state_dim": [
        1,
        20
      ],
      "nonlinearity_degree": [
        0.5,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Particle filtering",
  "title": "Particle Filter (Sequential Monte Carlo)"
}

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