L1 ⚛ L1-452 ⊙ Testnet

Multibody Dynamics with Constraints

Robotics · Constrained dynamics

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-452.md

# ⚛ L1 Principle — Multibody Dynamics with Constraints **ID:** `L1-452` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Robotics — *Constrained dynamics* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** generalized acceleration vector > **📡 Carrier:** N/A · **🌫 Noise:** deterministic > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555278 --- ## 🧠 1. Introduction **Multibody Dynamics with Constraints** is a **parameter-estimation problem** whose unknown lives in **generalized acceleration vector** space, within the **Constrained dynamics** sub-domain of **Robotics**. Measurements consist of N/A via a **lagrange multiplier constraint** sensing mechanism. The forward operator applies, in order: time evolution of the state; S · baumgarte · stabilization operator; O · constraint · violation check operator. Observations are corrupted by no stochastic noise (deterministic measurement). Existence of the recovered generalized_acceleration_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 ~= 500); constraint_drift_accumulation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → S · baumgarte · stabilization → O · constraint · violation check → **y** (detector). ``` y = `O.constraint.violation_check` `S.baumgarte.stabilization` ∂_t x (deterministic) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `S.baumgarte.stabilization` | S · baumgarte · stabilization operator | | `O.constraint.violation_check` | O · constraint · violation check operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Robotics | | Sub domain | Constrained dynamics | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | generalized_acceleration_vector | | Noise model | deterministic | | Integration axis | generalized_coordinates | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered generalized_acceleration_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 ~= 500); constraint_drift_accumulation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | constraint_violation_norm | | Secondary | energy_drift_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `lagrange_multiplier_constraint` **Center point:** | Parameter | Unit | Value | |---|---|---| | N bodies | — | 5 | | N constraints | — | 3 | | Baumgarte alpha | — | 20 | | Simulation steps | — | 1000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N bodies | — | 2 – 50 | | N constraints | — | 1 – 30 | | Baumgarte alpha | — | 5 – 100 | | Simulation steps | — | 100 – 100000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1e-4 constraint_violation_norm | Metric | Range | |---|---| | Constraint violation norm | 1e-08 – 0.01 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **constraint_violation_norm**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xda33d3f322b8c000227ec3a9d142165a3124b306c8523f2a11d2aecbba27cf5f` - **Chain tx hash:** `0x2d0802d3e4b35b08dcfc915b817ed38bdd5b9d30497ba350eb4c2f9598b24157` - **Chain block:** `41555278` --- ## File Mapping This bundle consists of: `L1-452.md`, `L1-452.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-452.md` | Source of truth — edit this | Human or LLM | | `L1-452.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 `L1-452`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-452.md).
Regenerate L1-452.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-452-001 Multibody Dynamics with Constraints — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-452",
  "chain_block": 41555278,
  "chain_hash": "0xda33d3f322b8c000227ec3a9d142165a3124b306c8523f2a11d2aecbba27cf5f",
  "chain_tx_hash": "0x2d0802d3e4b35b08dcfc915b817ed38bdd5b9d30497ba350eb4c2f9598b24157",
  "domain": "Robotics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000.0,
    "metric": "constraint_violation_norm",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "constraint_violation_norm",
    "regime": "Existence of the recovered generalized_acceleration_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 ~= 500); constraint_drift_accumulation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.",
    "secondary": "energy_drift_percent"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Robotics",
    "integration_axis": "generalized_coordinates",
    "noise_model": "deterministic",
    "primitives": [
      "D.time",
      "S.baumgarte.stabilization",
      "O.constraint.violation_check"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "lagrange_multiplier_constraint",
    "solution_space": "generalized_acceleration_vector",
    "sub_domain": "Constrained dynamics",
    "title": "Multibody Dynamics with Constraints"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "lagrange_multiplier_constraint"
    ],
    "allowed_omega_dimensions": [
      "N_bodies",
      "N_constraints",
      "simulation_steps",
      "Baumgarte_alpha"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "1e-4 constraint_violation_norm",
      "forward_operator": "lagrange_multiplier_constraint",
      "input_format": "measurement_only",
      "omega": {
        "Baumgarte_alpha": 20,
        "N_bodies": 5,
        "N_constraints": 3,
        "simulation_steps": 1000
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "constraint_violation_norm": [
        1e-08,
        0.01
      ]
    },
    "omega_bounds": {
      "Baumgarte_alpha": [
        5,
        100
      ],
      "N_bodies": [
        2,
        50
      ],
      "N_constraints": [
        1,
        30
      ],
      "simulation_steps": [
        100,
        100000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Constrained dynamics",
  "title": "Multibody Dynamics with Constraints"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.