L1 ⚛ L1-230 ⊙ Testnet

Elastodynamics — dynamic wave propagation in solids

Structural Mechanics · Elastic wave equation (P/S waves)

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⬇ L1-230.md

# ⚛ L1 Principle — Elastodynamics — dynamic wave propagation in solids **ID:** `L1-230` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Elastic wave equation (P/S waves)* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D displacement spacetime > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554023 --- ## 🧠 1. Introduction **Elastodynamics — dynamic wave propagation in solids** is a **linear inverse problem** whose unknown lives in **3D displacement spacetime** space, within the **Elastic wave equation (P/S waves)** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **accelerometers** sensing mechanism. The forward operator applies, in order: L · initial condition operator; L · hyperbolic wave operator; L · record · sensors operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · initial condition → L · hyperbolic wave → L · record · sensors → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.record.sensors` `L.hyperbolic_wave` `L.initial_condition` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.initial_condition` | L · initial condition operator | | `L.hyperbolic_wave` | L · hyperbolic wave operator | | `L.record.sensors` | L · record · sensors operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Elastic wave equation (P/S waves) | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | 3D_displacement_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `elastodynamics` · **Forward operator:** `elastodynamics_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 50000 | | Snr db | dB | 30 | | E error | — | 0 | | N times | — | 500 | | Bc error | — | 0 | | Nu error | — | 0 | | N sensors | — | 32 | | Rho error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 1000 – 10000000 | | Snr db | dB | 0 – 40 | | E error | — | 0.0 – 0.1 | | N times | — | 100 – 100000 | | Bc error | — | 0.0 – 0.2 | | Nu error | — | 0.0 – 0.05 | | N sensors | — | 4 – 4096 | | Rho error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 23.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3973d0cb866f99bf32f6fe74a6c965bbe9067cc293197d8e14fe2d3f8c0545e9` - **Chain tx hash:** `0xde8a7b13c70d6ad0d9dbbb0cd68393e95b5ff6254f8d8ec855c6172952421a6f` - **Chain block:** `41554023` --- ## File Mapping This bundle consists of: `L1-230.md`, `L1-230.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-230.md` | Source of truth — edit this | Human or LLM | | `L1-230.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 `L1-230`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-230.md).
Regenerate L1-230.json so every field matches the Markdown.
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L2-230-001 Elastodynamics — dynamic wave propagation in solids Mismatch-Only Spec

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📋 JSON metadata

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    "L_DAG": 3.3,
    "carrier": "mechanical",
    "difficulty_delta": 5,
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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    "sensing_mechanism": "accelerometers",
    "solution_space": "3D_displacement_spacetime",
    "sub_domain": "Elastic wave equation (P/S waves)",
    "title": "Elastodynamics \u2014 dynamic wave propagation in solids"
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      "input_format": "measurement_only",
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        1000,
        10000000
      ],
      "N_sensors": [
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      ],
      "N_times": [
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      ],
      "SNR_dB": [
        0,
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      ]
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Elastic wave equation (P/S waves)",
  "title": "Elastodynamics \u2014 dynamic wave propagation in solids"
}

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