L1 ⚛ L1-257 ⊙ Testnet

Acoustic Wave Equation — time-domain pressure field reconstruction

Acoustics · 3D linear acoustic wave propagation

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⬇ L1-257.md

# ⚛ L1 Principle — Acoustic Wave Equation — time-domain pressure field reconstruction **ID:** `L1-257` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *3D linear acoustic wave propagation* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D pressure field spacetime > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554035 --- ## 🧠 1. Introduction **Acoustic Wave Equation — time-domain pressure field reconstruction** is a **linear inverse problem** whose unknown lives in **3D pressure field spacetime** space, within the **3D linear acoustic wave propagation** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **pressure receivers** sensing mechanism. The forward operator applies, in order: L · initial condition operator; L · wave propagate operator; S · record · receivers 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 · wave propagate → S · record · receivers → Temporal integration → **y** (detector). ``` y = ∫_t dt `S.record.receivers` `L.wave_propagate` `L.initial_condition` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.initial_condition` | L · initial condition operator | | `L.wave_propagate` | L · wave propagate operator | | `S.record.receivers` | S · record · receivers operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | 3D linear acoustic wave propagation | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | 3D_pressure_field_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 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:** `acoustic_wave` · **Forward operator:** `acoustic_wave_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 64 | | Snr db | dB | 30 | | Fs khz | kHz | 100 | | C error | — | 0 | | N samples | — | 512 | | Rho error | — | 0 | | N receivers | — | 64 | | Receiver pos error | — | 0 | | Boundary reflectivity | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 512 | | W | px | 64 – 512 | | Z | — | 32 – 256 | | Snr db | dB | 0 – 40 | | Fs khz | kHz | 10 – 1000 | | C error | — | 0.0 – 0.1 | | N samples | — | 128 – 4096 | | Rho error | — | 0.0 – 0.1 | | N receivers | — | 16 – 512 | | Receiver pos error | — | 0.0 – 0.02 | | Boundary reflectivity | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x61eda6d05bf44aae410231c7f4aab76fade90cf4c14f16b7fca3f1f32a80ce19` - **Chain tx hash:** `0xef08073047b4e18f6d23fd7bd5e7b1edd900d26277384f73f0daab71ac1ef75b` - **Chain block:** `41554035` --- ## File Mapping This bundle consists of: `L1-257.md`, `L1-257.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-257.md` | Source of truth — edit this | Human or LLM | | `L1-257.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 `L1-257`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-257.md).
Regenerate L1-257.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-257-001 Acoustic Wave Equation — time-domain pressure field reconstruction Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-257",
  "chain_block": 41554035,
  "chain_hash": "0x61eda6d05bf44aae410231c7f4aab76fade90cf4c14f16b7fca3f1f32a80ce19",
  "chain_tx_hash": "0xef08073047b4e18f6d23fd7bd5e7b1edd900d26277384f73f0daab71ac1ef75b",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Acoustics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.initial_condition",
      "L.wave_propagate",
      "S.record.receivers",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "pressure_receivers",
    "solution_space": "3D_pressure_field_spacetime",
    "sub_domain": "3D linear acoustic wave propagation",
    "title": "Acoustic Wave Equation \u2014 time-domain pressure field reconstruction"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "acoustic_wave_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_receivers",
      "N_samples",
      "fs_kHz",
      "SNR_dB",
      "c_error",
      "rho_error",
      "receiver_pos_error",
      "boundary_reflectivity",
      "c_error",
      "rho_error",
      "receiver_pos_error",
      "boundary_reflectivity"
    ],
    "allowed_problem_classes": [
      "acoustic_wave"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "acoustic_wave_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_receivers": 64,
        "N_samples": 512,
        "SNR_dB": 30,
        "W": 128,
        "Z": 64,
        "boundary_reflectivity": 0.0,
        "c_error": 0.0,
        "fs_kHz": 100,
        "receiver_pos_error": 0.0,
        "rho_error": 0.0
      },
      "problem_class": "acoustic_wave"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        512
      ],
      "N_receivers": [
        16,
        512
      ],
      "N_samples": [
        128,
        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        512
      ],
      "Z": [
        32,
        256
      ],
      "boundary_reflectivity": [
        0.0,
        0.5
      ],
      "c_error": [
        0.0,
        0.1
      ],
      "fs_kHz": [
        10,
        1000
      ],
      "receiver_pos_error": [
        0.0,
        0.02
      ],
      "rho_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "3D linear acoustic wave propagation",
  "title": "Acoustic Wave Equation \u2014 time-domain pressure field reconstruction"
}

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