L1 ⚛ L1-267 ⊙ Testnet

Acoustic Emission — source localization

Acoustics · TDOA-based AE source localization

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⬇ L1-267.md

# ⚛ L1 Principle — Acoustic Emission — source localization **ID:** `L1-267` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *TDOA-based AE source localization* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** source xyz set > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554050 --- ## 🧠 1. Introduction **Acoustic Emission — source localization** is a **nonlinear inverse problem** whose unknown lives in **source xyz set** space, within the **TDOA-based AE source localization** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **ae piezoelectric sensors** sensing mechanism. The forward operator applies, in order: S · array capture operator; L · tdoa operator; L · hyperboloid intersect 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** → S · array capture → L · tdoa → L · hyperboloid intersect → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.hyperboloid_intersect` `L.tdoa` `S.array_capture` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.array_capture` | S · array capture operator | | `L.tdoa` | L · tdoa operator | | `L.hyperboloid_intersect` | L · hyperboloid intersect operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | TDOA-based AE source localization | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | source_xyz_set | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | localization_MAE_mm | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ae_tdoa` · **Forward operator:** `ae_tdoa_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 20 | | Fs mhz | MHz | 1 | | N events | — | 100 | | N sensors | — | 8 | | Anisotropy | — | 0 | | Pick time error | — | 0 | | Sensor pos error | — | 0 | | Wave speed error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | -5 – 40 | | Fs mhz | MHz | 0.1 – 40 | | N events | — | 10 – 10000 | | N sensors | — | 4 – 128 | | Anisotropy | — | 0.0 – 0.3 | | Pick time error | — | 0.0 – 10.0 | | Sensor pos error | — | 0.0 – 0.05 | | Wave speed error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 | Metric | Range | |---|---| | Localization mm | 0.1 – 100.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **localization_MAE_mm**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5956ab1d66911c32043293bd959b97688f11f393d2e2d76d98662aa6a6d9f997` - **Chain tx hash:** `0x7b640c6841911c3dccbcd09f86f04a9f8836629cc8c20e8e13e3f13bb73ef49b` - **Chain block:** `41554050` --- ## File Mapping This bundle consists of: `L1-267.md`, `L1-267.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-267.md` | Source of truth — edit this | Human or LLM | | `L1-267.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 `L1-267`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-267.md).
Regenerate L1-267.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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L2-267-001 Acoustic Emission — source localization Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-267",
  "chain_block": 41554050,
  "chain_hash": "0x5956ab1d66911c32043293bd959b97688f11f393d2e2d76d98662aa6a6d9f997",
  "chain_tx_hash": "0x7b640c6841911c3dccbcd09f86f04a9f8836629cc8c20e8e13e3f13bb73ef49b",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "localization_MAE_mm",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "localization_MAE_mm",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Acoustics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "S.array_capture",
      "L.tdoa",
      "L.hyperboloid_intersect",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "ae_piezoelectric_sensors",
    "solution_space": "source_xyz_set",
    "sub_domain": "TDOA-based AE source localization",
    "title": "Acoustic Emission \u2014 source localization"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ae_tdoa_forward"
    ],
    "allowed_omega_dimensions": [
      "N_sensors",
      "N_events",
      "fs_MHz",
      "SNR_dB",
      "sensor_pos_error",
      "wave_speed_error",
      "pick_time_error",
      "anisotropy",
      "sensor_pos_error",
      "wave_speed_error",
      "pick_time_error",
      "anisotropy"
    ],
    "allowed_problem_classes": [
      "ae_tdoa"
    ],
    "center_spec": {
      "epsilon_fn_center": "5.0",
      "forward_operator": "ae_tdoa_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_events": 100,
        "N_sensors": 8,
        "SNR_dB": 20,
        "anisotropy": 0.0,
        "fs_MHz": 1,
        "pick_time_error": 0.0,
        "sensor_pos_error": 0.0,
        "wave_speed_error": 0.0
      },
      "problem_class": "ae_tdoa"
    },
    "epsilon_bounds": {
      "localization_mm": [
        0.1,
        100.0
      ]
    },
    "omega_bounds": {
      "N_events": [
        10,
        10000
      ],
      "N_sensors": [
        4,
        128
      ],
      "SNR_dB": [
        -5,
        40
      ],
      "anisotropy": [
        0.0,
        0.3
      ],
      "fs_MHz": [
        0.1,
        40
      ],
      "pick_time_error": [
        0.0,
        10.0
      ],
      "sensor_pos_error": [
        0.0,
        0.05
      ],
      "wave_speed_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "TDOA-based AE source localization",
  "title": "Acoustic Emission \u2014 source localization"
}

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