L1 ⚛ L1-265 ⊙ Testnet

Acoustic Beamforming — DOA & imaging from array

Acoustics · Sensor-array DOA estimation

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⬇ L1-265.md

# ⚛ L1 Principle — Acoustic Beamforming — DOA & imaging from array **ID:** `L1-265` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *Sensor-array DOA estimation* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** angular power spectrum > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554049 --- ## 🧠 1. Introduction **Acoustic Beamforming — DOA & imaging from array** is a **linear inverse problem** whose unknown lives in **angular power spectrum** space, within the **Sensor-array DOA estimation** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **microphone array** sensing mechanism. The forward operator applies, in order: S · array capture operator; L · steering vector operator; L · power map operator; pixel-level spatial averaging on the detector. 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 · steering vector → L · power map → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.power_map` `L.steering_vector` `S.array_capture` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.array_capture` | S · array capture operator | | `L.steering_vector` | L · steering vector operator | | `L.power_map` | L · power map operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | Sensor-array DOA estimation | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | angular_power_spectrum | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | DOA_MAE_deg | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `doa_beamforming` · **Forward operator:** `doa_beamforming_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N mic | — | 16 | | Snr db | dB | 20 | | N sources | — | 2 | | N snapshots | — | 256 | | Sensor pos error | — | 0 | | Element gain error | — | 0 | | Element phase error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N mic | — | 4 – 256 | | Snr db | dB | -10 – 40 | | N sources | — | 1 – 8 | | N snapshots | — | 16 – 8192 | | Sensor pos error | — | 0.0 – 0.1 | | Element gain error | — | 0.0 – 0.2 | | Element phase error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.5 | Metric | Range | |---|---| | Doa deg | 0.1 – 10.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **DOA_MAE_deg**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7f79f6012053e88be1f95fb54349778fd6dfeeb0ee937d05f0ee560cc6add08f` - **Chain tx hash:** `0x4b234590397c21b94b417cdc38890342e0c837d8584dc707ff7f3a0b02259262` - **Chain block:** `41554049` --- ## File Mapping This bundle consists of: `L1-265.md`, `L1-265.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-265.md` | Source of truth — edit this | Human or LLM | | `L1-265.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 `L1-265`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-265.md).
Regenerate L1-265.json so every field matches the Markdown.
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L2-265-001 Acoustic Beamforming — DOA & imaging from array Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-265",
  "chain_block": 41554049,
  "chain_hash": "0x7f79f6012053e88be1f95fb54349778fd6dfeeb0ee937d05f0ee560cc6add08f",
  "chain_tx_hash": "0x4b234590397c21b94b417cdc38890342e0c837d8584dc707ff7f3a0b02259262",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "DOA_MAE_deg",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "DOA_MAE_deg",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "acoustic",
    "difficulty_delta": 3,
    "domain": "Acoustics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "S.array_capture",
      "L.steering_vector",
      "L.power_map",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "microphone_array",
    "solution_space": "angular_power_spectrum",
    "sub_domain": "Sensor-array DOA estimation",
    "title": "Acoustic Beamforming \u2014 DOA \u0026 imaging from array"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "doa_beamforming_forward"
    ],
    "allowed_omega_dimensions": [
      "N_mic",
      "N_snapshots",
      "N_sources",
      "SNR_dB",
      "element_gain_error",
      "element_phase_error",
      "sensor_pos_error",
      "element_gain_error",
      "element_phase_error",
      "sensor_pos_error"
    ],
    "allowed_problem_classes": [
      "doa_beamforming"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.5",
      "forward_operator": "doa_beamforming_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_mic": 16,
        "N_snapshots": 256,
        "N_sources": 2,
        "SNR_dB": 20,
        "element_gain_error": 0.0,
        "element_phase_error": 0.0,
        "sensor_pos_error": 0.0
      },
      "problem_class": "doa_beamforming"
    },
    "epsilon_bounds": {
      "doa_deg": [
        0.1,
        10.0
      ]
    },
    "omega_bounds": {
      "N_mic": [
        4,
        256
      ],
      "N_snapshots": [
        16,
        8192
      ],
      "N_sources": [
        1,
        8
      ],
      "SNR_dB": [
        -10,
        40
      ],
      "element_gain_error": [
        0.0,
        0.2
      ],
      "element_phase_error": [
        0.0,
        0.3
      ],
      "sensor_pos_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sensor-array DOA estimation",
  "title": "Acoustic Beamforming \u2014 DOA \u0026 imaging from array"
}

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