L1 ⚛ L1-260 ⊙ Testnet

Room Acoustics — image-source method (shoebox rooms)

Acoustics · Image-source mirror-reflection model

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⬇ L1-260.md

# ⚛ L1 Principle — Room Acoustics — image-source method (shoebox rooms) **ID:** `L1-260` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *Image-source mirror-reflection model* > **🎯 Problem class:** forward · **🧮 Solution space:** room impulse response 1D > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554036 --- ## 🧠 1. Introduction **Room Acoustics — image-source method (shoebox rooms)** is a **forward-model simulation** whose unknown lives in **room impulse response 1D** space, within the **Image-source mirror-reflection model** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **pressure mic** sensing mechanism. The forward operator applies, in order: L · mirror · images operator; L · delay sum operator; L · absorb 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 · mirror · images → L · delay sum → L · absorb → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.absorb` `L.delay_sum` `L.mirror.images` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.mirror.images` | L · mirror · images operator | | `L.delay_sum` | L · delay sum operator | | `L.absorb` | L · absorb operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | Image-source mirror-reflection model | | Carrier | acoustic | | Problem class | forward | | Solution space | room_impulse_response_1D | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 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:** `image_source` · **Forward operator:** `image_source_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H m | m | 3 | | L m | m | 6 | | W m | m | 8 | | Fs khz | kHz | 48 | | Max order | — | 20 | | Geometry error | — | 0 | | Src rec pos error | — | 0 | | Reflection coeff error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H m | m | 2 – 15 | | L m | m | 2 – 30 | | W m | m | 2 – 30 | | Fs khz | kHz | 8 – 96 | | Max order | — | 1 – 80 | | Geometry error | — | 0.0 – 0.02 | | Src rec pos error | — | 0.0 – 0.1 | | Reflection coeff error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x92baec9e350ee978330a22258a0d887b082d6e2e8cac88eeb9a7d1a538763155` - **Chain tx hash:** `0x1c72ee217e0dbd26fb1313a70396e766d262abbd5f98563becec5699705d1954` - **Chain block:** `41554036` --- ## File Mapping This bundle consists of: `L1-260.md`, `L1-260.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-260.md` | Source of truth — edit this | Human or LLM | | `L1-260.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 `L1-260`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-260.md).
Regenerate L1-260.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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L2-260-001 Room Acoustics — image-source method (shoebox rooms) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-260",
  "chain_block": 41554036,
  "chain_hash": "0x92baec9e350ee978330a22258a0d887b082d6e2e8cac88eeb9a7d1a538763155",
  "chain_tx_hash": "0x1c72ee217e0dbd26fb1313a70396e766d262abbd5f98563becec5699705d1954",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "acoustic",
    "difficulty_delta": 3,
    "domain": "Acoustics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.mirror.images",
      "L.delay_sum",
      "L.absorb",
      "int.temporal"
    ],
    "problem_class": "forward",
    "sensing_mechanism": "pressure_mic",
    "solution_space": "room_impulse_response_1D",
    "sub_domain": "Image-source mirror-reflection model",
    "title": "Room Acoustics \u2014 image-source method (shoebox rooms)"
  },
  "size_tiers": {
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      "image_source_forward"
    ],
    "allowed_omega_dimensions": [
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      "W_m",
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      "max_order",
      "fs_kHz",
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      "geometry_error",
      "src_rec_pos_error",
      "reflection_coeff_error",
      "geometry_error",
      "src_rec_pos_error"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "image_source_forward",
      "input_format": "measurement_only",
      "omega": {
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        "L_m": 6,
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        "fs_kHz": 48,
        "geometry_error": 0.0,
        "max_order": 20,
        "reflection_coeff_error": 0.0,
        "src_rec_pos_error": 0.0
      },
      "problem_class": "image_source"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        45.0
      ]
    },
    "omega_bounds": {
      "H_m": [
        2,
        15
      ],
      "L_m": [
        2,
        30
      ],
      "W_m": [
        2,
        30
      ],
      "fs_kHz": [
        8,
        96
      ],
      "geometry_error": [
        0.0,
        0.02
      ],
      "max_order": [
        1,
        80
      ],
      "reflection_coeff_error": [
        0.0,
        0.3
      ],
      "src_rec_pos_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Image-source mirror-reflection model",
  "title": "Room Acoustics \u2014 image-source method (shoebox rooms)"
}

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