L1 ⚛ L1-262 ⊙ Testnet

Underwater Acoustic Ray Tracing (Bellhop)

Acoustics · Range-depth ocean-acoustic ray / gaussian beam tracing

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-262.md

# ⚛ L1 Principle — Underwater Acoustic Ray Tracing (Bellhop) **ID:** `L1-262` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *Range-depth ocean-acoustic ray / gaussian beam tracing* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** transmission loss range depth > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554049 --- ## 🧠 1. Introduction **Underwater Acoustic Ray Tracing (Bellhop)** is a **linear inverse problem** whose unknown lives in **transmission loss range depth** space, within the **Range-depth ocean-acoustic ray / gaussian beam tracing** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **hydrophones** sensing mechanism. The forward operator applies, in order: isotropic point-source emission model; L · refract · sspe operator; L · bottom reflect 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** → Source emission → L · refract · sspe → L · bottom reflect → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.bottom_reflect` `L.refract.sspe` δ_source x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.source_emit` | Isotropic point-source emission model | | `L.refract.sspe` | L · refract · sspe operator | | `L.bottom_reflect` | L · bottom reflect operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | Range-depth ocean-acoustic ray / gaussian beam tracing | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | transmission_loss_range_depth | | 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 | TL_error_dB | | Secondary | arrival_time_MAE_ms | ## 📏 5. Operating Range (Ω) **Center problem class:** `bellhop_ray` · **Forward operator:** `bellhop_ray_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N rays | — | 10000 | | Snr db | dB | 30 | | N depth | — | 256 | | N range | — | 512 | | Freq hz | Hz | 1000 | | Ssp error | — | 0 | | Range error | — | 0 | | Bathymetry error | — | 0 | | Bottom properties error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N rays | — | 1000 – 1000000 | | Snr db | dB | -10 – 40 | | N depth | — | 32 – 1024 | | N range | — | 64 – 4096 | | Freq hz | Hz | 10 – 100000 | | Ssp error | — | 0.0 – 0.02 | | Range error | — | 0.0 – 50.0 | | Bathymetry error | — | 0.0 – 10.0 | | Bottom properties error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 | Metric | Range | |---|---| | Tl db | 0.5 – 20.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **TL_error_dB**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6b27bd1b0fd0e67b1aa427bac1373576e9dd06c3f39cb6f6c050ba1d840ca301` - **Chain tx hash:** `0x63b415cef453dc802d7f1c23afaea26358b183876297bf2d4aa424099e12bb92` - **Chain block:** `41554049` --- ## File Mapping This bundle consists of: `L1-262.md`, `L1-262.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-262.md` | Source of truth — edit this | Human or LLM | | `L1-262.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 `L1-262`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-262.md).
Regenerate L1-262.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-262-001 Underwater Acoustic Ray Tracing (Bellhop) Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-262",
  "chain_block": 41554049,
  "chain_hash": "0x6b27bd1b0fd0e67b1aa427bac1373576e9dd06c3f39cb6f6c050ba1d840ca301",
  "chain_tx_hash": "0x63b415cef453dc802d7f1c23afaea26358b183876297bf2d4aa424099e12bb92",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "TL_error_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "TL_error_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "arrival_time_MAE_ms"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Acoustics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.source_emit",
      "L.refract.sspe",
      "L.bottom_reflect",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "hydrophones",
    "solution_space": "transmission_loss_range_depth",
    "sub_domain": "Range-depth ocean-acoustic ray / gaussian beam tracing",
    "title": "Underwater Acoustic Ray Tracing (Bellhop)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "bellhop_ray_forward"
    ],
    "allowed_omega_dimensions": [
      "N_range",
      "N_depth",
      "N_rays",
      "freq_Hz",
      "SNR_dB",
      "ssp_error",
      "bathymetry_error",
      "bottom_properties_error",
      "range_error",
      "ssp_error",
      "bathymetry_error",
      "bottom_properties_error",
      "range_error"
    ],
    "allowed_problem_classes": [
      "bellhop_ray"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0",
      "forward_operator": "bellhop_ray_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_depth": 256,
        "N_range": 512,
        "N_rays": 10000,
        "SNR_dB": 30,
        "bathymetry_error": 0.0,
        "bottom_properties_error": 0.0,
        "freq_Hz": 1000,
        "range_error": 0.0,
        "ssp_error": 0.0
      },
      "problem_class": "bellhop_ray"
    },
    "epsilon_bounds": {
      "TL_dB": [
        0.5,
        20.0
      ]
    },
    "omega_bounds": {
      "N_depth": [
        32,
        1024
      ],
      "N_range": [
        64,
        4096
      ],
      "N_rays": [
        1000,
        1000000
      ],
      "SNR_dB": [
        -10,
        40
      ],
      "bathymetry_error": [
        0.0,
        10.0
      ],
      "bottom_properties_error": [
        0.0,
        0.3
      ],
      "freq_Hz": [
        10,
        100000
      ],
      "range_error": [
        0.0,
        50.0
      ],
      "ssp_error": [
        0.0,
        0.02
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Range-depth ocean-acoustic ray / gaussian beam tracing",
  "title": "Underwater Acoustic Ray Tracing (Bellhop)"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.