L1 ⚛ L1-263 ⊙ Testnet

Underwater Normal Modes — modal propagation (KRAKEN)

Acoustics · Shallow-water modal expansion

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⬇ L1-263.md

# ⚛ L1 Principle — Underwater Normal Modes — modal propagation (KRAKEN) **ID:** `L1-263` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *Shallow-water modal expansion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** modal eigenfunction set > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554049 --- ## 🧠 1. Introduction **Underwater Normal Modes — modal propagation (KRAKEN)** is a **linear inverse problem** whose unknown lives in **modal eigenfunction set** space, within the **Shallow-water modal expansion** sub-domain of **Acoustics**. Measurements consist of acoustic pressure waves recorded by transducers via a **hydrophones** sensing mechanism. The forward operator applies, in order: L · eigenvalue solve operator; L · mode sum operator; L · range propagate operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · eigenvalue solve → L · mode sum → L · range propagate → Frequency integration → **y** (detector). ``` y = ∫dω `L.range_propagate` `L.mode_sum` `L.eigenvalue_solve` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.eigenvalue_solve` | L · eigenvalue solve operator | | `L.mode_sum` | L · mode sum operator | | `L.range_propagate` | L · range propagate operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | Shallow-water modal expansion | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | modal_eigenfunction_set | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 5 | | L dag | 3 | ## 📡 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:** `kraken_normal_modes` · **Forward operator:** `kraken_normal_modes_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N depth | — | 256 | | N modes | — | 20 | | Freq hz | Hz | 500 | | Ssp error | — | 0 | | Waveguide depth error | — | 0 | | Bottom sound speed error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | -5 – 40 | | N depth | — | 32 – 1024 | | N modes | — | 3 – 100 | | Freq hz | Hz | 20 – 5000 | | Ssp error | — | 0.0 – 0.02 | | Waveguide depth error | — | 0.0 – 5.0 | | Bottom sound speed error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 23.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc90ab53ff8d85c26a9e9b23713ab46c1fedd15142992c9cdb21816ea3b7ffa6a` - **Chain tx hash:** `0x4553b253d9b17884b506948ea280f081d4b0e3588d1e0fba2bf2e3a2c78706cd` - **Chain block:** `41554049` --- ## File Mapping This bundle consists of: `L1-263.md`, `L1-263.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-263.md` | Source of truth — edit this | Human or LLM | | `L1-263.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 `L1-263`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-263.md).
Regenerate L1-263.json so every field matches the Markdown.
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⌥ Hierarchy

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L2-263-001 Underwater Normal Modes — modal propagation (KRAKEN) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-263",
  "chain_block": 41554049,
  "chain_hash": "0xc90ab53ff8d85c26a9e9b23713ab46c1fedd15142992c9cdb21816ea3b7ffa6a",
  "chain_tx_hash": "0x4553b253d9b17884b506948ea280f081d4b0e3588d1e0fba2bf2e3a2c78706cd",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "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": 3.0,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Acoustics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.eigenvalue_solve",
      "L.mode_sum",
      "L.range_propagate",
      "int.frequency"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "hydrophones",
    "solution_space": "modal_eigenfunction_set",
    "sub_domain": "Shallow-water modal expansion",
    "title": "Underwater Normal Modes \u2014 modal propagation (KRAKEN)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "kraken_normal_modes_forward"
    ],
    "allowed_omega_dimensions": [
      "N_modes",
      "N_depth",
      "freq_Hz",
      "SNR_dB",
      "ssp_error",
      "waveguide_depth_error",
      "bottom_sound_speed_error",
      "ssp_error",
      "waveguide_depth_error",
      "bottom_sound_speed_error"
    ],
    "allowed_problem_classes": [
      "kraken_normal_modes"
    ],
    "center_spec": {
      "epsilon_fn_center": "23.0",
      "forward_operator": "kraken_normal_modes_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_depth": 256,
        "N_modes": 20,
        "SNR_dB": 30,
        "bottom_sound_speed_error": 0.0,
        "freq_Hz": 500,
        "ssp_error": 0.0,
        "waveguide_depth_error": 0.0
      },
      "problem_class": "kraken_normal_modes"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_depth": [
        32,
        1024
      ],
      "N_modes": [
        3,
        100
      ],
      "SNR_dB": [
        -5,
        40
      ],
      "bottom_sound_speed_error": [
        0.0,
        0.2
      ],
      "freq_Hz": [
        20,
        5000
      ],
      "ssp_error": [
        0.0,
        0.02
      ],
      "waveguide_depth_error": [
        0.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Shallow-water modal expansion",
  "title": "Underwater Normal Modes \u2014 modal propagation (KRAKEN)"
}

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