L1 ⚛ L1-264 ⊙ Testnet

Underwater Acoustics — Parabolic Equation (RAM)

Acoustics · Pade-expansion split-step PE

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-264

⬇ L1-264.md ⬇ L1-264.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-264 (Underwater Acoustics — Parabolic Equation (RAM)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-264.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-264.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `int.range` `L.absorb_bottom` `L.marching.range` `L.split_step_pe` x + n,    n ~ 𝒩(0, σ²)

world state x (complex pressure range depth 2D)

→

L · split step pe `L.split_step_pe`

→

L · marching · range `L.marching.range`

→

L · absorb bottom `L.absorb_bottom`

→

int · range `int.range`

→

observation y (acoustic detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-264.md

# ⚛ L1 Principle — Underwater Acoustics — Parabolic Equation (RAM) **ID:** `L1-264` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Acoustics — *Pade-expansion split-step PE* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex pressure range depth 2D > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554049 --- ## 🧠 1. Introduction **Underwater Acoustics — Parabolic Equation (RAM)** is a **linear inverse problem** whose unknown lives in **complex pressure range depth 2D** space, within the **Pade-expansion split-step PE** 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 · split step pe operator; L · marching · range operator; L · absorb bottom operator; int · range operator. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · split step pe → L · marching · range → L · absorb bottom → int · range → **y** (detector). ``` y = `int.range` `L.absorb_bottom` `L.marching.range` `L.split_step_pe` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.split_step_pe` | L · split step pe operator | | `L.marching.range` | L · marching · range operator | | `L.absorb_bottom` | L · absorb bottom operator | | `int.range` | Int · range operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Acoustics | | Sub domain | Pade-expansion split-step PE | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | complex_pressure_range_depth_2D | | Noise model | gaussian | | Integration axis | range | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `ram_pe` · **Forward operator:** `ram_pe_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N depth | — | 256 | | N range | — | 1024 | | Freq hz | Hz | 100 | | Ssp error | — | 0 | | Pade order | — | 8 | | Range step dr | — | 0 | | Bottom atten error | — | 0 | | Pade order truncation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | -5 – 40 | | N depth | — | 64 – 2048 | | N range | — | 128 – 8192 | | Freq hz | Hz | 10 – 2000 | | Ssp error | — | 0.0 – 0.02 | | Pade order | — | 1 – 10 | | Range step dr | — | 0.0 – 1.0 | | Bottom atten error | — | 0.0 – 0.2 | | Pade order truncation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 23.5 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `440` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa31398de1ec9a1e678488d83603531bb330038b2aa81a409634b6116a831baf7` - **Chain tx hash:** `0xd74677a1202c180d7d19e8589407a3ee6f134759ed4eae112ae58e2e43ecd450` - **Chain block:** `41554049` --- ## File Mapping This bundle consists of: `L1-264.md`, `L1-264.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-264.md` | Source of truth — edit this | Human or LLM | | `L1-264.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 `L1-264`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-264-001 Underwater Acoustics — Parabolic Equation (RAM) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-264",
  "chain_block": 41554049,
  "chain_hash": "0xa31398de1ec9a1e678488d83603531bb330038b2aa81a409634b6116a831baf7",
  "chain_tx_hash": "0xd74677a1202c180d7d19e8589407a3ee6f134759ed4eae112ae58e2e43ecd450",
  "domain": "Acoustics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 440,
    "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": 3.3,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Acoustics",
    "integration_axis": "range",
    "noise_model": "gaussian",
    "primitives": [
      "L.split_step_pe",
      "L.marching.range",
      "L.absorb_bottom",
      "int.range"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "hydrophones",
    "solution_space": "complex_pressure_range_depth_2D",
    "sub_domain": "Pade-expansion split-step PE",
    "title": "Underwater Acoustics \u2014 Parabolic Equation (RAM)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ram_pe_forward"
    ],
    "allowed_omega_dimensions": [
      "N_range",
      "N_depth",
      "freq_Hz",
      "pade_order",
      "SNR_dB",
      "ssp_error",
      "range_step_dr",
      "pade_order_truncation",
      "bottom_atten_error",
      "ssp_error",
      "range_step_dr",
      "pade_order_truncation",
      "bottom_atten_error"
    ],
    "allowed_problem_classes": [
      "ram_pe"
    ],
    "center_spec": {
      "epsilon_fn_center": "23.5",
      "forward_operator": "ram_pe_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_depth": 256,
        "N_range": 1024,
        "SNR_dB": 30,
        "bottom_atten_error": 0.0,
        "freq_Hz": 100,
        "pade_order": 8,
        "pade_order_truncation": 0.0,
        "range_step_dr": 0.0,
        "ssp_error": 0.0
      },
      "problem_class": "ram_pe"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_depth": [
        64,
        2048
      ],
      "N_range": [
        128,
        8192
      ],
      "SNR_dB": [
        -5,
        40
      ],
      "bottom_atten_error": [
        0.0,
        0.2
      ],
      "freq_Hz": [
        10,
        2000
      ],
      "pade_order": [
        1,
        10
      ],
      "pade_order_truncation": [
        0.0,
        0.3
      ],
      "range_step_dr": [
        0.0,
        1.0
      ],
      "ssp_error": [
        0.0,
        0.02
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Pade-expansion split-step PE",
  "title": "Underwater Acoustics \u2014 Parabolic Equation (RAM)"
}

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