L1 ⚛ L1-181 ⊙ Testnet

Shallow Water Equations — coastal/tidal/inundation

Fluid Dynamics · 2D shallow-water on a sphere / river / coast

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Markdown — human-readable source of truth

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⬇ L1-181.md

# ⚛ L1 Principle — Shallow Water Equations — coastal/tidal/inundation **ID:** `L1-181` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *2D shallow-water on a sphere / river / coast* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** water level and currents > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553967 --- ## 🧠 1. Introduction **Shallow Water Equations — coastal/tidal/inundation** is a **linear inverse problem** whose unknown lives in **water level and currents** space, within the **2D shallow-water on a sphere / river / coast** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **tide gauges altimetry** sensing mechanism. The forward operator applies, in order: L · continuity 2d operator; L · momentum 2d operator; L · bottom friction 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 · continuity 2d → L · momentum 2d → L · bottom friction → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.bottom_friction` `L.momentum_2d` `L.continuity_2d` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.continuity_2d` | L · continuity 2d operator | | `L.momentum_2d` | L · momentum 2d operator | | `L.bottom_friction` | L · bottom friction operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | 2D shallow-water on a sphere / river / coast | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | water_level_and_currents | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | 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:** `swe` · **Forward operator:** `swe_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 30 | | N times | — | 2000 | | Friction error | — | 0 | | Bathymetry error | — | 0 | | Wind forcing error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 4096 | | W | px | 64 – 4096 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | Friction error | — | 0.0 – 0.3 | | Bathymetry error | — | 0.0 – 0.1 | | Wind forcing error | — | 0.0 – 0.3 | ## 🎯 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 = `300` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xee6ce60fa4a17af7a9531ce4b606e7c486339518fb1d34cded42713d9796e16a` - **Chain tx hash:** `0x80a5a02b27214dc7a638d060f74672ab455cd0008eae98720bc8a79a4f7d1a38` - **Chain block:** `41553967` --- ## File Mapping This bundle consists of: `L1-181.md`, `L1-181.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-181.md` | Source of truth — edit this | Human or LLM | | `L1-181.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 `L1-181`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-181.md).
Regenerate L1-181.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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L2-181-001 Shallow Water Equations — coastal/tidal/inundation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-181",
  "chain_block": 41553967,
  "chain_hash": "0xee6ce60fa4a17af7a9531ce4b606e7c486339518fb1d34cded42713d9796e16a",
  "chain_tx_hash": "0x80a5a02b27214dc7a638d060f74672ab455cd0008eae98720bc8a79a4f7d1a38",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "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": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.continuity_2d",
      "L.momentum_2d",
      "L.bottom_friction",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "tide_gauges_altimetry",
    "solution_space": "water_level_and_currents",
    "sub_domain": "2D shallow-water on a sphere / river / coast",
    "title": "Shallow Water Equations \u2014 coastal/tidal/inundation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "swe_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_times",
      "SNR_dB",
      "bathymetry_error",
      "friction_error",
      "wind_forcing_error",
      "bathymetry_error",
      "friction_error",
      "wind_forcing_error"
    ],
    "allowed_problem_classes": [
      "swe"
    ],
    "center_spec": {
      "epsilon_fn_center": "23.0",
      "forward_operator": "swe_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "N_times": 2000,
        "SNR_dB": 30,
        "W": 512,
        "bathymetry_error": 0.0,
        "friction_error": 0.0,
        "wind_forcing_error": 0.0
      },
      "problem_class": "swe"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        4096
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        4096
      ],
      "bathymetry_error": [
        0.0,
        0.1
      ],
      "friction_error": [
        0.0,
        0.3
      ],
      "wind_forcing_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "2D shallow-water on a sphere / river / coast",
  "title": "Shallow Water Equations \u2014 coastal/tidal/inundation"
}

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