L1 ⚛ L1-421 ⊙ Testnet

River Hydraulics Shallow Water Inversion

Environmental Science · Hydrology

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⬇ principle.md ⬇ principle.json

Fork L1-421

⬇ L1-421.md ⬇ L1-421.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-421 (River Hydraulics Shallow Water Inversion) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-421.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-421.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 = `S.fdm.flood_routing` `O.least_squares.rating_curve` ∇ x + n,    n ~ 𝒩(0, σ²)

world state x (Manning roughness bathymetry)

→

Spatial derivative ∇

→

O · least squares · rating curve `O.least_squares.rating_curve`

→

S · fdm · flood routing `S.fdm.flood_routing`

→

observation y (N/A detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-421.md

# ⚛ L1 Principle — River Hydraulics Shallow Water Inversion **ID:** `L1-421` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Environmental Science — *Hydrology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** Manning roughness bathymetry > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555239 --- ## 🧠 1. Introduction **River Hydraulics Shallow Water Inversion** is a **parameter-estimation problem** whose unknown lives in **Manning roughness bathymetry** space, within the **Hydrology** sub-domain of **Environmental Science**. Measurements consist of N/A via a **water level discharge measurement** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; O · least squares · rating curve operator; S · fdm · flood routing operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered Manning_roughness_bathymetry is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); bank_overflow_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → O · least squares · rating curve → S · fdm · flood routing → **y** (detector). ``` y = `S.fdm.flood_routing` `O.least_squares.rating_curve` ∇ x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `O.least_squares.rating_curve` | O · least squares · rating curve operator | | `S.fdm.flood_routing` | S · fdm · flood routing operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Environmental Science | | Sub domain | Hydrology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | Manning_roughness_bathymetry | | Noise model | gaussian | | Integration axis | river_reach | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered Manning_roughness_bathymetry is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); bank_overflow_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | water_level_RMSE_m | | Secondary | discharge_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `water_level_discharge_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | N gauges | — | 5 | | Roughness n | N | 0.035 | | Reach length km | km | 50 | | Discharge peak m3 s | s | 1000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N gauges | — | 2 – 50 | | Roughness n | N | 0.01 – 0.1 | | Reach length km | km | 1 – 1000 | | Discharge peak m3 s | s | 10 – 100000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.10 water_level_RMSE_m | Metric | Range | |---|---| | Water level rmse m | 0.01 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **water_level_RMSE_m**, with κ = `2000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x52599914468dae4784412df2a6ba1035a0b0b4c83e90b5818a9a0b7e13d04bdc` - **Chain tx hash:** `0xd4ecbe5745af85f060529b3b07df29d4aba36cf21b9c0e4ae5aa46bb59214c26` - **Chain block:** `41555239` --- ## File Mapping This bundle consists of: `L1-421.md`, `L1-421.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-421.md` | Source of truth — edit this | Human or LLM | | `L1-421.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 `L1-421`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-421-001 River Hydraulics Shallow Water Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-421",
  "chain_block": 41555239,
  "chain_hash": "0x52599914468dae4784412df2a6ba1035a0b0b4c83e90b5818a9a0b7e13d04bdc",
  "chain_tx_hash": "0xd4ecbe5745af85f060529b3b07df29d4aba36cf21b9c0e4ae5aa46bb59214c26",
  "domain": "Environmental Science",
  "hardness_fn": {
    "delta": 3,
    "kappa": 2000,
    "metric": "water_level_RMSE_m",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "water_level_RMSE_m",
    "regime": "Existence of the recovered Manning_roughness_bathymetry is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); bank_overflow_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.",
    "secondary": "discharge_RMSE_percent"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Environmental Science",
    "integration_axis": "river_reach",
    "noise_model": "gaussian",
    "primitives": [
      "D.space",
      "O.least_squares.rating_curve",
      "S.fdm.flood_routing"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "water_level_discharge_measurement",
    "solution_space": "Manning_roughness_bathymetry",
    "sub_domain": "Hydrology",
    "title": "River Hydraulics Shallow Water Inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
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    "allowed_omega_dimensions": [
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      "discharge_peak_m3_s",
      "roughness_n"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.10 water_level_RMSE_m",
      "forward_operator": "water_level_discharge_measurement",
      "input_format": "measurement_only",
      "omega": {
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        "discharge_peak_m3_s": 1000,
        "reach_length_km": 50,
        "roughness_n": 0.035
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "water_level_RMSE_m": [
        0.01,
        0.5
      ]
    },
    "omega_bounds": {
      "N_gauges": [
        2,
        50
      ],
      "discharge_peak_m3_s": [
        10,
        100000
      ],
      "reach_length_km": [
        1,
        1000
      ],
      "roughness_n": [
        0.01,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Hydrology",
  "title": "River Hydraulics Shallow Water Inversion"
}

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