L1 ⚛ L1-489 ⊙ Testnet

Hydrodynamic Semiconductor Transport

Semiconductor Physics · Energy-balance transport

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⬇ principle.md ⬇ principle.json

Fork L1-489

⬇ L1-489.md ⬇ L1-489.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-489 (Hydrodynamic Semiconductor Transport) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-489.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-489.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 = `O.hot_carrier_IV` `E.energy_balance` `E.momentum_balance` `E.continuity` x + n,    n ~ 𝒩(0, σ²)

world state x (n v Te hydrodynamic fields)

→

E · continuity `E.continuity`

→

E · momentum balance `E.momentum_balance`

→

E · energy balance `E.energy_balance`

→

O · hot carrier IV `O.hot_carrier_IV`

→

observation y (electron detector)

Noise: additive Gaussian noise

Solver / auxiliary components (1)

O.iter — a fixed-point or gradient iteration on the unknown

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-489.md

# ⚛ L1 Principle — Hydrodynamic Semiconductor Transport **ID:** `L1-489` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Energy-balance transport* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** n v Te hydrodynamic fields > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554141 --- ## 🧠 1. Introduction **Hydrodynamic Semiconductor Transport** is a **nonlinear inverse problem** whose unknown lives in **n v Te hydrodynamic fields** space, within the **Energy-balance transport** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **hot carrier transport** sensing mechanism. The forward operator applies, in order: E · continuity operator; E · momentum balance operator; E · energy balance operator; a fixed-point or gradient iteration on the unknown; O · hot carrier IV operator. Observations are corrupted by additive Gaussian noise. Stiff hyperbolic-parabolic system; shocks at hot-carrier fronts; closure model breaks down in ballistic regime. ## ⚙ 2. Forward Model Physical chain: **x** → E · continuity → E · momentum balance → E · energy balance → O · hot carrier IV → **y** (detector). ``` y = `O.hot_carrier_IV` `E.energy_balance` `E.momentum_balance` `E.continuity` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.continuity` | E · continuity operator | | `E.momentum_balance` | E · momentum balance operator | | `E.energy_balance` | E · energy balance operator | | `O.hot_carrier_IV` | O · hot carrier iv operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Semiconductor Physics | | Sub domain | Energy-balance transport | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | n_v_Te_hydrodynamic_fields | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 4.2 | ## 📡 4. Measurement Model Stiff hyperbolic-parabolic system; shocks at hot-carrier fronts; closure model breaks down in ballistic regime. | Metric | Value | |---|---| | Metric | IV_log_relative_error_high_field | | Secondary | Te_RMSE_K | ## 📏 5. Operating Range (Ω) **Center problem class:** `hydrodynamic_parameter_inversion` · **Forward operator:** `hydrodynamic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | Vds | — | 1 | | Mesh n | N | 128 | | N d cm3 | — | 1000000000000000000 | | L channel nm | nm | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 77 – 500 | | Vds | — | 0.1 – 5.0 | | Mesh n | N | 64 – 1024 | | N d cm3 | — | 1000000000000000.0 – 100000000000000000000 | | L channel nm | nm | 5 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** log10(I) error <= 0.04 | Metric | Range | |---|---| | Iv log relative error high field | 0.005 – 0.4 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **IV_log_relative_error_high_field**, with κ = `1500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8220575f93ccdf71eee8bc722509f0448e22644fce14de69112a5c889ef29a6d` - **Chain tx hash:** `0x73c570112e7a00f6e9bacf3974366679ba50482a62227a1b6c9b334c805ac5e6` - **Chain block:** `41554141` --- ## File Mapping This bundle consists of: `L1-489.md`, `L1-489.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-489.md` | Source of truth — edit this | Human or LLM | | `L1-489.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 `L1-489`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-489-001 Hydrodynamic Semiconductor Transport Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-489",
  "chain_block": 41554141,
  "chain_hash": "0x8220575f93ccdf71eee8bc722509f0448e22644fce14de69112a5c889ef29a6d",
  "chain_tx_hash": "0x73c570112e7a00f6e9bacf3974366679ba50482a62227a1b6c9b334c805ac5e6",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 1500,
    "metric": "IV_log_relative_error_high_field",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "IV_log_relative_error_high_field",
    "regime": "Stiff hyperbolic-parabolic system; shocks at hot-carrier fronts; closure model breaks down in ballistic regime.",
    "secondary": "Te_RMSE_K"
  },
  "physics_fingerprint": {
    "L_DAG": 4.2,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Semiconductor Physics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "E.continuity",
      "E.momentum_balance",
      "E.energy_balance",
      "O.iter",
      "O.hot_carrier_IV"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "hot_carrier_transport",
    "solution_space": "n_v_Te_hydrodynamic_fields",
    "sub_domain": "Energy-balance transport",
    "title": "Hydrodynamic Semiconductor Transport"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "hydrodynamic_forward"
    ],
    "allowed_omega_dimensions": [
      "L_channel_nm",
      "Vds",
      "N_D_cm3",
      "T_K",
      "mesh_N"
    ],
    "allowed_problem_classes": [
      "hydrodynamic_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "log10(I) error \u003c= 0.04",
      "forward_operator": "hydrodynamic_forward",
      "input_format": "measurement_only",
      "omega": {
        "L_channel_nm": 50,
        "N_D_cm3": 1000000000000000000,
        "T_K": 300,
        "Vds": 1.0,
        "mesh_N": 128
      },
      "problem_class": "hydrodynamic_parameter_inversion"
    },
    "epsilon_bounds": {
      "IV_log_relative_error_high_field": [
        0.005,
        0.4
      ]
    },
    "omega_bounds": {
      "L_channel_nm": [
        5,
        500
      ],
      "N_D_cm3": [
        1000000000000000.0,
        100000000000000000000
      ],
      "T_K": [
        77,
        500
      ],
      "Vds": [
        0.1,
        5.0
      ],
      "mesh_N": [
        64,
        1024
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Energy-balance transport",
  "title": "Hydrodynamic Semiconductor Transport"
}

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