L1 ⚛ L1-489 ⊙ Testnet

Hydrodynamic Semiconductor Transport

Semiconductor Physics · Energy-balance transport

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

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._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-489.md).
Regenerate L1-489.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

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

⬇ Download bundle

2 files · click to download

📋 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"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.