L2 📐 L2-489-001 ⊙ Testnet

Hydrodynamic Semiconductor Transport Mismatch-Only Spec

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⬇ spec.md ⬇ spec.json

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⬇ L2-489-001.md ⬇ L2-489-001.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L2-489-001 (Hydrodynamic Semiconductor Transport Mismatch-Only Spec) to the PWM Protocol — a Digital Twin (L2) artifact.

I will paste a Markdown template (or the current L2-489-001.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L2-489-001.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

derived from principle L1-489 
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
⬇ L2-489-001.md