L1 ⚛ L1-314 ⊙ Testnet

Quantum Scattering Theory

Quantum Mechanics · S-matrix and phase shifts

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⬇ L1-314.md

# ⚛ L1 Principle — Quantum Scattering Theory **ID:** `L1-314` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *S-matrix and phase shifts* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** phase shifts scattering amplitude > **📡 Carrier:** electron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554079 --- ## 🧠 1. Introduction **Quantum Scattering Theory** is a **nonlinear inverse problem** whose unknown lives in **phase shifts scattering amplitude** space, within the **S-matrix and phase shifts** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **cross section measurement** sensing mechanism. The forward operator applies, in order: E · lippmann schwinger operator; computes eigen-pairs of a linear operator; O · cross section operator. Observations are corrupted by Poisson counting noise. Well-posed forward; inverse scattering (reconstructing V from f(E,theta)) is Borg-Marchenko-style; unique with phase info. ## ⚙ 2. Forward Model Physical chain: **x** → E · lippmann schwinger → O · cross section → **y** (detector). ``` y = `O.cross_section` `E.lippmann_schwinger` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.lippmann_schwinger` | E · lippmann schwinger operator | | `O.cross_section` | O · cross section operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `E.eigensolve` | Computes eigen-pairs of a linear operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | S-matrix and phase shifts | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | phase_shifts_scattering_amplitude | | Noise model | poisson | | Integration axis | angle_and_energy | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Well-posed forward; inverse scattering (reconstructing V from f(E,theta)) is Borg-Marchenko-style; unique with phase info. | Metric | Value | |---|---| | Metric | sigma_total_relative_error | | Secondary | phase_shift_error_deg | ## 📏 5. Operating Range (Ω) **Center problem class:** `quantum_scattering` · **Forward operator:** `scattering_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | E ev | — | 10 | | L max | — | 8 | | N grid | — | 500 | | V well ev | — | 5 | | Target type | — | atomic | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | E ev | — | 0.001 – 1000000.0 | | L max | — | 1 – 50 | | N grid | — | 100 – 10000 | | V well ev | — | 0.1 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** sigma error <= 0.03 | Metric | Range | |---|---| | Sigma total relative error | 0.005 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **sigma_total_relative_error**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5eeb1cfc8baec60d6b737b7493896a6f892bbf0c686bce3979281e612c6a5823` - **Chain tx hash:** `0x465854a0ec7d1dd8f0e40494d21f7caf07ba95d67b5ad6dd432bf33f4f0c6df4` - **Chain block:** `41554079` --- ## File Mapping This bundle consists of: `L1-314.md`, `L1-314.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-314.md` | Source of truth — edit this | Human or LLM | | `L1-314.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 `L1-314`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-314.md).
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L2-314-001 Quantum Scattering Theory Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554079,
  "chain_hash": "0x5eeb1cfc8baec60d6b737b7493896a6f892bbf0c686bce3979281e612c6a5823",
  "chain_tx_hash": "0x465854a0ec7d1dd8f0e40494d21f7caf07ba95d67b5ad6dd432bf33f4f0c6df4",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
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    "kappa": 400,
    "metric": "sigma_total_relative_error",
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    "secondary": "phase_shift_error_deg"
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  "physics_fingerprint": {
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    "difficulty_delta": 5,
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    "integration_axis": "angle_and_energy",
    "noise_model": "poisson",
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    "sensing_mechanism": "cross_section_measurement",
    "solution_space": "phase_shifts_scattering_amplitude",
    "sub_domain": "S-matrix and phase shifts",
    "title": "Quantum Scattering Theory"
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      "l_max": [
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "S-matrix and phase shifts",
  "title": "Quantum Scattering Theory"
}

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