L1 ⚛ L1-318 ⊙ Testnet

Tight-Binding Electronic Structure

Quantum Mechanics · Minimal-basis electronic models

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⬇ L1-318.md

# ⚛ L1 Principle — Tight-Binding Electronic Structure **ID:** `L1-318` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Minimal-basis electronic models* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** tb parameter vector > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554080 --- ## 🧠 1. Introduction **Tight-Binding Electronic Structure** is a **linear inverse problem** whose unknown lives in **tb parameter vector** space, within the **Minimal-basis electronic models** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **arpes stm** sensing mechanism. The forward operator applies, in order: E · SK parameters operator; computes eigen-pairs of a linear operator; O · DOS band operator. Observations are corrupted by additive Gaussian noise. Well-posed; TB parameter fit from DFT is regularized. ## ⚙ 2. Forward Model Physical chain: **x** → E · SK parameters → O · DOS band → **y** (detector). ``` y = `O.DOS_band` `E.SK_parameters` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.SK_parameters` | E · sk parameters operator | | `O.DOS_band` | O · dos band 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 | Minimal-basis electronic models | | Carrier | electron | | Problem class | linear_inverse | | Solution space | tb_parameter_vector | | Noise model | gaussian | | Integration axis | k_space | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed; TB parameter fit from DFT is regularized. | Metric | Value | |---|---| | Metric | band_L2_error_eV | | Secondary | DOS_L1_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `tight_binding` · **Forward operator:** `tb_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N atoms | — | 2 | | N kpoints | — | 100 | | N orbitals | — | 18 | | N neighbor shells | — | 2 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N atoms | — | 1 – 1000 | | N kpoints | — | 10 – 10000 | | N orbitals | — | 4 – 200 | | N neighbor shells | — | 1 – 10 | ## 🎯 6. Tolerance (ε) **Center tolerance:** band L2 <= 0.05 eV | Metric | Range | |---|---| | Band l2 error ev | 0.01 – 2.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **band_L2_error_eV**, with κ = `150` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf2135fd521c9de2927ec4264589e1980198da9e1f8c57b442f910f1bd0fbf48e` - **Chain tx hash:** `0x1e781f92a9cd7a2d8b12b41152f6cdc1356cd319874c3c6b6c9a82e60968475b` - **Chain block:** `41554080` --- ## File Mapping This bundle consists of: `L1-318.md`, `L1-318.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-318.md` | Source of truth — edit this | Human or LLM | | `L1-318.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 `L1-318`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-318.md).
Regenerate L1-318.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-318-001 Tight-Binding Electronic Structure Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-318",
  "chain_block": 41554080,
  "chain_hash": "0xf2135fd521c9de2927ec4264589e1980198da9e1f8c57b442f910f1bd0fbf48e",
  "chain_tx_hash": "0x1e781f92a9cd7a2d8b12b41152f6cdc1356cd319874c3c6b6c9a82e60968475b",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 150,
    "metric": "band_L2_error_eV",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "band_L2_error_eV",
    "regime": "Well-posed; TB parameter fit from DFT is regularized.",
    "secondary": "DOS_L1_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Quantum Mechanics",
    "integration_axis": "k_space",
    "noise_model": "gaussian",
    "primitives": [
      "E.SK_parameters",
      "E.eigensolve",
      "O.DOS_band"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "arpes_stm",
    "solution_space": "tb_parameter_vector",
    "sub_domain": "Minimal-basis electronic models",
    "title": "Tight-Binding Electronic Structure"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "tb_forward"
    ],
    "allowed_omega_dimensions": [
      "N_orbitals",
      "N_atoms",
      "N_kpoints",
      "N_neighbor_shells"
    ],
    "allowed_problem_classes": [
      "tight_binding"
    ],
    "center_spec": {
      "epsilon_fn_center": "band L2 \u003c= 0.05 eV",
      "forward_operator": "tb_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_atoms": 2,
        "N_kpoints": 100,
        "N_neighbor_shells": 2,
        "N_orbitals": 18
      },
      "problem_class": "tight_binding"
    },
    "epsilon_bounds": {
      "band_L2_error_eV": [
        0.01,
        2.0
      ]
    },
    "omega_bounds": {
      "N_atoms": [
        1,
        1000
      ],
      "N_kpoints": [
        10,
        10000
      ],
      "N_neighbor_shells": [
        1,
        10
      ],
      "N_orbitals": [
        4,
        200
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Minimal-basis electronic models",
  "title": "Tight-Binding Electronic Structure"
}

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