L1 ⚛ L1-480 ⊙ Testnet

Lattice QCD Path Integral

Particle Physics · Lattice field theory

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⬇ L1-480.md

# ⚛ L1 Principle — Lattice QCD Path Integral **ID:** `L1-480` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Particle Physics — *Lattice field theory* > **🎯 Problem class:** statistical inverse · **🧮 Solution space:** QCD observable spectrum > **📡 Carrier:** particle · **🌫 Noise:** monte carlo statistical > **⚖ Difficulty (δ):** 50 · **⛓ Block:** 41555301 --- ## 🧠 1. Introduction **Lattice QCD Path Integral** is a **statistical inverse problem** whose unknown lives in **QCD observable spectrum** space, within the **Lattice field theory** sub-domain of **Particle Physics**. Measurements consist of particle interactions in a detector via a **lattice gauge mc sampling** sensing mechanism. The forward operator applies, in order: S · hmc · hybrid monte carlo operator; gradient / divergence with respect to position; O · correlator · hadron spectrum operator. Observations are corrupted by monte carlo statistical. Existence of the recovered QCD_observable_spectrum is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000000.0); discretization_error_O_a2 dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Monte carlo statistical sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · hmc · hybrid monte carlo → Spatial derivative → O · correlator · hadron spectrum → **y** (detector). ``` y = `O.correlator.hadron_spectrum` ∇ `S.hmc.hybrid_monte_carlo` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.hmc.hybrid_monte_carlo` | S · hmc · hybrid monte carlo operator | | `D.space` | Gradient / divergence with respect to position | | `O.correlator.hadron_spectrum` | O · correlator · hadron spectrum operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Particle Physics | | Sub domain | Lattice field theory | | Carrier | particle | | Problem class | statistical_inverse | | Solution space | QCD_observable_spectrum | | Noise model | monte_carlo_statistical | | Integration axis | spacetime_lattice | | Difficulty delta | 50 | | L dag | 6 | ## 📡 4. Measurement Model Existence of the recovered QCD_observable_spectrum is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000000.0); discretization_error_O_a2 dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Monte carlo statistical sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | hadron_mass_RMSE_MeV | | Secondary | continuum_extrapolation_chi2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `statistical_inverse` · **Forward operator:** `lattice_gauge_mc_sampling` **Center point:** | Parameter | Unit | Value | |---|---|---| | N configs | — | 500 | | N l spatial | — | 32 | | N t temporal | — | 64 | | Beta coupling | — | 6.2 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N configs | — | 100 – 10000 | | N l spatial | — | 8 – 64 | | N t temporal | — | 16 – 128 | | Beta coupling | — | 5.5 – 7.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5 hadron_mass_RMSE_MeV | Metric | Range | |---|---| | Hadron mass rmse mev | 0.5 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **hadron_mass_RMSE_MeV**, with κ = `10000000000.0` and δ = `50`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x328a83a9fb2a8e5db58e86bf5dce897a2fad750fb0eb332808a9313010e62593` - **Chain tx hash:** `0xdc01e867600c259e0693960671052d94ea9616497a226a91ad446cb2b965ad65` - **Chain block:** `41555301` --- ## File Mapping This bundle consists of: `L1-480.md`, `L1-480.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-480.md` | Source of truth — edit this | Human or LLM | | `L1-480.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 `L1-480`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-480.md).
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📋 JSON metadata

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    "sub_domain": "Lattice field theory",
    "title": "Lattice QCD Path Integral"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Lattice field theory",
  "title": "Lattice QCD Path Integral"
}

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