L1 ⚛ L1-180 ⊙ Testnet

DNS — direct numerical simulation

Fluid Dynamics · Full resolution of Kolmogorov scales

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⬇ L1-180.md

# ⚛ L1 Principle — DNS — direct numerical simulation **ID:** `L1-180` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Full resolution of Kolmogorov scales* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** fully resolved NS solution > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553966 --- ## 🧠 1. Introduction **DNS — direct numerical simulation** is a **linear inverse problem** whose unknown lives in **fully resolved NS solution** space, within the **Full resolution of Kolmogorov scales** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **dns reference data** sensing mechanism. The forward operator applies, in order: momentum balance (Navier-Stokes / Euler); mass-balance: ∂_t ρ + ∇·(ρv) = 0; L · spectral or fd operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Most-expensive; Re^{9/4} grid points required. ## ⚙ 2. Forward Model Physical chain: **x** → Momentum equation → Continuity equation → L · spectral or fd → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.spectral_or_fd` ∂_t ρ + ∇·(ρv) ∂_t(ρv) + ∇·(ρv⊗v) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.momentum` | Momentum balance (navier-stokes / euler) | | `L.continuity` | Mass-balance: ∂_t ρ + ∇·(ρv) = 0 | | `L.spectral_or_fd` | L · spectral or fd operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Full resolution of Kolmogorov scales | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | fully_resolved_NS_solution | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 3.5 | ## 📡 4. Measurement Model Most-expensive; Re^{9/4} grid points required. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `dns` · **Forward operator:** `dns_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Z | — | 512 | | Snr db | dB | 40 | | N times | — | 10000 | | Bc error | — | 0 | | Re lambda | — | 100 | | Time step error | — | 0 | | Grid sufficiency error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 16384 | | W | px | 256 – 16384 | | Z | — | 128 – 8192 | | Snr db | dB | 10 – 60 | | N times | — | 1000 – 10000000 | | Bc error | — | 0.0 – 0.2 | | Re lambda | — | 10 – 2000 | | Time step error | — | 0.0 – 0.1 | | Grid sufficiency error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4b903247c54a8666a972b31f15d6dd5d66e57ceef03286c2fc1f7ed5ef03222e` - **Chain tx hash:** `0x2d2156f4ee7b470bf7e21aededd64161a5f4fadb0063a5741999c8c5bafcfdff` - **Chain block:** `41553966` --- ## File Mapping This bundle consists of: `L1-180.md`, `L1-180.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-180.md` | Source of truth — edit this | Human or LLM | | `L1-180.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 `L1-180`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-180.md).
Regenerate L1-180.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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L2-180-001 DNS — direct numerical simulation Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553966,
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  "domain": "Fluid Dynamics",
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  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 10,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
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      "L.continuity",
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    "sensing_mechanism": "dns_reference_data",
    "solution_space": "fully_resolved_NS_solution",
    "sub_domain": "Full resolution of Kolmogorov scales",
    "title": "DNS \u2014 direct numerical simulation"
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      "N_times": [
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      "W": [
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      "bc_error": [
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Full resolution of Kolmogorov scales",
  "title": "DNS \u2014 direct numerical simulation"
}

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