L1 ⚛ L1-191 ⊙ Testnet

Convection-Diffusion-Reaction — transport with source terms

Fluid Dynamics · CDR equation for reactive scalar

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⬇ L1-191.md

# ⚛ L1 Principle — Convection-Diffusion-Reaction — transport with source terms **ID:** `L1-191` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *CDR equation for reactive scalar* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** reactive scalar field > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553978 --- ## 🧠 1. Introduction **Convection-Diffusion-Reaction — transport with source terms** is a **nonlinear inverse problem** whose unknown lives in **reactive scalar field** space, within the **CDR equation for reactive scalar** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **concentration spectroscopy** sensing mechanism. The forward operator applies, in order: L · convection operator; L · diffusion operator; L · reaction kinetics operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · convection → L · diffusion → L · reaction kinetics → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.reaction_kinetics` `L.diffusion` `L.convection` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.convection` | L · convection operator | | `L.diffusion` | L · diffusion operator | | `L.reaction_kinetics` | L · reaction kinetics operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | CDR equation for reactive scalar | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | reactive_scalar_field | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `cdr` · **Forward operator:** `cdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 30 | | D error | — | 0 | | N times | — | 500 | | Velocity error | — | 0 | | Rate const error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Snr db | dB | 0 – 40 | | D error | — | 0.0 – 0.2 | | N times | — | 50 – 100000 | | Velocity error | — | 0.0 – 0.1 | | Rate const error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x1ae153e4014a58a0cef769b4b2cf2a300f74d0e8d81c5e5cddb7112cb981befe` - **Chain tx hash:** `0x89a963dc5d54436c61fe4ab3e09ac5d165d72957559c28f517fa3874cae3303b` - **Chain block:** `41553978` --- ## File Mapping This bundle consists of: `L1-191.md`, `L1-191.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-191.md` | Source of truth — edit this | Human or LLM | | `L1-191.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 `L1-191`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-191.md).
Regenerate L1-191.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-191-001 Convection-Diffusion-Reaction — transport with source terms Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-191",
  "chain_block": 41553978,
  "chain_hash": "0x1ae153e4014a58a0cef769b4b2cf2a300f74d0e8d81c5e5cddb7112cb981befe",
  "chain_tx_hash": "0x89a963dc5d54436c61fe4ab3e09ac5d165d72957559c28f517fa3874cae3303b",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 280,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.convection",
      "L.diffusion",
      "L.reaction_kinetics",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "concentration_spectroscopy",
    "solution_space": "reactive_scalar_field",
    "sub_domain": "CDR equation for reactive scalar",
    "title": "Convection-Diffusion-Reaction \u2014 transport with source terms"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "cdr_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_times",
      "SNR_dB",
      "rate_const_error",
      "D_error",
      "velocity_error",
      "rate_const_error",
      "D_error",
      "velocity_error"
    ],
    "allowed_problem_classes": [
      "cdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "cdr_forward",
      "input_format": "measurement_only",
      "omega": {
        "D_error": 0.0,
        "H": 256,
        "N_times": 500,
        "SNR_dB": 30,
        "W": 256,
        "rate_const_error": 0.0,
        "velocity_error": 0.0
      },
      "problem_class": "cdr"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "D_error": [
        0.0,
        0.2
      ],
      "H": [
        32,
        2048
      ],
      "N_times": [
        50,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "rate_const_error": [
        0.0,
        0.3
      ],
      "velocity_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "CDR equation for reactive scalar",
  "title": "Convection-Diffusion-Reaction \u2014 transport with source terms"
}

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