L1 ⚛ L1-400 ⊙ Testnet

Hemodynamics (Navier-Stokes Cardiovascular)

Computational Biology · Cardiovascular modeling

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⬇ L1-400.md

# ⚛ L1 Principle — Hemodynamics (Navier-Stokes Cardiovascular) **ID:** `L1-400` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Cardiovascular modeling* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 3D velocity pressure field > **📡 Carrier:** N/A · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555217 --- ## 🧠 1. Introduction **Hemodynamics (Navier-Stokes Cardiovascular)** is a **parameter-estimation problem** whose unknown lives in **3D velocity pressure field** space, within the **Cardiovascular modeling** sub-domain of **Computational Biology**. Measurements consist of N/A via a **blood flow velocity measurement** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · fsi · fluid structure operator; O · chi2 · 4dflow mri operator. Observations are corrupted by measurement gaussian. Existence of the recovered 3D_velocity_pressure_field 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 ~= 2000); MRI_velocity_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Spatial derivative → S · fsi · fluid structure → O · chi2 · 4dflow mri → **y** (detector). ``` y = `O.chi2.4dflow_mri` `S.fsi.fluid_structure` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.fsi.fluid_structure` | S · fsi · fluid structure operator | | `O.chi2.4dflow_mri` | O · chi2 · 4dflow mri operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Cardiovascular modeling | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | 3D_velocity_pressure_field | | Noise model | measurement_gaussian | | Integration axis | 3d_vascular | | Difficulty delta | 5 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered 3D_velocity_pressure_field 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 ~= 2000); MRI_velocity_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | WSS_RMSE_Pa | | Secondary | pressure_drop_RMSE_mmHg | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `blood_flow_velocity_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | Re reynolds | — | 2000 | | Mri voxel mm | mm | 2 | | N mesh elements | — | 500000 | | Cardiac cycle s | s | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Re reynolds | — | 100 – 5000 | | Mri voxel mm | mm | 0.5 – 5.0 | | N mesh elements | — | 10000 – 5000000 | | Cardiac cycle s | s | 0.5 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 WSS_RMSE_Pa | Metric | Range | |---|---| | Wss rmse pa | 0.05 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **WSS_RMSE_Pa**, with κ = `100000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x54810c5dfcd075e620d4cd14e8c1bb3861660ebbc04b51b54b265d32bc9178c8` - **Chain tx hash:** `0xbd399fe67a4e1d72025a46ec52ba758d45d1ac6c7ded7d2536a4111985f8a6fa` - **Chain block:** `41555217` --- ## File Mapping This bundle consists of: `L1-400.md`, `L1-400.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-400.md` | Source of truth — edit this | Human or LLM | | `L1-400.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 `L1-400`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-400.md).
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L2-400-001 Hemodynamics (Navier-Stokes Cardiovascular) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_hash": "0x54810c5dfcd075e620d4cd14e8c1bb3861660ebbc04b51b54b265d32bc9178c8",
  "chain_tx_hash": "0xbd399fe67a4e1d72025a46ec52ba758d45d1ac6c7ded7d2536a4111985f8a6fa",
  "domain": "Computational Biology",
  "hardness_fn": {
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    "metric": "WSS_RMSE_Pa",
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    "regime": "Existence of the recovered 3D_velocity_pressure_field 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 ~= 2000); MRI_velocity_noise dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "pressure_drop_RMSE_mmHg"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "N/A",
    "difficulty_delta": 5,
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    "integration_axis": "3d_vascular",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.space",
      "S.fsi.fluid_structure",
      "O.chi2.4dflow_mri"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "blood_flow_velocity_measurement",
    "solution_space": "3D_velocity_pressure_field",
    "sub_domain": "Cardiovascular modeling",
    "title": "Hemodynamics (Navier-Stokes Cardiovascular)"
  },
  "size_tiers": {
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      "blood_flow_velocity_measurement"
    ],
    "allowed_omega_dimensions": [
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      "Re_Reynolds",
      "cardiac_cycle_s",
      "MRI_voxel_mm"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.5 WSS_RMSE_Pa",
      "forward_operator": "blood_flow_velocity_measurement",
      "input_format": "measurement_only",
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        "N_mesh_elements": 500000,
        "Re_Reynolds": 2000,
        "cardiac_cycle_s": 1.0
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "WSS_RMSE_Pa": [
        0.05,
        3.0
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    },
    "omega_bounds": {
      "MRI_voxel_mm": [
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        5.0
      ],
      "N_mesh_elements": [
        10000,
        5000000
      ],
      "Re_Reynolds": [
        100,
        5000
      ],
      "cardiac_cycle_s": [
        0.5,
        2.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cardiovascular modeling",
  "title": "Hemodynamics (Navier-Stokes Cardiovascular)"
}

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