L1 ⚛ L1-227 ⊙ Testnet

Poroelasticity — Biot coupled solid/fluid

Structural Mechanics · Biot consolidation theory

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⬇ L1-227.md

# ⚛ L1 Principle — Poroelasticity — Biot coupled solid/fluid **ID:** `L1-227` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Biot consolidation theory* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** coupled u p fields > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554023 --- ## 🧠 1. Introduction **Poroelasticity — Biot coupled solid/fluid** is a **linear inverse problem** whose unknown lives in **coupled u p fields** space, within the **Biot consolidation theory** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **piezometer dic** sensing mechanism. The forward operator applies, in order: L · biot coupling operator; L · darcy flow operator; L · effective stress 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 · biot coupling → L · darcy flow → L · effective stress → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.effective_stress` `L.darcy_flow` `L.biot_coupling` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.biot_coupling` | L · biot coupling operator | | `L.darcy_flow` | L · darcy flow operator | | `L.effective_stress` | L · effective stress operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Biot consolidation theory | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | coupled_u_p_fields | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `poroelastic` · **Forward operator:** `poroelastic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 10000 | | Snr db | dB | 30 | | E error | — | 0 | | M error | — | 0 | | N times | — | 200 | | Biot alpha error | — | 0 | | Permeability error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 100 – 1000000 | | Snr db | dB | 0 – 40 | | E error | — | 0.0 – 0.1 | | M error | — | 0.0 – 0.1 | | N times | — | 10 – 100000 | | Biot alpha error | — | 0.0 – 0.1 | | Permeability error | — | 0.0 – 0.3 | ## 🎯 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 = `440` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6f026e1819b7ef782ad9f1b73b3cd50b817300f7775114060babf96f99ceb227` - **Chain tx hash:** `0x0fd3e88eed11488fe0baf6e58cd887b3e13f0fa70ed1702b706679715043e3eb` - **Chain block:** `41554023` --- ## File Mapping This bundle consists of: `L1-227.md`, `L1-227.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-227.md` | Source of truth — edit this | Human or LLM | | `L1-227.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 `L1-227`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-227.md).
Regenerate L1-227.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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L2-227-001 Poroelasticity — Biot coupled solid/fluid Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-227",
  "chain_block": 41554023,
  "chain_hash": "0x6f026e1819b7ef782ad9f1b73b3cd50b817300f7775114060babf96f99ceb227",
  "chain_tx_hash": "0x0fd3e88eed11488fe0baf6e58cd887b3e13f0fa70ed1702b706679715043e3eb",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 440,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.biot_coupling",
      "L.darcy_flow",
      "L.effective_stress",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "piezometer_dic",
    "solution_space": "coupled_u_p_fields",
    "sub_domain": "Biot consolidation theory",
    "title": "Poroelasticity \u2014 Biot coupled solid/fluid"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "poroelastic_forward"
    ],
    "allowed_omega_dimensions": [
      "N_DOF",
      "N_times",
      "SNR_dB",
      "permeability_error",
      "biot_alpha_error",
      "M_error",
      "E_error",
      "permeability_error",
      "biot_alpha_error",
      "M_error",
      "E_error"
    ],
    "allowed_problem_classes": [
      "poroelastic"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "poroelastic_forward",
      "input_format": "measurement_only",
      "omega": {
        "E_error": 0.0,
        "M_error": 0.0,
        "N_DOF": 10000,
        "N_times": 200,
        "SNR_dB": 30,
        "biot_alpha_error": 0.0,
        "permeability_error": 0.0
      },
      "problem_class": "poroelastic"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "E_error": [
        0.0,
        0.1
      ],
      "M_error": [
        0.0,
        0.1
      ],
      "N_DOF": [
        100,
        1000000
      ],
      "N_times": [
        10,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "biot_alpha_error": [
        0.0,
        0.1
      ],
      "permeability_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Biot consolidation theory",
  "title": "Poroelasticity \u2014 Biot coupled solid/fluid"
}

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