L1 ⚛ L1-214 ⊙ Testnet

Linear Buckling — eigenvalue stability analysis

Structural Mechanics · Linear buckling load factor

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-214.md

# ⚛ L1 Principle — Linear Buckling — eigenvalue stability analysis **ID:** `L1-214` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Structural Mechanics — *Linear buckling load factor* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** buckling load factor mode > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554011 --- ## 🧠 1. Introduction **Linear Buckling — eigenvalue stability analysis** is a **linear inverse problem** whose unknown lives in **buckling load factor mode** space, within the **Linear buckling load factor** sub-domain of **Structural Mechanics**. Measurements consist of mechanical vibrations or strain signals via a **load deflection** sensing mechanism. The forward operator applies, in order: L · geom stiffness operator; L · eigenvalue operator; L · critical mode operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Sensitive to imperfections; Koiter analysis required for post-buckling. ## ⚙ 2. Forward Model Physical chain: **x** → L · geom stiffness → L · eigenvalue → L · critical mode → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.critical_mode` `L.eigenvalue` `L.geom_stiffness` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.geom_stiffness` | L · geom stiffness operator | | `L.eigenvalue` | L · eigenvalue operator | | `L.critical_mode` | L · critical mode operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Structural Mechanics | | Sub domain | Linear buckling load factor | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | buckling_load_factor_mode | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Sensitive to imperfections; Koiter analysis required for post-buckling. | Metric | Value | |---|---| | Metric | lambda_cr_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `buckling` · **Forward operator:** `buckling_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N dof | — | 5000 | | Snr db | dB | 30 | | N modes | — | 10 | | Bc error | — | 0 | | Material error | — | 0 | | Load path error | — | 0 | | Geom imperfect error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N dof | — | 100 – 500000 | | Snr db | dB | 0 – 40 | | N modes | — | 1 – 50 | | Bc error | — | 0.0 – 0.2 | | Material error | — | 0.0 – 0.1 | | Load path error | — | 0.0 – 0.1 | | Geom imperfect error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 | Metric | Range | |---|---| | Lambda cr rel | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **lambda_cr_rel_error_percent**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x145c91aff13842f69d45746260520c520ff8826493b9f28d286fd7a66d6fd85e` - **Chain tx hash:** `0xf7887ba572be443409eaabf70023d6a9cff4db227c80393881b806d0adc6e833` - **Chain block:** `41554011` --- ## File Mapping This bundle consists of: `L1-214.md`, `L1-214.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-214.md` | Source of truth — edit this | Human or LLM | | `L1-214.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 `L1-214`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-214.md).
Regenerate L1-214.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.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-214-001 Linear Buckling — eigenvalue stability analysis Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-214",
  "chain_block": 41554011,
  "chain_hash": "0x145c91aff13842f69d45746260520c520ff8826493b9f28d286fd7a66d6fd85e",
  "chain_tx_hash": "0xf7887ba572be443409eaabf70023d6a9cff4db227c80393881b806d0adc6e833",
  "domain": "Structural Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "lambda_cr_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "lambda_cr_rel_error_percent",
    "regime": "Sensitive to imperfections; Koiter analysis required for post-buckling.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Structural Mechanics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.geom_stiffness",
      "L.eigenvalue",
      "L.critical_mode",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "load_deflection",
    "solution_space": "buckling_load_factor_mode",
    "sub_domain": "Linear buckling load factor",
    "title": "Linear Buckling \u2014 eigenvalue stability analysis"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "buckling_forward"
    ],
    "allowed_omega_dimensions": [
      "N_DOF",
      "N_modes",
      "SNR_dB",
      "geom_imperfect_error",
      "material_error",
      "bc_error",
      "load_path_error",
      "geom_imperfect_error",
      "material_error",
      "bc_error",
      "load_path_error"
    ],
    "allowed_problem_classes": [
      "buckling"
    ],
    "center_spec": {
      "epsilon_fn_center": "5.0",
      "forward_operator": "buckling_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_DOF": 5000,
        "N_modes": 10,
        "SNR_dB": 30,
        "bc_error": 0.0,
        "geom_imperfect_error": 0.0,
        "load_path_error": 0.0,
        "material_error": 0.0
      },
      "problem_class": "buckling"
    },
    "epsilon_bounds": {
      "lambda_cr_rel": [
        0.5,
        50.0
      ]
    },
    "omega_bounds": {
      "N_DOF": [
        100,
        500000
      ],
      "N_modes": [
        1,
        50
      ],
      "SNR_dB": [
        0,
        40
      ],
      "bc_error": [
        0.0,
        0.2
      ],
      "geom_imperfect_error": [
        0.0,
        0.1
      ],
      "load_path_error": [
        0.0,
        0.1
      ],
      "material_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Linear buckling load factor",
  "title": "Linear Buckling \u2014 eigenvalue stability analysis"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.