L1 ⚛ L1-336 ⊙ Testnet

Rubber Elasticity Theory

Materials Science · Entropic elasticity of networks

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-336.md

# ⚛ L1 Principle — Rubber Elasticity Theory **ID:** `L1-336` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Entropic elasticity of networks* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** stress strain curve > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554129 --- ## 🧠 1. Introduction **Rubber Elasticity Theory** is a **nonlinear inverse problem** whose unknown lives in **stress strain curve** space, within the **Entropic elasticity of networks** sub-domain of **Materials Science**. Measurements consist of none via a **mechanical test** sensing mechanism. The forward operator applies, in order: E · network entropy operator; E · affine deformation operator; O · stress strain operator. Observations are corrupted by additive Gaussian noise. Well-posed; inversion of (n_c, C_2) from uniaxial alone is ill-conditioned — requires biaxial. ## ⚙ 2. Forward Model Physical chain: **x** → E · network entropy → E · affine deformation → O · stress strain → **y** (detector). ``` y = `O.stress_strain` `E.affine_deformation` `E.network_entropy` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.network_entropy` | E · network entropy operator | | `E.affine_deformation` | E · affine deformation operator | | `O.stress_strain` | O · stress strain operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Entropic elasticity of networks | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | stress_strain_curve | | Noise model | gaussian | | Integration axis | strain | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Well-posed; inversion of (n_c, C_2) from uniaxial alone is ill-conditioned — requires biaxial. | Metric | Value | |---|---| | Metric | stress_strain_L2_error_MPa | | Secondary | n_c_relative_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `rubber_elasticity` · **Forward operator:** `rubber_elasticity_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 298 | | Lambda max | — | 4 | | N c mol m3 | — | 100 | | N data points | — | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 200 – 400 | | Lambda max | — | 1.1 – 10 | | N c mol m3 | — | 10 – 10000 | | N data points | — | 20 – 5000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** stress-strain L2 <= 0.08 MPa | Metric | Range | |---|---| | Stress strain l2 error mpa | 0.01 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **stress_strain_L2_error_MPa**, with κ = `60` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3e98678fd4b0378cb9f45297103c9980ab9af912538f6fee032a1dcb5c805db0` - **Chain tx hash:** `0x3f2ca31f1e395bf139e6592c2532a13fda72a87995c8681193a27f6ce4533f1e` - **Chain block:** `41554129` --- ## File Mapping This bundle consists of: `L1-336.md`, `L1-336.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-336.md` | Source of truth — edit this | Human or LLM | | `L1-336.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 `L1-336`._ _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 (L1-336.md).
Regenerate L1-336.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 ▾

L2-336-001 Rubber Elasticity Theory Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-336",
  "chain_block": 41554129,
  "chain_hash": "0x3e98678fd4b0378cb9f45297103c9980ab9af912538f6fee032a1dcb5c805db0",
  "chain_tx_hash": "0x3f2ca31f1e395bf139e6592c2532a13fda72a87995c8681193a27f6ce4533f1e",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 3,
    "kappa": 60,
    "metric": "stress_strain_L2_error_MPa",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "stress_strain_L2_error_MPa",
    "regime": "Well-posed; inversion of (n_c, C_2) from uniaxial alone is ill-conditioned \u2014 requires biaxial.",
    "secondary": "n_c_relative_error"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Materials Science",
    "integration_axis": "strain",
    "noise_model": "gaussian",
    "primitives": [
      "E.network_entropy",
      "E.affine_deformation",
      "O.stress_strain"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "mechanical_test",
    "solution_space": "stress_strain_curve",
    "sub_domain": "Entropic elasticity of networks",
    "title": "Rubber Elasticity Theory"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "rubber_elasticity_forward"
    ],
    "allowed_omega_dimensions": [
      "lambda_max",
      "n_c_mol_m3",
      "T_K",
      "N_data_points"
    ],
    "allowed_problem_classes": [
      "rubber_elasticity"
    ],
    "center_spec": {
      "epsilon_fn_center": "stress-strain L2 \u003c= 0.08 MPa",
      "forward_operator": "rubber_elasticity_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_data_points": 100,
        "T_K": 298,
        "lambda_max": 4,
        "n_c_mol_m3": 100
      },
      "problem_class": "rubber_elasticity"
    },
    "epsilon_bounds": {
      "stress_strain_L2_error_MPa": [
        0.01,
        1.0
      ]
    },
    "omega_bounds": {
      "N_data_points": [
        20,
        5000
      ],
      "T_K": [
        200,
        400
      ],
      "lambda_max": [
        1.1,
        10
      ],
      "n_c_mol_m3": [
        10,
        10000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Entropic elasticity of networks",
  "title": "Rubber Elasticity Theory"
}

🎁

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.