L1 ⚛ L1-476 ⊙ Testnet

de Gennes-Doi-Edwards Reptation Theory

Polymer Physics · Entangled melt dynamics

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

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-476.md

# ⚛ L1 Principle — de Gennes-Doi-Edwards Reptation Theory **ID:** `L1-476` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Polymer Physics — *Entangled melt dynamics* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** relaxation spectrum H tau > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555300 --- ## 🧠 1. Introduction **de Gennes-Doi-Edwards Reptation Theory** is a **linear inverse problem** whose unknown lives in **relaxation spectrum H tau** space, within the **Entangled melt dynamics** sub-domain of **Polymer Physics**. Measurements consist of none via a **oscillatory rheometry** sensing mechanism. The forward operator applies, in order: E · doi edwards tube operator; O · composite method operator; int · rheology operator; O · viscoelastic spectrum operator. Observations are corrupted by additive Gaussian noise. Well-posed for monodisperse melts; polydisperse inversion is ill-conditioned in the transition zone between Rouse and terminal regimes. ## ⚙ 2. Forward Model Physical chain: **x** → E · doi edwards tube → O · composite method → int · rheology → O · viscoelastic spectrum → **y** (detector). ``` y = `O.viscoelastic_spectrum` `int.rheology` `O.composite_method` `E.doi_edwards_tube` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.doi_edwards_tube` | E · doi edwards tube operator | | `O.composite_method` | O · composite method operator | | `int.rheology` | Int · rheology operator | | `O.viscoelastic_spectrum` | O · viscoelastic spectrum operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Polymer Physics | | Sub domain | Entangled melt dynamics | | Carrier | none | | Problem class | linear_inverse | | Solution space | relaxation_spectrum_H_tau | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Well-posed for monodisperse melts; polydisperse inversion is ill-conditioned in the transition zone between Rouse and terminal regimes. | Metric | Value | |---|---| | Metric | log_G_prime_RMSE | | Secondary | eta_0_relative_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `rheological_spectrum_inversion` · **Forward operator:** `reptation_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Pdi | — | 1.05 | | T c | — | 25 | | M e kda | — | 5 | | N over ne | — | 20 | | Strain pct | — | 1 | | Omega range decades | — | 7 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Pdi | — | 1.01 – 3.0 | | T c | — | -50 – 200 | | M e kda | — | 0.5 – 50.0 | | N over ne | — | 5 – 200 | | Strain pct | — | 0.1 – 10.0 | | Omega range decades | — | 3 – 10 | ## 🎯 6. Tolerance (ε) **Center tolerance:** log10 G'(omega) RMSE <= 0.05 | Metric | Range | |---|---| | Log g prime rmse | 0.03 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **log_G_prime_RMSE**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8ce98f5a72d471ae0540b0ff01c8ef6e4304310fcd72872cd73c28baf8f7e308` - **Chain tx hash:** `0x9872e5ee09c179fb14c5db94f09e9a5aacc41d20ac4e270ea9ee5d77f1b86250` - **Chain block:** `41555300` --- ## File Mapping This bundle consists of: `L1-476.md`, `L1-476.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-476.md` | Source of truth — edit this | Human or LLM | | `L1-476.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 `L1-476`._ _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 (L1-476.md).
Regenerate L1-476.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 ▾

L2-476-001 de Gennes-Doi-Edwards Reptation Theory Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-476",
  "chain_block": 41555300,
  "chain_hash": "0x8ce98f5a72d471ae0540b0ff01c8ef6e4304310fcd72872cd73c28baf8f7e308",
  "chain_tx_hash": "0x9872e5ee09c179fb14c5db94f09e9a5aacc41d20ac4e270ea9ee5d77f1b86250",
  "domain": "Polymer Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "log_G_prime_RMSE",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "log_G_prime_RMSE",
    "regime": "Well-posed for monodisperse melts; polydisperse inversion is ill-conditioned in the transition zone between Rouse and terminal regimes.",
    "secondary": "eta_0_relative_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Polymer Physics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.doi_edwards_tube",
      "O.composite_method",
      "int.rheology",
      "O.viscoelastic_spectrum"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "oscillatory_rheometry",
    "solution_space": "relaxation_spectrum_H_tau",
    "sub_domain": "Entangled melt dynamics",
    "title": "de Gennes-Doi-Edwards Reptation Theory"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "reptation_forward"
    ],
    "allowed_omega_dimensions": [
      "N_over_Ne",
      "M_e_kDa",
      "PDI",
      "omega_range_decades",
      "T_C",
      "strain_pct"
    ],
    "allowed_problem_classes": [
      "rheological_spectrum_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "log10 G\u0027(omega) RMSE \u003c= 0.05",
      "forward_operator": "reptation_forward",
      "input_format": "measurement_only",
      "omega": {
        "M_e_kDa": 5.0,
        "N_over_Ne": 20,
        "PDI": 1.05,
        "T_C": 25,
        "omega_range_decades": 7,
        "strain_pct": 1.0
      },
      "problem_class": "rheological_spectrum_inversion"
    },
    "epsilon_bounds": {
      "log_G_prime_RMSE": [
        0.03,
        0.3
      ]
    },
    "omega_bounds": {
      "M_e_kDa": [
        0.5,
        50.0
      ],
      "N_over_Ne": [
        5,
        200
      ],
      "PDI": [
        1.01,
        3.0
      ],
      "T_C": [
        -50,
        200
      ],
      "omega_range_decades": [
        3,
        10
      ],
      "strain_pct": [
        0.1,
        10.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Entangled melt dynamics",
  "title": "de Gennes-Doi-Edwards Reptation 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.