L1 ⚛ L1-335 ⊙ Testnet

Flory-Huggins Polymer Solution Theory

Materials Science · Polymer solution thermodynamics

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⬇ L1-335.md

# ⚛ L1 Principle — Flory-Huggins Polymer Solution Theory **ID:** `L1-335` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Polymer solution thermodynamics* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** phi T phase boundary > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554128 --- ## 🧠 1. Introduction **Flory-Huggins Polymer Solution Theory** is a **linear inverse problem** whose unknown lives in **phi T phase boundary** space, within the **Polymer solution thermodynamics** sub-domain of **Materials Science**. Measurements consist of none via a **cloud point turbidimetry** sensing mechanism. The forward operator applies, in order: E · mixing entropy operator; E · interaction chi operator; computes eigen-pairs of a linear operator; O · phase diagram operator. Observations are corrupted by additive Gaussian noise. Well-posed; chi(T) inversion from cloud-point curves is mildly ill-conditioned (entropy/enthalpy trade-off). ## ⚙ 2. Forward Model Physical chain: **x** → E · mixing entropy → E · interaction chi → O · phase diagram → **y** (detector). ``` y = `O.phase_diagram` `E.interaction_chi` `E.mixing_entropy` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.mixing_entropy` | E · mixing entropy operator | | `E.interaction_chi` | E · interaction chi operator | | `O.phase_diagram` | O · phase diagram operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `E.eigensolve` | Computes eigen-pairs of a linear operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Polymer solution thermodynamics | | Carrier | none | | Problem class | linear_inverse | | Solution space | phi_T_phase_boundary | | Noise model | gaussian | | Integration axis | composition | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed; chi(T) inversion from cloud-point curves is mildly ill-conditioned (entropy/enthalpy trade-off). | Metric | Value | |---|---| | Metric | phase_boundary_K_error | | Secondary | chi_AB_relative_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `flory_huggins` · **Forward operator:** `flory_huggins_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N a | — | 100 | | N b | — | 100 | | T k | — | 300 | | Chi 0 | — | 0.6 | | Chi slope | — | 0.001 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N a | — | 10 – 10000 | | N b | — | 10 – 10000 | | Chi 0 | — | 0.1 – 2.0 | | T k range | — | 200 – 500 | | Chi slope | — | 0 – 0.01 | ## 🎯 6. Tolerance (ε) **Center tolerance:** phase boundary error <= 2 K | Metric | Range | |---|---| | Phase boundary k error | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **phase_boundary_K_error**, with κ = `80` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x1569fda13b503d650bebc7e018da659b862499b84b07411484cfb74366e6391b` - **Chain tx hash:** `0x16d9b8ac2a5b8ac2c0e90b98feb2fb80c4087d5c57cef9eecf232a021e87baef` - **Chain block:** `41554128` --- ## File Mapping This bundle consists of: `L1-335.md`, `L1-335.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-335.md` | Source of truth — edit this | Human or LLM | | `L1-335.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 `L1-335`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-335.md).
Regenerate L1-335.json so every field matches the Markdown.
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L2-335-001 Flory-Huggins Polymer Solution Theory Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-335",
  "chain_block": 41554128,
  "chain_hash": "0x1569fda13b503d650bebc7e018da659b862499b84b07411484cfb74366e6391b",
  "chain_tx_hash": "0x16d9b8ac2a5b8ac2c0e90b98feb2fb80c4087d5c57cef9eecf232a021e87baef",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 3,
    "kappa": 80,
    "metric": "phase_boundary_K_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "phase_boundary_K_error",
    "regime": "Well-posed; chi(T) inversion from cloud-point curves is mildly ill-conditioned (entropy/enthalpy trade-off).",
    "secondary": "chi_AB_relative_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Materials Science",
    "integration_axis": "composition",
    "noise_model": "gaussian",
    "primitives": [
      "E.mixing_entropy",
      "E.interaction_chi",
      "E.eigensolve",
      "O.phase_diagram"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "cloud_point_turbidimetry",
    "solution_space": "phi_T_phase_boundary",
    "sub_domain": "Polymer solution thermodynamics",
    "title": "Flory-Huggins Polymer Solution Theory"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "flory_huggins_forward"
    ],
    "allowed_omega_dimensions": [
      "N_A",
      "N_B",
      "T_K",
      "chi_0",
      "chi_slope"
    ],
    "allowed_problem_classes": [
      "flory_huggins"
    ],
    "center_spec": {
      "epsilon_fn_center": "phase boundary error \u003c= 2 K",
      "forward_operator": "flory_huggins_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_A": 100,
        "N_B": 100,
        "T_K": 300,
        "chi_0": 0.6,
        "chi_slope": 0.001
      },
      "problem_class": "flory_huggins"
    },
    "epsilon_bounds": {
      "phase_boundary_K_error": [
        0.5,
        30.0
      ]
    },
    "omega_bounds": {
      "N_A": [
        10,
        10000
      ],
      "N_B": [
        10,
        10000
      ],
      "T_K_range": [
        200,
        500
      ],
      "chi_0": [
        0.1,
        2.0
      ],
      "chi_slope": [
        0,
        0.01
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Polymer solution thermodynamics",
  "title": "Flory-Huggins Polymer Solution Theory"
}

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