L1 ⚛ L1-329 ⊙ Testnet

CALPHAD Thermodynamic Modeling

Materials Science · Multi-component phase equilibria

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⬇ L1-329.md

# ⚛ L1 Principle — CALPHAD Thermodynamic Modeling **ID:** `L1-329` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Multi-component phase equilibria* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** gibbs energy surfaces > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554127 --- ## 🧠 1. Introduction **CALPHAD Thermodynamic Modeling** is a **nonlinear inverse problem** whose unknown lives in **gibbs energy surfaces** space, within the **Multi-component phase equilibria** sub-domain of **Materials Science**. Measurements consist of none via a **phase diagram measurement** sensing mechanism. The forward operator applies, in order: E · gibbs surface operator; adds a prior term that biases the solution toward smoothness/sparsity; O · phase equilibrium operator. Observations are corrupted by additive Gaussian noise. Convex per phase but multi-phase minimization is non-convex; consistent globally with Gibbs phase rule. ## ⚙ 2. Forward Model Physical chain: **x** → E · gibbs surface → O · phase equilibrium → **y** (detector). ``` y = `O.phase_equilibrium` `E.gibbs_surface` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.gibbs_surface` | E · gibbs surface operator | | `O.phase_equilibrium` | O · phase equilibrium operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Multi-component phase equilibria | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | gibbs_energy_surfaces | | Noise model | gaussian | | Integration axis | composition_temperature | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Convex per phase but multi-phase minimization is non-convex; consistent globally with Gibbs phase rule. | Metric | Value | |---|---| | Metric | phase_fraction_L1_error | | Secondary | solvus_temperature_error_K | ## 📏 5. Operating Range (Ω) **Center problem class:** `calphad` · **Forward operator:** `calphad_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N phases | — | 5 | | T k range | — | 300 – 1500 | | N components | — | 3 | | Composition grid n | N | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N phases | — | 2 – 20 | | N components | — | 2 – 10 | | T k range max | — | 1000 – 3000 | | T k range min | — | 77 – 500 | | Composition grid n | N | 20 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** phase fraction L1 <= 0.03 | Metric | Range | |---|---| | Phase fraction l1 error | 0.005 – 0.25 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **phase_fraction_L1_error**, with κ = `200` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9874a408f48315d6293ebc2cc6d11b62429d60c03d1148cacf2a1068d9766a73` - **Chain tx hash:** `0x85a771537ef27d5a408bab56c6dcb32b43e8b55ec856a75c2079da56b2686daa` - **Chain block:** `41554127` --- ## File Mapping This bundle consists of: `L1-329.md`, `L1-329.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-329.md` | Source of truth — edit this | Human or LLM | | `L1-329.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 `L1-329`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-329.md).
Regenerate L1-329.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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L2-329-001 CALPHAD Thermodynamic Modeling Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-329",
  "chain_block": 41554127,
  "chain_hash": "0x9874a408f48315d6293ebc2cc6d11b62429d60c03d1148cacf2a1068d9766a73",
  "chain_tx_hash": "0x85a771537ef27d5a408bab56c6dcb32b43e8b55ec856a75c2079da56b2686daa",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 200,
    "metric": "phase_fraction_L1_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "phase_fraction_L1_error",
    "regime": "Convex per phase but multi-phase minimization is non-convex; consistent globally with Gibbs phase rule.",
    "secondary": "solvus_temperature_error_K"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "none",
    "difficulty_delta": 5,
    "domain": "Materials Science",
    "integration_axis": "composition_temperature",
    "noise_model": "gaussian",
    "primitives": [
      "E.gibbs_surface",
      "O.regularize",
      "O.phase_equilibrium"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "phase_diagram_measurement",
    "solution_space": "gibbs_energy_surfaces",
    "sub_domain": "Multi-component phase equilibria",
    "title": "CALPHAD Thermodynamic Modeling"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "calphad_forward"
    ],
    "allowed_omega_dimensions": [
      "N_components",
      "N_phases",
      "T_K_range",
      "composition_grid_N"
    ],
    "allowed_problem_classes": [
      "calphad"
    ],
    "center_spec": {
      "epsilon_fn_center": "phase fraction L1 \u003c= 0.03",
      "forward_operator": "calphad_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_components": 3,
        "N_phases": 5,
        "T_K_range": [
          300,
          1500
        ],
        "composition_grid_N": 50
      },
      "problem_class": "calphad"
    },
    "epsilon_bounds": {
      "phase_fraction_L1_error": [
        0.005,
        0.25
      ]
    },
    "omega_bounds": {
      "N_components": [
        2,
        10
      ],
      "N_phases": [
        2,
        20
      ],
      "T_K_range_max": [
        1000,
        3000
      ],
      "T_K_range_min": [
        77,
        500
      ],
      "composition_grid_N": [
        20,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Multi-component phase equilibria",
  "title": "CALPHAD Thermodynamic Modeling"
}

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