L1 ⚛ L1-478 ⊙ Testnet

DLVO Colloidal Force Theory

Polymer Physics · Colloidal stability

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⬇ L1-478.md

# ⚛ L1 Principle — DLVO Colloidal Force Theory **ID:** `L1-478` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Polymer Physics — *Colloidal stability* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** pair potential V of h > **📡 Carrier:** ion · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555300 --- ## 🧠 1. Introduction **DLVO Colloidal Force Theory** is a **nonlinear inverse problem** whose unknown lives in **pair potential V of h** space, within the **Colloidal stability** sub-domain of **Polymer Physics**. Measurements consist of ions detected after acceleration or extraction via a **colloidal probe AFM** sensing mechanism. The forward operator applies, in order: E · vdW operator; E · double layer operator; an unspecified linear measurement operator; O · force distance operator. Observations are corrupted by additive Gaussian noise. Well-posed when both V_vdW and V_EDL contribute; ill-conditioned when one dominates (high ionic strength → secondary minimum masking). ## ⚙ 2. Forward Model Physical chain: **x** → E · vdW → E · double layer → Generic linear operator → O · force distance → **y** (detector). ``` y = `O.force_distance` A `E.double_layer` `E.vdW` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.vdW` | E · vdw operator | | `E.double_layer` | E · double layer operator | | `L.linear_op` | An unspecified linear measurement operator | | `O.force_distance` | O · force distance operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Polymer Physics | | Sub domain | Colloidal stability | | Carrier | ion | | Problem class | nonlinear_inverse | | Solution space | pair_potential_V_of_h | | Noise model | gaussian | | Integration axis | separation | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed when both V_vdW and V_EDL contribute; ill-conditioned when one dominates (high ionic strength → secondary minimum masking). | Metric | Value | |---|---| | Metric | V_of_h_RMSE_kT | | Secondary | aggregation_rate_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `dlvo_parameter_inversion` · **Forward operator:** `dlvo_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 298 | | I mm | mm | 10 | | R nm | nm | 100 | | Psi 0 mv | — | -40 | | A hamaker zj | — | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 273 – 373 | | I mm | mm | 0.1 – 1000 | | R nm | nm | 10 – 5000 | | Psi 0 mv | — | -120 – 120 | | A hamaker zj | — | 0.5 – 20.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** V(h) RMSE <= 0.3 k_B T | Metric | Range | |---|---| | V of h rmse kt | 0.1 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **V_of_h_RMSE_kT**, with κ = `80` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4d8f1be2284ec379bed19e7de846fd5c81093b9a0a820df4419f275cf9741e79` - **Chain tx hash:** `0xda5dbcb7cfcce87f8e60452909f0e3f7b5d2726cddea09e46655d45ee656dc3d` - **Chain block:** `41555300` --- ## File Mapping This bundle consists of: `L1-478.md`, `L1-478.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-478.md` | Source of truth — edit this | Human or LLM | | `L1-478.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 `L1-478`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-478.md).
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📋 JSON metadata

{
  "artifact_id": "L1-478",
  "chain_block": 41555300,
  "chain_hash": "0x4d8f1be2284ec379bed19e7de846fd5c81093b9a0a820df4419f275cf9741e79",
  "chain_tx_hash": "0xda5dbcb7cfcce87f8e60452909f0e3f7b5d2726cddea09e46655d45ee656dc3d",
  "domain": "Polymer Physics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 80,
    "metric": "V_of_h_RMSE_kT",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "V_of_h_RMSE_kT",
    "regime": "Well-posed when both V_vdW and V_EDL contribute; ill-conditioned when one dominates (high ionic strength \u2192 secondary minimum masking).",
    "secondary": "aggregation_rate_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "ion",
    "difficulty_delta": 3,
    "domain": "Polymer Physics",
    "integration_axis": "separation",
    "noise_model": "gaussian",
    "primitives": [
      "E.vdW",
      "E.double_layer",
      "L.linear_op",
      "O.force_distance"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "colloidal_probe_AFM",
    "solution_space": "pair_potential_V_of_h",
    "sub_domain": "Colloidal stability",
    "title": "DLVO Colloidal Force Theory"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "dlvo_forward"
    ],
    "allowed_omega_dimensions": [
      "A_Hamaker_zJ",
      "psi_0_mV",
      "I_mM",
      "R_nm",
      "T_K"
    ],
    "allowed_problem_classes": [
      "dlvo_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "V(h) RMSE \u003c= 0.3 k_B T",
      "forward_operator": "dlvo_forward",
      "input_format": "measurement_only",
      "omega": {
        "A_Hamaker_zJ": 5.0,
        "I_mM": 10,
        "R_nm": 100,
        "T_K": 298,
        "psi_0_mV": -40
      },
      "problem_class": "dlvo_parameter_inversion"
    },
    "epsilon_bounds": {
      "V_of_h_RMSE_kT": [
        0.1,
        5.0
      ]
    },
    "omega_bounds": {
      "A_Hamaker_zJ": [
        0.5,
        20.0
      ],
      "I_mM": [
        0.1,
        1000
      ],
      "R_nm": [
        10,
        5000
      ],
      "T_K": [
        273,
        373
      ],
      "psi_0_mV": [
        -120,
        120
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Colloidal stability",
  "title": "DLVO Colloidal Force Theory"
}

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