L1 ⚛ L1-286 ⊙ Testnet

Mantle Convection — high-Ra thermal convection

Geophysics · Extended Boussinesq mantle flow

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⬇ principle.md ⬇ principle.json

Fork L1-286

⬇ L1-286.md ⬇ L1-286.json

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You are helping me submit a MODIFICATION of L1-286 (Mantle Convection — high-Ra thermal convection) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-286.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-286.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_t dt `L.rheology` `L.energy` `L.stokes_infinite_prandtl` x + n,    n ~ 𝒩(0, σ²)

world state x (mantle flow and thermal structure)

→

L · stokes infinite prandtl `L.stokes_infinite_prandtl`

→

L · energy `L.energy`

→

L · rheology `L.rheology`

→

Temporal integration ∫_t dt

→

observation y (thermal detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-286.md

# ⚛ L1 Principle — Mantle Convection — high-Ra thermal convection **ID:** `L1-286` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Extended Boussinesq mantle flow* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** mantle flow and thermal structure > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554065 --- ## 🧠 1. Introduction **Mantle Convection — high-Ra thermal convection** is a **nonlinear inverse problem** whose unknown lives in **mantle flow and thermal structure** space, within the **Extended Boussinesq mantle flow** sub-domain of **Geophysics**. Measurements consist of thermal radiation / temperature measurements via a **seismic tomography constraint** sensing mechanism. The forward operator applies, in order: L · stokes infinite prandtl operator; L · energy operator; L · rheology operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Chaotic for Ra > 10^7; initial condition of mantle is unknown. ## ⚙ 2. Forward Model Physical chain: **x** → L · stokes infinite prandtl → L · energy → L · rheology → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.rheology` `L.energy` `L.stokes_infinite_prandtl` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.stokes_infinite_prandtl` | L · stokes infinite prandtl operator | | `L.energy` | L · energy operator | | `L.rheology` | L · rheology operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Extended Boussinesq mantle flow | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | mantle_flow_and_thermal_structure | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Chaotic for Ra > 10^7; initial condition of mantle is unknown. | Metric | Value | |---|---| | Metric | flow_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `mantle_convection` · **Forward operator:** `mantle_convection_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 128 | | Ra | — | 1e+07 | | Snr db | dB | 25 | | N times | — | 100 | | Bc error | — | 0 | | Rheology error | — | 0.1 | | Time history unknown | — | 0.3 | | Viscosity contrast error | — | 0.2 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 32 – 1024 | | Ra | — | 100000.0 – 1000000000.0 | | Snr db | dB | 0 – 40 | | N times | — | 10 – 10000 | | Bc error | — | 0.0 – 0.3 | | Rheology error | — | 0.0 – 0.3 | | Time history unknown | — | 0.0 – 0.5 | | Viscosity contrast error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15.0 | Metric | Range | |---|---| | Flow rel | 1.0 – 60.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **flow_rel_error_percent**, with κ = `1600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6c41c889e917cbf9bf0f5f86ccdb1ce1fa181f681d8df7288a2eec67eea3d4ba` - **Chain tx hash:** `0x7aa1fc0f0655ea4954c7121ad8f04879dad9246b8e7371551f4678dc225ffd1f` - **Chain block:** `41554065` --- ## File Mapping This bundle consists of: `L1-286.md`, `L1-286.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-286.md` | Source of truth — edit this | Human or LLM | | `L1-286.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 `L1-286`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-286-001 Mantle Convection — high-Ra thermal convection Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-286",
  "chain_block": 41554065,
  "chain_hash": "0x6c41c889e917cbf9bf0f5f86ccdb1ce1fa181f681d8df7288a2eec67eea3d4ba",
  "chain_tx_hash": "0x7aa1fc0f0655ea4954c7121ad8f04879dad9246b8e7371551f4678dc225ffd1f",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 1600,
    "metric": "flow_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "flow_rel_error_percent",
    "regime": "Chaotic for Ra \u003e 10^7; initial condition of mantle is unknown.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "thermal",
    "difficulty_delta": 10,
    "domain": "Geophysics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.stokes_infinite_prandtl",
      "L.energy",
      "L.rheology",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "seismic_tomography_constraint",
    "solution_space": "mantle_flow_and_thermal_structure",
    "sub_domain": "Extended Boussinesq mantle flow",
    "title": "Mantle Convection \u2014 high-Ra thermal convection"
  },
  "size_tiers": {
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      "mantle_convection_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_times",
      "Ra",
      "SNR_dB",
      "rheology_error",
      "viscosity_contrast_error",
      "bc_error",
      "time_history_unknown",
      "rheology_error",
      "viscosity_contrast_error",
      "bc_error",
      "time_history_unknown"
    ],
    "allowed_problem_classes": [
      "mantle_convection"
    ],
    "center_spec": {
      "epsilon_fn_center": "15.0",
      "forward_operator": "mantle_convection_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_times": 100,
        "Ra": 10000000.0,
        "SNR_dB": 25,
        "W": 128,
        "Z": 128,
        "bc_error": 0.0,
        "rheology_error": 0.1,
        "time_history_unknown": 0.3,
        "viscosity_contrast_error": 0.2
      },
      "problem_class": "mantle_convection"
    },
    "epsilon_bounds": {
      "flow_rel": [
        1.0,
        60.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_times": [
        10,
        10000
      ],
      "Ra": [
        100000.0,
        1000000000.0
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        32,
        1024
      ],
      "bc_error": [
        0.0,
        0.3
      ],
      "rheology_error": [
        0.0,
        0.3
      ],
      "time_history_unknown": [
        0.0,
        0.5
      ],
      "viscosity_contrast_error": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Extended Boussinesq mantle flow",
  "title": "Mantle Convection \u2014 high-Ra thermal convection"
}

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