L1 ⚛ L1-293 ⊙ Testnet

Subsurface Temperature — geothermal gradient inversion

Geophysics · Borehole temperature geothermal gradient

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⬇ principle.md ⬇ principle.json

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⬇ L1-293.md ⬇ L1-293.json

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You are helping me submit a MODIFICATION of L1-293 (Subsurface Temperature — geothermal gradient inversion) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-293.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-293.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 = ∫_A dA `L.paleoclimate_signal` `L.heat_flux` `L.1d_heat_conduction` x + n,    n ~ 𝒩(0, σ²)

world state x (temperature depth profile)

→

L · 1d heat conduction `L.1d_heat_conduction`

→

L · heat flux `L.heat_flux`

→

L · paleoclimate signal `L.paleoclimate_signal`

→

Spatial integration ∫_A dA

→

observation y (thermal detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-293.md

# ⚛ L1 Principle — Subsurface Temperature — geothermal gradient inversion **ID:** `L1-293` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Borehole temperature geothermal gradient* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** temperature depth profile > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554066 --- ## 🧠 1. Introduction **Subsurface Temperature — geothermal gradient inversion** is a **linear inverse problem** whose unknown lives in **temperature depth profile** space, within the **Borehole temperature geothermal gradient** sub-domain of **Geophysics**. Measurements consist of thermal radiation / temperature measurements via a **borehole temperature log** sensing mechanism. The forward operator applies, in order: L · 1d heat conduction operator; L · heat flux operator; L · paleoclimate signal operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · 1d heat conduction → L · heat flux → L · paleoclimate signal → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.paleoclimate_signal` `L.heat_flux` `L.1d_heat_conduction` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.1d_heat_conduction` | L · 1d heat conduction operator | | `L.heat_flux` | L · heat flux operator | | `L.paleoclimate_signal` | L · paleoclimate signal operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Borehole temperature geothermal gradient | | Carrier | thermal | | Problem class | linear_inverse | | Solution space | temperature_depth_profile | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `subsurface_temp` · **Forward operator:** `subsurface_temp_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 40 | | N depths | — | 500 | | Terrain error | — | 0 | | Surface temp error | — | 0 | | Thermal conductivity error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 10 – 60 | | N depths | — | 10 – 10000 | | Terrain error | — | 0.0 – 0.2 | | Surface temp error | — | 0.0 – 2.0 | | Thermal conductivity error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x073104cc47cd67eac1a6e82f351c53bbe2d2cb42fce14686412780fe079deb6e` - **Chain tx hash:** `0x59720e45ebc23ef8d267c0abc6eef0ae15d3189ad4712a0ea5e10b45f46e59d8` - **Chain block:** `41554066` --- ## File Mapping This bundle consists of: `L1-293.md`, `L1-293.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-293.md` | Source of truth — edit this | Human or LLM | | `L1-293.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 `L1-293`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-293-001 Subsurface Temperature — geothermal gradient inversion Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-293",
  "chain_block": 41554066,
  "chain_hash": "0x073104cc47cd67eac1a6e82f351c53bbe2d2cb42fce14686412780fe079deb6e",
  "chain_tx_hash": "0x59720e45ebc23ef8d267c0abc6eef0ae15d3189ad4712a0ea5e10b45f46e59d8",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "thermal",
    "difficulty_delta": 3,
    "domain": "Geophysics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.1d_heat_conduction",
      "L.heat_flux",
      "L.paleoclimate_signal",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "borehole_temperature_log",
    "solution_space": "temperature_depth_profile",
    "sub_domain": "Borehole temperature geothermal gradient",
    "title": "Subsurface Temperature \u2014 geothermal gradient inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "subsurface_temp_forward"
    ],
    "allowed_omega_dimensions": [
      "N_depths",
      "SNR_dB",
      "thermal_conductivity_error",
      "surface_temp_error",
      "terrain_error",
      "thermal_conductivity_error",
      "surface_temp_error",
      "terrain_error"
    ],
    "allowed_problem_classes": [
      "subsurface_temp"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "subsurface_temp_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_depths": 500,
        "SNR_dB": 40,
        "surface_temp_error": 0.0,
        "terrain_error": 0.0,
        "thermal_conductivity_error": 0.0
      },
      "problem_class": "subsurface_temp"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_depths": [
        10,
        10000
      ],
      "SNR_dB": [
        10,
        60
      ],
      "surface_temp_error": [
        0.0,
        2.0
      ],
      "terrain_error": [
        0.0,
        0.2
      ],
      "thermal_conductivity_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Borehole temperature geothermal gradient",
  "title": "Subsurface Temperature \u2014 geothermal gradient inversion"
}

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