L1 ⚛ L1-278 ⊙ Testnet

Earthquake Source Inversion — finite-fault slip

Geophysics · Finite-fault slip from teleseismic + strong-motion

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⬇ principle.md ⬇ principle.json

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⬇ L1-278.md ⬇ L1-278.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-278 (Earthquake Source Inversion — finite-fault slip) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-278.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-278.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.linearize` `L.source_time` `L.green_function` x + n,    n ~ 𝒩(0, σ²)

world state x (2D slip distribution)

→

L · green function `L.green_function`

→

L · source time `L.source_time`

→

L · linearize `L.linearize`

→

Temporal integration ∫_t dt

→

observation y (acoustic detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-278.md

# ⚛ L1 Principle — Earthquake Source Inversion — finite-fault slip **ID:** `L1-278` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Finite-fault slip from teleseismic + strong-motion* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D slip distribution > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554052 --- ## 🧠 1. Introduction **Earthquake Source Inversion — finite-fault slip** is a **linear inverse problem** whose unknown lives in **2D slip distribution** space, within the **Finite-fault slip from teleseismic + strong-motion** sub-domain of **Geophysics**. Measurements consist of acoustic pressure waves recorded by transducers via a **teleseismic strong motion gps** sensing mechanism. The forward operator applies, in order: L · green function operator; L · source time operator; L · linearize operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Ill-posed for finite-fault; regularization essential. ## ⚙ 2. Forward Model Physical chain: **x** → L · green function → L · source time → L · linearize → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.linearize` `L.source_time` `L.green_function` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.green_function` | L · green function operator | | `L.source_time` | L · source time operator | | `L.linearize` | L · linearize operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Finite-fault slip from teleseismic + strong-motion | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | 2D_slip_distribution | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 3.7 | ## 📡 4. Measurement Model Ill-posed for finite-fault; regularization essential. | Metric | Value | |---|---| | Metric | slip_correlation_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `finite_fault` · **Forward operator:** `finite_fault_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N samples | — | 2048 | | N stations | — | 50 | | N subfaults | — | 200 | | Fault geometry error | — | 0 | | Green function error | — | 0.1 | | Rupture velocity error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N samples | — | 100 – 65536 | | N stations | — | 5 – 1000 | | N subfaults | — | 10 – 10000 | | Fault geometry error | — | 0.0 – 0.3 | | Green function error | — | 0.0 – 0.3 | | Rupture velocity error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **slip_correlation_percent**, with κ = `800` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x55689a911261e3aeeaffd3e2690ae9308a5d7eb6f9a6c2eb1d34d8e9350a8e86` - **Chain tx hash:** `0xe5f82a61a0e02220a4d679fff313c81226ad9c7dc6e391fad773b37c4826c2eb` - **Chain block:** `41554052` --- ## File Mapping This bundle consists of: `L1-278.md`, `L1-278.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-278.md` | Source of truth — edit this | Human or LLM | | `L1-278.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 `L1-278`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-278-001 Earthquake Source Inversion — finite-fault slip Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-278",
  "chain_block": 41554052,
  "chain_hash": "0x55689a911261e3aeeaffd3e2690ae9308a5d7eb6f9a6c2eb1d34d8e9350a8e86",
  "chain_tx_hash": "0xe5f82a61a0e02220a4d679fff313c81226ad9c7dc6e391fad773b37c4826c2eb",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 800,
    "metric": "slip_correlation_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "slip_correlation_percent",
    "regime": "Ill-posed for finite-fault; regularization essential.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "acoustic",
    "difficulty_delta": 10,
    "domain": "Geophysics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.green_function",
      "L.source_time",
      "L.linearize",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "teleseismic_strong_motion_gps",
    "solution_space": "2D_slip_distribution",
    "sub_domain": "Finite-fault slip from teleseismic + strong-motion",
    "title": "Earthquake Source Inversion \u2014 finite-fault slip"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "finite_fault_forward"
    ],
    "allowed_omega_dimensions": [
      "N_subfaults",
      "N_stations",
      "N_samples",
      "SNR_dB",
      "green_function_error",
      "rupture_velocity_error",
      "fault_geometry_error",
      "green_function_error",
      "rupture_velocity_error",
      "fault_geometry_error"
    ],
    "allowed_problem_classes": [
      "finite_fault"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "finite_fault_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_samples": 2048,
        "N_stations": 50,
        "N_subfaults": 200,
        "SNR_dB": 25,
        "fault_geometry_error": 0.0,
        "green_function_error": 0.1,
        "rupture_velocity_error": 0.0
      },
      "problem_class": "finite_fault"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_samples": [
        100,
        65536
      ],
      "N_stations": [
        5,
        1000
      ],
      "N_subfaults": [
        10,
        10000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "fault_geometry_error": [
        0.0,
        0.3
      ],
      "green_function_error": [
        0.0,
        0.3
      ],
      "rupture_velocity_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Finite-fault slip from teleseismic + strong-motion",
  "title": "Earthquake Source Inversion \u2014 finite-fault slip"
}

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