L1 ⚛ L1-464 ⊙ Testnet

Arps Decline Curve Analysis

Petroleum Engineering · Production forecasting

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⬇ principle.md ⬇ principle.json

Fork L1-464

⬇ L1-464.md ⬇ L1-464.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-464 (Arps Decline Curve Analysis) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-464.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-464.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 = `S.bootstrapping.uncertainty` `O.least_squares.nls` f(·) x

world state x (decline parameter vector)

→

Pointwise nonlinearity f(·)

→

O · least squares · nls `O.least_squares.nls`

→

S · bootstrapping · uncertainty `S.bootstrapping.uncertainty`

→

observation y (N/A detector)

Noise: log-normal multiplicative noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-464.md

# ⚛ L1 Principle — Arps Decline Curve Analysis **ID:** `L1-464` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Petroleum Engineering — *Production forecasting* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** decline parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555280 --- ## 🧠 1. Introduction **Arps Decline Curve Analysis** is a **parameter-estimation problem** whose unknown lives in **decline parameter vector** space, within the **Production forecasting** sub-domain of **Petroleum Engineering**. Measurements consist of N/A via a **production decline fitting** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · least squares · nls operator; S · bootstrapping · uncertainty operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered decline_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 10); rate_interference_from_offset_wells dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → O · least squares · nls → S · bootstrapping · uncertainty → **y** (detector). ``` y = `S.bootstrapping.uncertainty` `O.least_squares.nls` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.least_squares.nls` | O · least squares · nls operator | | `S.bootstrapping.uncertainty` | S · bootstrapping · uncertainty operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Petroleum Engineering | | Sub domain | Production forecasting | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | decline_parameter_vector | | Noise model | lognormal | | Integration axis | temporal_production | | Difficulty delta | 3 | | L dag | 2 | ## 📡 4. Measurement Model Existence of the recovered decline_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 10); rate_interference_from_offset_wells dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | EUR_prediction_RMSE_percent | | Secondary | rate_match_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `production_decline_fitting` **Center point:** | Parameter | Unit | Value | |---|---|---| | Q i bopd | — | 500 | | B exponent | — | 1.5 | | D i per month | — | 0.05 | | N months history | — | 24 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Q i bopd | — | 10 – 100000 | | B exponent | — | 0.0 – 2.0 | | D i per month | — | 0.01 – 0.5 | | N months history | — | 6 – 120 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15 EUR_prediction_RMSE_percent | Metric | Range | |---|---| | Eur prediction rmse percent | 3 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **EUR_prediction_RMSE_percent**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xee068934b9db9a1d8314c260f50c43460e48cf39c84f686ed6afe33cd6a730a6` - **Chain tx hash:** `0x81edc2ef5a403072191f9ae75c4d8fa6de26aa65902981cb8808437124498940` - **Chain block:** `41555280` --- ## File Mapping This bundle consists of: `L1-464.md`, `L1-464.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-464.md` | Source of truth — edit this | Human or LLM | | `L1-464.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 `L1-464`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-464-001 Arps Decline Curve Analysis — Nominal + Mismatch Specs

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📋 JSON metadata

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  "artifact_id": "L1-464",
  "chain_block": 41555280,
  "chain_hash": "0xee068934b9db9a1d8314c260f50c43460e48cf39c84f686ed6afe33cd6a730a6",
  "chain_tx_hash": "0x81edc2ef5a403072191f9ae75c4d8fa6de26aa65902981cb8808437124498940",
  "domain": "Petroleum Engineering",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "EUR_prediction_RMSE_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "EUR_prediction_RMSE_percent",
    "regime": "Existence of the recovered decline_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 10); rate_interference_from_offset_wells dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.",
    "secondary": "rate_match_RMSE_percent"
  },
  "physics_fingerprint": {
    "L_DAG": 2.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Petroleum Engineering",
    "integration_axis": "temporal_production",
    "noise_model": "lognormal",
    "primitives": [
      "N.pointwise",
      "O.least_squares.nls",
      "S.bootstrapping.uncertainty"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "production_decline_fitting",
    "solution_space": "decline_parameter_vector",
    "sub_domain": "Production forecasting",
    "title": "Arps Decline Curve Analysis"
  },
  "size_tiers": {
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      "b_exponent"
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    ],
    "center_spec": {
      "epsilon_fn_center": "15 EUR_prediction_RMSE_percent",
      "forward_operator": "production_decline_fitting",
      "input_format": "measurement_only",
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        "N_months_history": 24,
        "b_exponent": 1.5,
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    "omega_bounds": {
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        0.5
      ],
      "N_months_history": [
        6,
        120
      ],
      "b_exponent": [
        0.0,
        2.0
      ],
      "q_i_bopd": [
        10,
        100000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Production forecasting",
  "title": "Arps Decline Curve Analysis"
}

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