L1 ⚛ L1-903 ◆ Frontier — not yet benchmarked

Cancer as Evolution — Adaptive Therapy

Oncology · Evolutionary Dynamics

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Introduction

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Open frontier — governing equation defined, not yet benchmarked. Help build the digital twin or first benchmark and earn PWM.

Cancer as Evolution — Adaptive Therapy (Evolutionary Dynamics) is a problem in Oncology. The forward model maps the hidden the unknown quantity to a measurement. The inverse goal is to recover the the unknown quantity from the observed data.

Governing Equation

Competing sensitive/resistant clones under drug schedule u(t): dx_s/dt = r_s x_s(1−N/K) − d·u·x_s, dx_r/dt = r_r x_r(1−N/K); control to delay competitive release.
Oncology L_DAG TTP months

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Digital Twins

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Each digital twin (L2) is a concrete instantiation of this principle's forward operator with a specific Ω parameter space. Benchmarks (L3) are seeded from each twin.

# Digital Twin ID
1 Adaptive Dosing-Schedule Twin L2-903

Contents

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On-Chain Artifact Registry

Base Sepolia → Base Mainnet on graduation
L1
Principle — Cancer as Evolution — Adaptive Therapy L1-903 Testnet

PWM Registry — Principle #903

Cancer as Evolution — Adaptive Therapy  ·  P = (E, G, W, C)

E

Forward Model

Competing sensitive/resistant clones under drug schedule u(t): dx_s/dt = r_s x_s(1−N/K) − d·u·x_s, dx_r/dt = r_r x_r(1−N/K); control to delay competitive release.

Sensing: —

Carrier: —

Problem class: —

Recover: —

Noise model: —

G

DAG Decomposition — G = (V, A)

L_DAG:

W

Well-Posedness Certificate

Existence

—

Uniqueness

—

Stability

—

C

Error-Bounding Methodology

Primary: TTP months

Hardness function: grand_challenge

📝 Markdown source — L1-903.md

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Improve L1-903 — submit with or without uploading. Accepted submissions earn the 1/16 modify share of A(t).

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No files, no typing — we submit a check of L1-903 for you once; it goes through review and earns the 1/16 share. One free no-upload Principle per account.

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-903

⬇ L1-903.md ⬇ L1-903.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-903 (Cancer as Evolution — Adaptive Therapy) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-903.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-903.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]