Jos De Roo

Branches of Insights – brains

In Branches of Insights – brains, each case is a small, carefully constructed program developed using the ARC (Answer • Reason • Check) methodology. The goal is to produce compact and verifiable programs that read like short scientific abstracts.

Each case is not just a black box that produces an outcome. Instead, it functions as a self-contained, end-to-end account of a computation, explicitly showing:

• what question is being answered,
• why the answer is justified, and
• how that justification has been tested.

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The ARC Methodology: Answer • Reason • Check

ARC is a lightweight methodology for designing small, trustworthy computational artifacts. Each case is built to deliver a “triad of trust”:

1. Answer The program computes a clear answer to a well-specified question.

2. Reason Why The program produces a structured explanation—expressed in ordinary language and grounded in explicit rules, assumptions, or domain knowledge—explaining why the answer follows from the inputs.

3. Check The program runs explicit checks designed to detect violations of assumptions, boundary conditions, or edge cases. When these checks fail, they do so in a visible and traceable way.

The result is a computation with a complete, auditable trace. A reader can see exactly what was done, under which assumptions it was done, and how the program evaluates the reliability of its own output.

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P3: Prompt → Program → Proof

The discipline underlying these ARC cases is referred to as P3: a pragmatic Prompt → Program → Proof workflow. It starts from three basic ingredients:

• Data: the facts, measurements, or inputs,
• Logic: the rules, models, or constraints, and
• Question: the clearly defined problem to be answered.

In this setting, “proof” is understood in a practical, engineering sense rather than as an abstract mathematical derivation. It emerges from combining:

• a narrative explanation of why the result is valid, and
• the verification code embedded in the program.

Formally:

Proof = Reason Why + Check

A Triad of Trust

Transforming raw data into reliable, actionable insight is a central challenge in modern analytic workflows. The P3 method addresses this by using a large language model (LLM) only at design time, to assist with question-directed program synthesis.

The process is:

1. Formulate a prompt that specifies what kind of program is needed.
2. State the question precisely.
3. Provide the relevant data, rules, and assumptions.

4. Use the LLM to synthesize a self-contained program that:

   • ingests these inputs,
   • computes the answer,
   • generates the reason (the structured explanation), and
   • implements the check (the verification procedure).

From Synthesis to Runtime

This method combines the flexibility of generative AI with the rigor of symbolic systems:

• At design time, the LLM is used to generate or refine the program based on the prompt, data, and logic.
• At runtime, only the synthesized program is executed. The LLM is no longer involved.

During execution, the program:

• produces the answer,
• emits the explanation of why that answer is correct under the specified assumptions, and
• runs its own checks.

Every output is therefore verifiable by design. Each case is a self-contained artifact with an internal test harness. It can be:

• integrated into automated pipelines,
• inspected by auditors or peers, and
• deployed operationally with a clear account of its behavior and limitations.

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How to Read a Case

Each branch (case) is designed to be self-contained, readable, and reproducible. It is intended to be accessible to a broad audience:

• If you are a student, you should be able to follow the logical progression from inputs and assumptions to answer and checks.
• If you are a practitioner, you should find the code and checks straightforward to audit and adapt.
• If you are simply curious, you should be able to modify parameters, rerun the program, and directly observe how the outputs change.

A practical way to read a case is:

1. Identify the question being asked and the final answer reported.
2. Examine the reason to see how the premises and rules support that answer.

3. Inspect the check to understand what is being verified—for example:

   • whether a known identity holds,
   • whether a conservation law is respected, or
   • whether an error remains within a specified bound.

If a check fails, the program reports a specific violation. That failure is treated as a valuable signal for refinement and learning, rather than something to hide.

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The Tree of Insights

As these cases accumulate, they form a growing “tree of insights.”

• Answers from earlier cases can serve as inputs or assumptions in later cases.
• Reasons and checks maintain a consistent level of rigor, helping ensure that the overall structure remains coherent and trustworthy.

In this way, Branches of Insights – brains supports the gradual construction of a transparent, testable network of computational insights, where each branch documents not only what is concluded, but also why and how it has been verified.