This document is a supplementary document to the Banya Framework Comprehensive Report. It is an operational manual describing the concrete methods for deriving physical constants and laws using the Banya Framework. These are the exact methods used by Han Hyukjin and AI (Claude). Anyone who follows this manual can reproduce the same results.

Science Mining Method

Banya Framework Operational Manual

Inventor: Han Hyukjin (bokkamsun@gmail.com)

Date: 2026-03-23

Chapter 1. Overall Structure

Banya Framework science mining is a 4-step loop. The more you repeat this loop, the larger the library grows, and the larger the library grows, the fewer places hidden values can escape to.

4-Step Loop

Why a Loop

Think of simultaneous equations. If there are 5 unknowns and only 2 equations, you cannot solve it. With 3 equations, the solution narrows. With 4, it is nearly determined. With 5, a unique solution emerges.

The Banya Framework loop works the same way. If Round 1 yields 1 discovery, Round 2 re-substitutes that discovery and reduces the unknowns by 1. Round 3 reduces them by 2. The more you iterate, the more the solution converges. The $\alpha$ derivation converged from 0.53% to 0.00006% in just 4 rounds.

Chapter 2. Banya Framework 5 Steps (Core Engine)

These 5 steps are repeated every round. The $\alpha$ derivation, the $\theta_W$ derivation, and the mass hierarchy all follow this structure.

Step 1: Start from the Banya Equation

This single line is the starting point. We never deviate from it. The Banya Equation consists of 4 axes (time, space, observer, superposition) and 1 operator (CAS). All physics emerges from within this structure.

Step 2: Norm Substitution

Multiple substitution paths are possible. Each path yields different physics. This is the core of the Banya Framework. Starting from the same equation, different constants are derived depending on the substitution path.

Substitution paths used so far:

Path selection criteria: The substitution path is determined by the domain of the physical quantity to be derived. Coupling constant → CAS cost path. Mass → energy-time path. Information content → area-information path. Symmetry → symmetric space decomposition path. When the target is clear, the path narrows to one.

Step 3: Constant + Hypothesis Substitution

The more you insert, the fewer unknowns remain. This is why we run the loop.

What can be inserted:

• Existing physical constants: $c$, $\hbar$, $G$, $\Lambda$, $\alpha$, $\sin^2\theta_W$, etc.
• Discoveries from lib.html: D-01 through D-15, already verified
• Hypotheses from lib.html: H-01 through H-18, structural correspondence confirmed but quantitative proof incomplete
• By-products from previous rounds: large error but visible structure

Step 4: Domain Transform

Domain transform examples:

Step 5: Discovery + Verdict

However, even results with large errors are collected as by-products if structure is visible. These by-products often become decisive clues in the next round.

Verdict criteria clarification: The 5-step verdict (error within 1% = discovery) is the initial registration threshold. The supervisor review Grade A (error within 0.1%) is the precision grade. After registration as a discovery, grades A/B/C are assigned based on precision. Within 1% means discovery registration; within 0.1% means Grade A discovery.

Round Repetition

The $\alpha$ derivation reached 0.00006% in just 4 rounds. Re-substituting the previous results into Step 3 every round improves precision.

Chapter 3. Parallel Expert Verification

5 to 10 expert agents are deployed simultaneously on a single task. Each attacks the same target via a different path.

Why Parallel

• Trying only 1 path traps you in that path's bias
• Running 5 paths simultaneously reveals where they converge
• If 3 or more converge on the same value, it is not coincidence

An analogy: when searching for treasure, if 1 person digs in 1 direction, finding it requires luck. If 5 people dig in 5 directions simultaneously, the point where 3 of them meet is the treasure.

Assignment Example

The actual assignment used during the $\theta_W$ derivation:

What Experts Receive

What is provided identically to each expert:

1. Full CAS Axioms -- H-11 through H-14: operator outside time, TOCTOU lock, collapse = write, self-reference
2. All discoveries and hypotheses from lib.html -- this is the weapons list. Not providing it is like fighting bare-handed
3. Existing results for the given task -- outputs from previous rounds
4. A clear target -- provide specific numbers. Example: "Find the formula closest to 0.23122"

Chapter 4. Supervisor Review (Numerology Filtering)

When the experts return with results, the supervisor (human or AI supervisor) reviews them. This is the most important step. Experts are biased toward their own paths. Only the supervisor sees the whole picture.

Review Criteria

Numerology Filtering

Combinations of $\pi$, $e$, and integers can approximate almost any number to within 0.1%. This is the trap of numerology. Mathematical coincidence must be distinguished from physical necessity.

Filtering rules:

• Every number in the formula must originate from the Banya Framework structure
• If "why this number" cannot be answered, it is put on hold

Review Grades

Chapter 5. Library Accumulation (lib.html)

Register discoveries and hypotheses in lib.html. These become weapons for the next round. The more weapons, the fewer unknowns in the next round.

Registration Criteria

Library Usage

In Step 3 (constant substitution) of the Banya Framework 5 steps, insert items from lib.html alongside existing physical constants.

This is how it was actually used:

• Inserting $\alpha$ yielded $\theta_W$
• Inserting $\theta_W$ yielded $\eta$ (baryon-to-photon ratio)
• One discovery is the seed of the next discovery

Re-substitution Map

Track which discovery gave birth to which discovery:

The larger this map grows, the tighter the framework's connections become. It is like adding conditions to a system of simultaneous equations.

Chapter 6. CAS Axioms (Required Prior Knowledge)

These are the 4 CAS axioms that every expert must understand before starting work. If you run the framework without understanding these, you fall into the misconception that "CAS operates within time." The interpretation of all results goes wrong.

Axiom 1: CAS Is an Operator Outside Time

An analogy: in a computer, the CAS instruction executes atomically within a single CPU clock. From the outside, it happens all at once "as if time did not flow." Nature's CAS is the same. It operates outside the time domain.

Axiom 2: $\hbar$ = TOCTOU Lock Cost

TOCTOU (Time Of Check to Time Of Use) refers to the problem in computer science where "the state changes between the time of checking and the time of using." CAS solves this problem with a lock. The minimum cost of that lock is $\hbar$. That is why $\Delta x \cdot \Delta p \geq \hbar/2$.

Axiom 3: Wavefunction Collapse = Write

Why does the wavefunction collapse upon observation? No one answered this for 100 years. The Banya Framework's answer: observation is a write, and a write is determining 1 state out of many. When a write occurs, superposition is resolved. That is collapse.

Axiom 4: Banya Equation Self-Reference

The Banya Equation references itself. If $\delta$ exists, CAS operates; if CAS operates, $\hbar$ cost is incurred; if cost is incurred, DATA is recorded; if DATA is recorded, time and space arise; if time and space arise, $\delta$ exists. It is circular, but a self-consistent circle.

Chapter 7. Document Rules

Terminology Legend -- Use Only These 5

When marking status in all HTML files, all tables, and all introductions, use only these 5 terms. All similar terms (unresolved, in progress, partial success, structure confirmed, deriving, etc.) are all deprecated and replaced with these 5.

Deprecated Term Mapping

Color Rules -- No Colored Fonts

Do not change text color. If emphasis is needed, use badges (tags). Use strong tags (bold). Inline style="color:..." is prohibited.

Block Usage Rules

File Rules

CSS Rules

All HTML files include a single common.css via link. Inline style tags prohibited. Inline color prohibited. All visual rules are defined only in common.css.

Required HTML Structure

1. Introduction -- Scientific value of this discovery + current status (choose one of solved/discovery/hypothesis/WIP/awaiting, displayed as badge)
2. Body -- Record the full Banya Framework 5-step process by round. Document every path and every value without omission
3. discovery-block or hypothesis-block -- Package core formulas in separate blocks. Green for solved/discovery, orange for hypothesis
4. Discovery hierarchy -- If subordinate to a parent discovery, display as hierarchy
5. page-nav -- Interconnect all HTML files
6. Footer -- Same format as alpha.html

Chapter 8. Practical Cycle Example

This is the actual process of $\alpha = 1/137$ derivation. It converged from 0.53% to 0.00006% in just 4 rounds.

Round 1: Zeroth-Order Approximation

Round 2: Precision Derivation

Round 3: Information-Theoretic Interpretation

Round 4: Cosmic Scale Re-substitution

Re-substituting the previous results into Step 3 every round improves precision. This is the core of Banya Framework science mining.

Chapter 9. Precautions

1. Trust the Framework, Doubt the Results

2. Do Not Discard By-products

Collect results even if the error is large, as long as structure is visible. Without Round 1 (0.53%) of the $\alpha$ derivation, Round 2 (Wyler's formula, 0.00006%) would never have been reached. The zeroth-order approximation was the seed of the precision derivation.

3. Beware of Numerology

4. Beware of Circular Reasoning

If you reverse-engineer a measured value and claim "this formula is correct," that is circular. Every value in the formula must be independently derived. Example: if you insert $\alpha = 1/137.036$ and derive $\alpha = 1/137.036$, that is circular. It is completely meaningless.

5. Never Skip the Supervisor

Even if all 5 experts say "correct," the supervisor must still review. Experts are biased toward their own paths. Only the supervisor sees the whole picture. Anything adopted without supervisor review will inevitably cause problems later.

Chapter 10. Tools

Combine these tools and run the loop. The more you run, the larger the library grows, the higher the precision, and the more new discoveries emerge. That is science mining.

Anyone who takes these tools and follows this manual to run the loop can reproduce the same results. The Banya Framework is not the intuition of a specific person, but an engine anyone can run.