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.
Banya Framework Operational Manual
Inventor: Han Hyukjin (bokkamsun@gmail.com)
Date: 2026-03-23
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.
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.
These 5 steps are repeated every round. The $\alpha$ derivation, the $\theta_W$ derivation, and the mass hierarchy all follow this structure.
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.
Substitute the axes of the Banya Equation with physically meaningful variables.
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:
| Substitution Path | What the Axes Become | What Was Derived |
|---|---|---|
| CAS Cost Structure | Cost of R, C, S respectively | $\alpha$, $\theta_W$ |
| Energy-Time | time to energy, space to momentum | Uncertainty principle, mass hierarchy |
| Area-Information | observer to information content, superposition to entropy | Bekenstein bound, information-theoretic interpretation of $\alpha$ |
| Symmetric Space Decomposition | 4 axes to $SO(5,2)$ symmetric space | Wyler formula correspondence |
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.
Insert existing physical constants, discoveries and hypotheses from lib.html, and by-products from previous rounds.
The more you insert, the fewer unknowns remain. This is why we run the loop.
What can be inserted:
Transform the substituted result into a different domain. New relations emerge during transformation.
Domain transform examples:
| Before Transform | After Transform | What Emerged |
|---|---|---|
| time domain | energy domain | Mass-energy relation |
| CAS cost | coupling constant | $\alpha$ = volume ratio |
| geometric volume ratio | information-theoretic bits | $\alpha = 1\text{bit}/137\text{bit}$ |
| micro scale | cosmic scale | $\Lambda \cdot l_p^2 = \alpha^{57}$ |
Compare the obtained value with experimentally measured values. The verdict criteria are clear.
| Error Range | Verdict | Action |
|---|---|---|
| Within 1% | Discovery | Register in lib.html |
| 1% ~ 10% | Candidate | Refine in the next round |
| Over 10% | Discard | Discard it |
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.
The $\alpha$ derivation reached 0.00006% in just 4 rounds. Re-substituting the previous results into Step 3 every round improves precision.
5 to 10 expert agents are deployed simultaneously on a single task. Each attacks the same target via a different path.
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.
The actual assignment used during the $\theta_W$ derivation:
Partition the cost of each CAS stage (R, C, S) by volume ratio to trace $\sin^2\theta_W$.
Run coupling constants from the grand unification energy down to the electroweak scale to back-trace $\theta_W$.
Explore the geometric path where the electroweak mixing angle emerges from the $SO(5,2)$ symmetric space.
Extract $\theta_W$ from the bit allocation between Compare and Read within the CAS 137-bit structure.
Back-trace clues related to $\theta_W$ from the by-products of the $\alpha$ derivation process.
What is provided identically to each expert:
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.
| # | Criterion | Description |
|---|---|---|
| 1 | Numerical Accuracy | What is the error percentage? |
| 2 | Physical Justification | Can "why this formula" be explained? |
| 3 | Banya Framework Consistency | Is there no contradiction with existing derivations? |
| 4 | Circular Reasoning | Was it merely reverse-engineered from measured values? |
| 5 | Numerology Risk | Has mathematical coincidence been distinguished from physical necessity? |
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:
In $3/\pi^2$, 3 is the CAS 3 stages (R, C, S), and $\pi^2$ is the domain curvature. Both originate from the Banya Framework structure. Pass.
| Grade | Condition | Action |
|---|---|---|
| A | Physically necessary and error within 0.1% | Register as discovery |
| B | Structural correspondence confirmed, error within 1% | Register as discovery, continue refinement |
| C | Candidate, further verification needed | Register as hypothesis, re-verify in next round |
| D | Numerology risk or circular reasoning | Discard |
Register discoveries and hypotheses in lib.html. These become weapons for the next round. The more weapons, the fewer unknowns in the next round.
| Category | Condition | Tag |
|---|---|---|
| Discovery | Error within 1%, physical justification secured | Green |
| Hypothesis | Structural correspondence confirmed, quantitative proof incomplete | Yellow |
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:
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.
The Banya Framework has 14 axioms (see banya.html Axiom System). Of these, the following 4 are essential knowledge 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.
In the Banya Equation, CAS is on the quantum bracket (observer + superposition) side. It is outside the time domain. Going from R to C to S is not temporal order but logical dependency.
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.
The minimum cost of locking to prevent state change between Compare and Swap is $\hbar$ (Axiom 4). The uncertainty principle is not "a limit of nature" but "a cost of computation." Additionally, the TOCTOU lock register (Axiom 5) physically enforces this 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 $\hbar$ (Axiom 4). And the TOCTOU lock register (Axiom 5) is the physical mechanism that implements this lock. That is why $\Delta x \cdot \Delta p \geq \hbar/2$.
When CAS executes on superposition (multiple states), it becomes observer (1 determined state) and is recorded as DATA. The answer to the 100-year mystery: because it is a 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.
From $\delta$'s existence, OPERATOR operates, cost $\hbar$, DATA is recorded, time and space, the universe. A single line of the Banya Equation answers "why does the universe exist."
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.
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.
| Term | Meaning | Badge | Block |
|---|---|---|---|
| Hit | Error within 1% + physical justification secured. Done | Hit | discovery-block (green border) |
| Discovery | New formula/relation confirmed. Re-substitutable factor | Discovery | discovery-block (green border) |
| Hypothesis | Structural correspondence confirmed. Quantitative proof not yet done | Hypothesis | hypothesis-block (orange border) |
| In Progress | Started but not completed. Additional work needed | In Progress | default block (gray border) |
| Pending | Derivation complete. Waiting for experimental verification | Pending | default block (gray border) |
| Deprecated Term | Replacement Term |
|---|---|
| Unresolved | WIP |
| In progress, Deriving | WIP |
| Partial success | Discovery (if partial, specify scope after: "Discovery -- leptons only") |
| Structure confirmed | Solved |
| Awaiting experiment | Awaiting |
| On hold | WIP |
| Success, Complete | Solved |
Do not change text color. If emphasis is needed, use badges (tags). Use strong tags (bold). Inline style="color:..." is prohibited.
| Category | Color | Usage |
|---|---|---|
| Discovery/Solved | Green (#2ea043) | discovery-block border, tag-solved badge, tag-discovery badge, lib-card left line |
| Hypothesis | Orange (#d29922) | hypothesis-block border, tag-hypothesis badge, lib-card left line, warn-block |
| WIP/Awaiting | Gray (#30363d) | default block border, tag-wip badge. No special emphasis |
| Links | Blue (#58a6ff) | a tags. Only this is blue |
| Body text | Default (#c9d1d9) | All body text. No color change |
| Block | Purpose | Visual |
|---|---|---|
| discovery-block | Solved formulas, confirmed discoveries | Green border + green background |
| hypothesis-block | Hypotheses, unproven formulas | Orange border + orange background |
| math-block | Formulas (status-independent) | Gray border |
| pre | Code, structure diagrams | Gray border |
| lib-card | lib.html factor cards | Left line: discovery=green, hypothesis=orange |
| Status | File Format | Notes |
|---|---|---|
| Solved/Discovery | HTML file (alpha.html standard template) | Record the full Banya Framework 5-step process by round |
| WIP | md file (mark "WIP" in title) | For session records |
| Same constant improved | Update existing HTML | Do not create a new file |
| New constant | Create separate HTML | Add to page-nav |
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.
This is the actual process of $\alpha = 1/137$ derivation. It converged from 0.53% to 0.00006% in just 4 rounds.
Execute 5 steps. Start from the Banya Equation, 4-axis geometric norm substitution, substitute $\pi^4$ and $\sqrt{2}$, energy domain transform.
Result: $1/\alpha = \pi^4 \cdot \sqrt{2} = 137.76$
Error: 0.53%
By-product: Geometric structure confirmed. Clue that 4-axis orthogonality is the skeleton of $\alpha$.
Re-substitute Round 1 by-products. 4 domains + 3 internal degrees of freedom = 7 degrees of freedom. Calculate 7-dimensional phase space volume ratio.
Correspondence with Wyler's formula (1969) discovered.
Result: $1/\alpha = 137.036082$
Error: 0.00006%
By-product: Provided physical basis for Wyler's formula. Filled a gap that had been empty for 57 years.
Re-substitute Round 2 results. Calculate the information content of 1 CAS event as Shannon entropy.
Result: $\alpha = 1\text{bit}/137\text{bit}$
Interpretation: $\alpha$ is the 1 bit occupied by Compare out of the total 137 bits of information in 1 CAS event. The concentration of charge information.
Re-substitute Round 3 results. Connect Planck length and cosmological constant.
Result: $\Lambda \cdot l_p^2 = \alpha^{57}$
By-product: Koide deviation $= -15\alpha^3$, electron-proton mass ratio approximation.
| Round | Input | Output | Error |
|---|---|---|---|
| 1 | Banya Eq. + $\pi^4 \cdot \sqrt{2}$ | $1/\alpha = 137.76$ | 0.53% |
| 2 | + 3 internal DOF | $1/\alpha = 137.036082$ | 0.00006% |
| 3 | + information theory | $\alpha = 1\text{bit}/137\text{bit}$ | structural |
| 4 | + cosmological constant | $\Lambda \cdot l_p^2 = \alpha^{57}$ | 121/122 digits |
Re-substituting the previous results into Step 3 every round improves precision. This is the core of Banya Framework science mining.
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.
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.
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.
| Tool | Role | Description |
|---|---|---|
| Banya Framework 5 Steps | Core Engine | Recursive substitution structure that derives physical constants starting from the Banya Equation |
| Expert Agents (5~10) | Multi-path Attack | Deploy multiple paths simultaneously on a single task to find the convergence point |
| lib.html | Factor Library | Discoveries D-01 through D-42, hypotheses H-01 through H-47. Weapons for the next round |
| banya.html | Comprehensive Hub | Discovery hierarchy, challenge resolution list, overall structure overview |
| Session Records (md) | Continuity Assurance | Preserve work contents across sessions so the next session can continue |
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.