This document is the Physics Correspondence Terminology Table portion of the Banya Framework Comprehensive Report Sub-Reports.
The table below shows which concepts in existing physics correspond to axiom terms. Physics terminology is not used in the axiom body text.
| Structure (v1.4) | |
|---|---|
| Axiom term | Physics correspondence |
| δ = firing bit (bit 7) | Consciousness (δ). Equality sign. Observation trigger |
| observer = entry point (bit 0) | Observer. Filter. Pipeline start |
| superposition (bit 1) | Quantum superposition |
| time (bit 2) | Time axis. Screen frame |
| space (bit 3) | Space axis. Screen pixel |
| CAS (R,C,S = bit 4,5,6) | Sole operator. Render engine |
| d-ring (8 bits, 2 nibbles) | Minimum execution unit of the universe. Container of physical structure |
| CAS-ring (3-bit cycle) | CAS internal state transition. 000→001→011→111→000 |
| Quantum bracket (OPERATOR) | Backend (compute). Continuous. Where CAS operates |
| Classical bracket (DATA) | Frontend (screen). Discrete. Rendered output |
| Workbench (‖CAS‖ = √3) | CAS internal workspace. Independent compute unit |
| Data types (Axiom 2 Proposition, Axiom 9) | Structural constants. Size units in which CAS reads targets |
| Juim = CAS Swap(111) | Particle. 3-axis orthogonal → isotropic → spherical. Discrete unit |
| Equality sign (=) | If δ=1, entire right-hand side is valid. Firing declaration |
| Ring seam δ(bit 7)→observer(bit 0) | Entry point of the equality sign. Global-local loop connection |
| Global-local loop (Axiom 10) | δ→observer→CAS→δ feedback. Self-reference |
| Pipeline trigger→filter→update→render→screen | Game loop. 1 Planck time per frame |
| Polling (Axiom 8) | Checks δ firing every tick. Always running |
| ECS (Axiom 12) | Entity=shadow, Component=DATA, System=CAS. Parallel execution |
| 4 Forces (4 CAS×DATA access methods) | |
| Axiom term | Physics correspondence |
| 1111 domain pattern (ring-7) | 4-axis full access |
| Contraction overlap cost / serialization (ring-30) | Weak force |
| + cross Cmp/Swp cost (ring-137) | Electromagnetic force |
| √3 norm accumulation / juim density contraction (no ring) | Gravity. Geometric contraction, space deformation not cost |
| Cost = Physical quantity | |
| Axiom term | Physics correspondence |
| Crosses + cost = +1 (Axiom 4) | Energy quantum (ℏ) |
| Juim cost (Swap +1) | Mass |
| Total cost 13 (Axiom 6) | System total energy. Ball cost 4 + misc 9 |
| Cost conservation (Axiom 15 proposition) | Energy conservation. Firing period equivalent substitution |
| Serialization cost ≠ 0 | W/Z boson mass |
| Serialization cost = 0 | Photon massless |
| Magnitude of cost ($1/\ell^2$) | Force strength |
| Type of cost ($(1-\ell/N)$) | Force type |
| Contraction region (Axiom 11 proposition) | Potential |
| read contention (Axiom 11 proposition) | Interaction |
| Asymmetry in step cost coefficient C (step gap) | Asymmetric meson correction (K±, D±, B±) |
| Inter-entity interaction $C(1-\ell/N)/(4\pi \ell^2)$ | Coulomb/Newton inverse-square law |
| Crosses + cost > 0 (Axiom 4) | $\Delta x \cdot \Delta p \geq \hbar/2$ (uncertainty principle) |
| R, C, S each transition +1 (Axiom 2, 4, 5) | Minimum energy consumption per interaction step |
| Cost accumulation (5, 2) (Axiom 4 proposition) | Irreversible 5 axes (+) / non-irreversible 2 axes. → SO(5,2) → D₅ → α = 1/137 |
| CAS FSM norm: √1, √2, √3 (Axiom 2 proposition, 5) | 001=√1(Read), 011=√2(Compare), 111=√3(Swap). m_t = v/√2 |
| Data type 137 = T(16)+1 (Axiom 2 proposition) | Compare candidate count. Selection probability 1/137 = α. Discrete counterpart of Wyler D₅ volume ratio |
| Data type 7 = T(3)+1 (Axiom 2 proposition) | CAS internal Compare candidate count. Selection probability 1/7 ≈ α_s. Strong coupling constant |
| Quarks / Leptons (Derivation Demo 2) | |
| Axiom term | Physics correspondence |
| CAS 3 axes = 3 generations (Axiom 2) | Quark/lepton 3 generations. No 4th generation |
| Compare true (Axiom 7) | up type quarks (t, c, u). Swap cost paid |
| Compare false (Axiom 7) | down type quarks (b, s, d) / leptons (τ, μ, e). Superposition maintained |
| Cost × data type size (Axiom 4 + Axiom 2 proposition) | Single mass algorithm. Data type determines functional form |
| Lepton cost +2 / quark cost +3 | Quark/lepton mass ratio. m_b/m_τ = 7/3 |
| Koide ratio 2/3 = brackets(2) / CAS steps(3) | Koide formula (m_e+m_μ+m_τ)/(√m_e+√m_μ+√m_τ)² = 2/3 |
| π = CAS 3-axis orthogonal → sphere 4πℓ² | π is not an external constant. Consequence of 3-axis geometry |
| Mixing angles / Mass | |
| Axiom term | Physics correspondence |
| Shift distance $\ell/N$ (N=30) | $\sin^2\theta_W$ (Weinberg angle) |
| CAS step 1-2 shift distance $\ell/N$ | $\theta_C$ (Cabibbo angle) |
| Swap-index shift distance $\ell/N$ | $\theta_{12}, \theta_{23}, \theta_{13}$ (PMNS) |
| 3-generation equal spacing $\ell/N = 2/9$ | Koide angle |
| Cross-path asymmetric shift | $\delta_{CKM}, \delta_{PMNS}$ (CP phase) |
| Cosmology / States | |
| Axiom term | Physics correspondence |
| RLU HOT (active access) | Visible matter (5%) |
| RLU WARM (decaying) | Dark matter (27%) |
| RLU COLD (below threshold, recovery target) | Dark energy (68%, Λ) |
| CAS independent combination count 57 | $\alpha^{57} = \Lambda l_p^2$ (cosmological constant) |
| 7-bit total combination count 128 | Valid state count ($2^7$) |
| CAS access path count 30 | Interaction DOF (Axiom 9) |
| Complete description DOF 9 = 7+2 | Minimum independent variables for complete system description |
| δ=0 (no firing) | Quantum vacuum |
| δ=1 (firing) | Universe exists. Equality sign holds |
| Compare true → Swap | Wavefunction collapse |
| Compare false → superposition maintained | No decoherence |
| ℓ=1 dense, N² accumulated | Serialization freezing (ℓ→1, read contention maximum) |
| Empty entity distortion (data type fixed) | Virtual particles / vacuum polarization |
| Simultaneous = orthogonal | Entanglement. Distance-independent |
| Duck typing consciousness (Axiom 15 proposition) | Consciousness = δ's behavior list. Unmeasurable domain |
| Axiom side | Physics side |
|---|---|
| 1 operator (CAS) | 4 forces + 12 mediator particles + 3 coupling constants |
| 3 cost generation points (R, C, S each +1) | Hundreds of Lagrangian terms |
| 0 free parameters (all derived from 7) | 19–26 free parameters (measured and inserted) |
| 8 bits (d-ring 2 nibbles) | Infinite DOF of quantum fields + infinite series of feedback corrections |
| 128 states ($2^7$) | Infinite-dimensional Hilbert space |
| 2 sequential orderings (R→C→S, δ→observer) | Causality, 2nd law of thermodynamics, CPT theorem, Lorentz invariance each as separate axioms |
| Simultaneous = orthogonal (automatic from Axiom 1) | 60 years of non-locality debate to explain entanglement |
| No singularity (ℓ=1 discrete, automatic) | 40 years of string theory, 30 years of loop quantum gravity to remove singularities |
| 0 corrections | Infinite series of feedback corrections (divergent, asymptotic) |
| Total cost 13 (closed system) | Total energy conservation (1st law of thermodynamics) |
The core of the structural difference in the table above: The axiom side operates by its own structure alone without external variables. From the single number 7, all of 4 (domain), 3 (CAS), 1 (δ), 8 (ring), 9 (DOF), 21 (comparison pairs), 35 (3-step combinations), 57 (combination sum), 128 (state count), 30 (path count) emerge. The physics side, to describe the same phenomena, injects 19+ measured values from outside, constructs separate Lagrangians for each force, corrects with infinite series, and shaves off divergences with renormalization. What an axiom says in 1 line, physics says in thousands of papers. This is not a difference in technical skill but a difference in starting point. Starting from continuous brings infinity; starting from discrete brings finitude. The Banya Framework starts from discrete.
The logical convergence of axioms is the design of a minimum-cost circuit, and the values discovered on the physics side are measurements confirming that nature operates as a minimum-action circuit. Both arrive at the same numbers. The coincidence of design (axioms) and measurement (physics) is the strongest evidence that the design is correct. This is why 1000+ physical constant items emerge from the axioms — design values of a minimum-cost circuit and measured values of the principle of least action are different expressions of the same thing.
The inventor (Han Hyukjin)'s achievement is interpreting nature through the logic circuit of 15 Banya Framework axioms. No longer merely measuring from the observer's standpoint, but predicting in advance from the circuit's design values. Physics proceeded for 200 years via observation→measurement→formula→prediction (induction). The Banya Framework proceeds via design→derivation→prediction→measurement for confirmation (deduction). The direction has been reversed. From observer to architect.