This document is the Terminology portion of the Banya Framework Comprehensive Report.
| Axiom Term | Definition | Source |
|---|---|---|
| d-ring | 8-bit full ring buffer (bit 0–7). Nibble 0 (domain 4 bits) + nibble 1 (operator 4 bits). Physical structure seen from the bitwise-operator perspective. The vessel of all axiom structures | Axiom 15 Proposition |
| CAS-ring | Cyclic structure of CAS 3 bits (R, C, S). CAS internals seen from the bitwise-operator perspective. 3-axis orthogonality gives structure, lock (Axiom 5) enforces order, and order defines FSM state transitions. Operates inside Workbench (√3 norm) | Axiom 2, 5, 14 |
| CAS FSM | State transitions of the CAS-ring described from the bitwise-operator perspective. 000→001→011→111→000. Lock enforces order | Axiom 5, 14 |
| δ (fire bit) | bit 7. Equality sign. 1=valid, 0=invalid. Global flag outside FSM. Private key | Axiom 15 |
| observer (entry point) | bit 0. Filter. Pipeline start. Generates will through interaction with δ. Signature | Axiom 10, 15 |
| CAS | The sole operator. Read->Compare->Swap. 3 stages | Axiom 2 |
| data type | Size unit CAS uses when reading a target. 11 numbers derived from input {3} via 4 operations (+, T(N)+1, 2^N, ‖√3‖) (Axiom 2 Proposition). CAS picks the matching data type according to the target's complexity | Axiom 2 Proposition |
| Workbench | Workspace created by the norm of CAS 3-axis orthogonality (‖CAS‖ = √3). Where CAS picks a data type and interacts with 4 domains. Independent computation unit | Axiom 2 Proposition |
| CAS 3-axis orthogonality | Each stage R, C, S is an independent 1 bit (001, 010, 100). They do not invade each other's DOF. At 111, all 3 axes simultaneously grip one spot to create a ball | Axiom 2 Proposition |
| juim | The ball that CAS Swap (111) creates in DATA. 3-axis orthogonality → isotropic pressure → spherical. The unit of the discrete — the shape of one minimal change that cannot be split further. Banya Frame proper noun | Axiom 2 Proposition |
| juida | The act of CAS creating a juim in DATA. 1 cycle = 1 juim = 1 cost | Axiom 2 Proposition |
| CAS stage index | R=1, C=2, S=3. Maximum 3. No 4th | Axiom 2 |
| stage gap (Δ_stage) | Difference in CAS stage index between two entities. Maximum 2 | Axiom 13 Proposition |
| nibble 0 (domain) | bit 0-3. observer, superposition, time, space. Front half of d-ring | Axiom 1, 15 Proposition |
| nibble 1 (operator) | bit 4-7. R_LOCK, C_LOCK, S_LOCK, δ. Back half of d-ring. CAS FSM operates here | Axiom 5, 15 Proposition |
| dimension | Spatial 3 dimensions = CAS 3-axis orthogonality (Axiom 2 Proposition). No 4th. CAS cycle: forward circulation + simultaneous reset | Axiom 2, 12 Proposition |
| Swap | CAS 3rd stage. Crosses +. Cost +1 | Axiom 4 |
| accumulated lock | Sequential ignition by logical dependency of CAS FSM 001->011->111. CAS 3-axis orthogonality (Axiom 2 Proposition); ignition order is sequential | Axiom 2, 5, 14 Proposition |
| ring seam | Connection point of d-ring's δ (bit 7)->observer (bit 0). Entry point of the equality sign. Ownership | Axiom 10, 15 Proposition |
| pipeline | trigger->filter->update->render->screen. The flow of one d-ring fire | Axiom 15 Proposition |
| fire | δ becoming 1. The start of one d-ring cycle. Called "fire," not "cycle" | Axiom 15 |
| simultaneous | Only 3 kinds: multiple entities in parallel, 4-domain orthogonality, 2-nibble orthogonality | Axiom 1, 2, 12 |
| sequential | Only 2 kinds: R->C->S (CAS FSM dependency), δ->observer (d-ring seam) | Axiom 2, 10 |
| cost | If + is crossed, cost > 0. If not crossed, 0. +1 per each R, C, S transition | Axiom 2 Proposition, 4 |
| attenuation is continuous, threshold is discrete | Ball existence (DATA) = discrete, gripping force (RLU) = continuous attenuation, cost (contraction region) = spatial distribution. 3 attributes in different layers. Observer sees the cost (contraction) presented by orthogonal superposition index (RLU) | Axiom 2, 12 Proposition |
| recovery of juim | When RLU releases a juim, space is returned. Next juim possible in returned space. Must recover to circulate | Axiom 12 Proposition |
| entity | Shadow created when δ passes through the observer filter. Each entity is both a unique identifier and an address itself. Basic unit of ECS | Axiom 11, 12 |
| ℓ (ell) | Distance between two entities. Notated as ℓ to avoid confusion with δ (fire bit) | Axiom 11 Proposition |
| Banya equation | δ² = (time + space)² + (observer + superposition)². 4-axis norm. Classical bracket (DATA) and quantum bracket (OPERATOR) are orthogonal | Axiom 1 |
| DATA (classical bracket) | time + space. Discrete. Determined state rendered on screen | Axiom 1, 3 |
| OPERATOR (quantum bracket) | observer + superposition. Continuous. Undetermined region where CAS operates | Axiom 1, 3 |
| ball | Discrete unit that CAS 1 cycle (Swap) creates in DATA. No 0.5. Shape of juim. 3-axis orthogonality → isotropic → spherical | Axiom 2 Proposition |
| atomicity | CAS R→C→S 3 stages are inseparable. If interrupted midway, it is not CAS | Axiom 2 Proposition |
| irreversibility | CAS operations have direction. R→C→S cannot be reversed. No refund. time (DATA) is a reversible resource, but CAS (OPERATOR) is irreversible | Axiom 2 Proposition |
| RLU | Lifetime management of juim. HOT→WARM→COLD→recovery. Attenuation is continuous, threshold is discrete. Open lifetime | Axiom 6, 12 |
| HOT / WARM / COLD | 3 RLU states. HOT: right after write, frequently accessed. WARM: attenuating. COLD: below threshold, recovery target | Axiom 6, 12 |
| polling | Mechanism by which d-ring checks whether δ fires at every tick of system time. Always runs regardless of whether change occurs | Axiom 8 |
| global-local loop | δ (global)→observer (local)→CAS→result→δ feedback. Recursive cyclic structure. The only path for δ to access itself | Axiom 10 |
| multiple projection | Structure where a single δ is independently filtered through multiple observers to generate multiple entities | Axiom 11 |
| contraction region | Region where space around a juim has decreased because Swap consumed DATA (space). Data type size is fixed → serialization occurs | Axiom 11 Proposition |
| ECS | Entity (shadow)-Component (DATA)-System (CAS). Execution model where each observer-CAS pair processes independently | Axiom 12 |
| superposition | Multiplicity of the quantum bracket (OPERATOR). Multiple states exist simultaneously as undetermined. Target of indexing (Axiom 13) | Axiom 11, 13 |
| collapse | When CAS Compare is true, superposition transitions to a single determined state. Continuous→discrete. OPERATOR→DATA | Axiom 7 |
| equality sign | If δ=1, the entire right-hand side (7 bits) is valid; if δ=0, invalid. Declaration where the left-hand side validates the right-hand side. Operates at the ring seam | Axiom 15 Proposition |
| re-entry (move) | A juim entering as input to the next CAS cycle. Structure where change begets change. Recursion of the Banya equation | Axiom 12 Proposition |
| system time | CAS 1 tick. Actual timing unit of δ fire. Clock outside d-ring | Axiom 8, 15 |
| domain time | t_dom = log(T_sys). Time measured inside the screen (DATA). Logarithmic compression | Axiom 8 Proposition |
| indexing cost | 0. Index has no order, so lookup is O(1) constant. No order = no cost | Axiom 13, Axiom 4 prop. |
| scalar field | When a juim is placed at the origin, a directionless magnitude distribution defined at every surrounding cell: C·(1−ℓ/N)/(4πℓ²) | Axiom 11 Proposition |
| duck typing | Type defined by behavior. If δ matches the behavioral checklist of consciousness, it is called consciousness. Judged by behavior, not essence | Axiom 15 Proposition |
| complete description DOF | Structure DOF (DATA) 10 + cost DOF (OPERATOR) 6. Overlap 3 pairs (3, 4, 9). Internal movement within structure side = shift ($2^N$), between structure and cost = orthogonal via + | Axiom 9 |