Ontic Relational Theory · Book I
THE GRAMMAR OF REALITY
The Onto — Primitive Relational UnitS = (O, E, F)
ONE ONTO · THREE INTERNAL CHANNELS
Onto State Selector
Channel Reading Window
Foundational Statement
The Onto is the smallest ordered relational state.
Choose one valid Octet tri-bit. The three-dimensional form reveals its ordered channels: Origin, Essence, and Form. No particle, metric, or physical measurement is assumed at this level.
Choose one valid Octet tri-bit. The three-dimensional form reveals its ordered channels: Origin, Essence, and Form. No particle, metric, or physical measurement is assumed at this level.
3D Tri-Bit Octet Visualizer Window
Drag canvas to rotate geometry
Active State S
101
Mirror M(S)
010
Hamming dH
3 Bits
Weight w(S)
2 Bits
Class Transition
Reality ↔ Phantom
State Selector Window
Path Trail Console Window
Click canvas or nodes to record path...
8×8 Transition Matrix Heatmap Window
Valid Links: 0 / 64
Click any matrix cell to test transition topology...
OPS Laws Definition Window
1. Completenessexecutable
|Ω₈| = 2³ = 8; complete tri-bit enumeration.
|Ω₈| = 2³ = 8; complete tri-bit enumeration.
2. Projectionexecutable
Reality = {101, 110, 111}.
Reality = {101, 110, 111}.
3. Silenceexecutable
Silence = {000}.
Silence = {000}.
4. Thresholdexecutable
Threshold = {100}.
Threshold = {100}.
5. Phantomexecutable
Phantom = {001, 010, 011}.
Phantom = {001, 010, 011}.
6. Essence Recordschematic
ME(n+1) = ME(n) + f(Sn).
ME(n+1) = ME(n) + f(Sn).
7. Allowancechecker
Reality→Reality/Silence; Silence→Any; Threshold→Silence/Reality; Phantom→Phantom/Silence.
Reality→Reality/Silence; Silence→Any; Threshold→Silence/Reality; Phantom→Phantom/Silence.
Transition Control Input Window
Transition Diagnostic Window
Awaiting input transition check...
Dihedral Word Analyzer & CSL Screen Window
Tri-Bit Constraint
Awaiting word sequence...
Mirror Orbit Configuration Window
Orbit Trajectory Display Window
Awaiting orbit parameters...
Generator Seed Window
Saturation Log Window
Awaiting closure seed input...
Canonical Ontic Closure Register
Canonical basis ready
Click “Generate Canonical Closure Basis” to compute canonical structure.
Closure Basis Inspector
Select any row in the Canonical Ontic Closure Register below to inspect its record, reciprocal partner, weight, delta vector, and Reciprocal legality profile.
| # | Canonical Element Type | Record Representation (r) | Reciprocal Representative (r†) | Weight w(r) | Delta Vector Δ(r) | Reciprocal Legality Profile |
|---|---|---|---|---|---|---|
| Click "Enforce Laws & Saturate Ledger" to execute saturation. | ||||||
Essence Record ConstructionExecutable
Hn+1 = Hn ∥ Sn
Mn+1 = Mn ⊕ Sn
Essence Diagnostic Window
Awaiting an ordered Onto history...
Augmented-State Generator
Onto domain
8
Signature domain
8
Maximum pairs
64
Generation and Saturation WindowReady
The generator operates on X=(S,M), applies Law 7, and updates M′=M⊕S.
Reachable Augmented States
| # | S | Class | M | X=(S,M) | First generation |
|---|---|---|---|---|---|
| No generation executed. | |||||
Formal Boundary
H preserves the exact ordered history and may grow. M is a finite tri-bit signature and may recur. Saturation of Ω₈×Ω₈ establishes closure only for this finite signature construction under Law 7. It does not replace the separate Canonical Ontic Closure Basis.
Canonical Word GeneratorFinite Search
Alphabet
Ω₈
Seeds
8
Equivalence
DL + M
Generation StatusReady
Choose a maximum length and execute the bounded generator.
Counts by Word Length
| L | Linear Law-7 words | Cyclic legal words | Primitive cyclic words | Canonical classes | Status |
|---|---|---|---|---|---|
| No generation executed. | |||||
Canonical Representatives at Selected Length0 classes
| # | Canonical word | L | p | k | Sop | w | Class signature | Orbit |
|---|---|---|---|---|---|---|---|---|
| No representatives generated. | ||||||||
Executed Formal Rules
Seeds: every state in Ω₈. Extension: append only through Law 7. Cyclic legality: final-to-first must be allowed. Primitive: exact repetitions are excluded. Equivalence: rotation, reversal, mirror, and mirror-reversal. Canonical selection: lexicographically least representation. Boundary: Lmax is a computational limit, not global ontic saturation.