Ontic Relational Theory · Book I
THE GRAMMAR OF REALITY
This simulator executes the formal definitions and finite constructions stated in Book I, Research Edition 1.1. It contains no mass assignment, physical mapping, continuum geometry, or Book II model.
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.
Ontic Octet Three-Cube
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...
OPS 8×8 Transition Topology
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.
OPS Law 7 Input
OPS Allowance Diagnostic
Awaiting input transition check...
Word Structure and Local Legality
Tri-Bit Constraint
Awaiting word sequence...
Finite Operation Orbit
Orbit Trajectory Display Window
Choose a state, operation, and iteration count.
Operation Status
Mirror M is the defined reciprocal complement. Reversal and channel-cycle operations are finite structural analysis tools. Their orbits demonstrate recurrence and fixed points; they are not declared to be the canonical OPS evolution operator.
Generator Seed Window
Ready
Finite Stabilization Log
Awaiting closure seed input...
Canonical Ontic Closure Basis
Ready
|R₃| = 8×7×7 = 392 → 196 reciprocal classes
B = 196 + 7 = 203 · 𝒮ORT = 2406
AA profile
—
AF profile
—
FF profile
—
Reciprocal total
—
Ready
No records generated yet.
Construct the finite basis from adjacent-distinct three-state records and seven nonzero direction masks.
Basis Lens
Select a row to inspect its representative, reciprocal or paired form, weight, and delta.
| # | Basis Type | Representative | Reciprocal / Paired Form | Weight w(r) | Delta Vector Δ(r) | Law 7 Profile |
|---|---|---|---|---|---|---|
| No basis constructed. | ||||||
Essence Record TraceSchematic
ME(n+1) = ME(n) + f(Sn)
Ready
Essence Diagnostic Window
Awaiting an ordered Onto history...
Formal Boundary
The simulator displays the ordered Essence-bit trace carried by the selected Onto history. Because Book I leaves f(Sn) unspecified, it does not invent a numerical memory update or an augmented state law.
Bounded Legal Word GeneratorFinite Search
Ready
Alphabet
Ω₈
Seeds
8
Generation StatusReady
Choose a maximum length and execute the bounded generator.
Generated words will stream here.
Counts by Word Length
| L | Linear Law-7 words | Cyclic legal words | Primitive cyclic words | Status |
|---|---|---|---|---|
| No generation executed. | ||||
Generated Words at Selected Length0 words
| # | Word | L | p | k | Sop | w | Class signature | M(W) | WR |
|---|---|---|---|---|---|---|---|---|---|
| No words generated. | |||||||||
Executed Formal Rules
Seeds: every state in Ω₈. Extension: append only through OPS Law 7. Cyclic legality: final-to-first must also be allowed. Primitive: the least exact period equals the full length. Derived invariants: L, p, k, rotational symmetry Sop, weight, class signature, mirror, and reversal. Boundary: Lmax is a computational limit, not a proof of global word closure.