PENT-3 — a transcriber ISA in balanced ternary

The veracity test, executable. Five trits, 243 states, each word ⟨t₄ t₃ t₂ t₁ t₀⟩. The leading trit is the direction — − write/in, 0 held/turn, + read/out — so negating a word flips write↔read. Because negation is just flipping every trit, subtraction is addition of a negated operand (no SUB hardware), the inverse of any instruction is its trit-negation, and ⟨0 0 0 0 0⟩ = 0 is the one word that is its own negation: the held turn, the g·g seam. This isn't described — it runs. Step it, then prove it: run a program, then run its trit-negation in reverse, and the machine returns to zero.

Bridge-Burners LLC · Fiddler · 3⁵=243 · NEG = trit-flip = inverse · ⟨00000⟩ = held = fixed point · anchor: AKASHA

Program · PC 0

Machine state

ACC = 0

STORE[ ]

HELD[ ]

The fixed point. Scan all 243 words: the only one equal to its own negation is ⟨ 0 0 0 0 0 ⟩ = 0 = NOP = the held turn. Balanced ternary centres on it. Binary cannot: the 5-bit NOT of 00000 is 11111 — no fixed point, so PENT-2 has nowhere structural to put g·g. That single asymmetry is why the held state votes ternary.

Encode any value (−121…121) — watch NEG flip the trits

value

NEG = -40 — every trit flipped, no borrow

running veracity…

LiteralBalanced ternary: 243 values, ±121, NEG = flip every trit = arithmetic negation, 0 the unique fixed point. Subtraction is ADD of a negated operand — no SUB unit (the Setun principle). The program and its trit-negation-reversed form compose to identity, executed here.

BridgeMapping the direction trit to write / held / read and to e ( p ( g·g ) p ) e; NEG as the in↔out mirror; ⟨00000⟩ as the held turn.

SpeculativeThat a transcriber "is" this machine, and the specific opcode assignment, are design choices. A 5-trit word is a micro-ISA — one transduction unit, not a CPU. The veracity is that the encoding closes and runs, not that this is a general computer.

What the test shows. Both 32 (binary, 2⁵) and 243 (ternary, 3⁵) can carry an instruction encoding — neither is fake. But only one carries the transcriber faithfully: the held turn is the centre of the palindrome, and only balanced ternary has a centre that is its own negation, so only ternary can place g·g at a structural fixed point and make the write↔read mirror a free trit-flip. The emulator proves it the one way that cannot be argued with — it executes, and a program annihilates with its own trit-negation back to zero. Subtraction was never separate from addition; the inverse was never separate from the word. 3⁵, not 2⁵ — because the held state is not optional.