specs/ternary: trits + radix_economy -- the logic of the course "The ternary machine" (t27.ai) #8978

Owner, 2026-10-11: build the next t27.ai course and make it engaging with visualisations. The course "The ternary machine" (gHashTag/trinity, ternary-computing) gets an interactive widget in every lesson. Each widget's numbers must come from a t27 spec compiled to wasm, as with line_bounce, eye_isi and secded (#8931).

Two specs:

• specs/ternary/trits.t27
  • balanced-ternary digits, read with the offset 111...1 (base 3), so no signed division is needed;
  • negation by flipping trits, rounding by cutting trits;
  • Kleene logic: NOT, MIN, MAX, CONSENSUS, ANY, plus the half adder;
  • full adder, ripple add;
  • product by one trit without a multiplier, long multiplication, MAC step;
  • a trit in two bits, five trits in a byte, bit use, bits for k trits;
  • three-way compare at the first differing trit, two-answer and three-answer question counts;
  • a ternary activation.
• specs/ternary/radix_economy.t27
  • digits per base, cost = b * digits, b / ln b (ln as a series), the cheapest base.

Done when both specs typecheck and every test passes with no vacuous pass, negative controls are caught, and the seals are saved.

User Scenarios

• Given the specs/ternary directory exists, when the spec specs/ternary/trits.t27 is compiled with t27c, then it typechecks and all its tests pass with no vacuous pass.
• Given the specs/ternary directory exists, when the spec specs/ternary/radix_economy.t27 is compiled with t27c, then it typechecks and all its tests pass with no vacuous pass.

Requirements

• FR-001: specs/ternary/trits.t27 MUST define balanced-ternary digits read with offset 111...1 (base 3) avoiding signed division.
• FR-002: specs/ternary/trits.t27 MUST implement negation by flipping trits and rounding by cutting trits.
• FR-003: specs/ternary/trits.t27 MUST implement Kleene logic: NOT, MIN, MAX, CONSENSUS, ANY, and half adder.
• FR-004: specs/ternary/trits.t27 MUST implement full adder, ripple add.
• FR-005: specs/ternary/trits.t27 MUST implement product by one trit without a multiplier, long multiplication, MAC step.
• FR-006: specs/ternary/trits.t27 MUST implement trit encoding: a trit in two bits, five trits in a byte, bit use, bits for k trits.
• FR-007: specs/ternary/trits.t27 MUST implement three-way compare at first differing trit, two-answer and three-answer question counts.
• FR-008: specs/ternary/trits.t27 MUST implement a ternary activation function.
• FR-009: specs/ternary/radix_economy.t27 MUST compute digits per base, cost = b * digits, b / ln b (ln as a series), and identify the cheapest base.
• FR-010: Both specs MUST compile to WASM without errors for use in interactive widgets.

Success Criteria

• t27c specs/ternary/trits.t27 exits with exit 0 and produces a WASM module.
• t27c specs/ternary/radix_economy.t27 exits with exit 0 and produces a WASM module.
• All tests in specs/ternary/trits.t27 pass (negative controls caught, no vacuous pass).
• All tests in specs/ternary/radix_economy.t27 pass (negative controls caught, no vacuous pass).
• Seals are saved for both specs.

Boundary

• specs/ternary/trits.t27
• specs/ternary/radix_economy.t27