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TIDAR: Correct by Construction
tidar-correct-by-construction
1. **Triads are atomic**: Cannot create partial triads
SKILL.md
Full skill instructions
TIDAR: Correct by Construction
Triadic Interleaving Dispatch with Agents for Reading/writing — where invalid states are unrepresentable
Core Insight
Correct by construction means: if it compiles/type-checks, GF(3) is conserved.
TIDAR Tree (depth 3):
Root (0)
┌──────────────┼──────────────┐
-1 │ 0 │ +1
┌───┼───┐ ┌───┼───┐ ┌───┼───┐
-1 0 +1 -1 0 +1 -1 0 +1
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
27 leaves (3³), each balanced triad sums to 0
Type-Level Invariants
# GF(3) is enforced at construction — no runtime checks needed
triad = Triad.build(minus, middle, plus) # Only way to create
# Compile-time: triad.sum() == 0 is GUARANTEED
The 40-Agent Structure
| Level | Agents | Role |
|---|---|---|
| 0 | 1 | Root coordinator (ERGODIC) |
| 1 | 3 | Branch managers (-1, 0, +1) |
| 2 | 9 | Sub-coordinators (3×3) |
| 3 | 27 | Leaf workers (3³) |
| Total | 40 | GF(3) conserved at each level |
Correct-by-Construction Rules
- Triads are atomic: Cannot create partial triads
- Balance is intrinsic: Triad = (MINUS, MIDDLE, PLUS), sum = 0
- Tree is complete: Every node has exactly 0 or 3 children
- Pre-hooks are mandatory: Read before write, encoded in types
- Middle-path collapse: Only MIDDLE nodes emit final results
Usage
from tidar_cbc import TIDARTree, Triad, Trit
# Build tree — only balanced constructions allowed
tree = TIDARTree.build_depth_3(seed=1069)
# Cannot create unbalanced:
# Triad(Trit.PLUS, Trit.PLUS, Trit.PLUS) # TYPE ERROR
# Dispatch with pre-hooks
async for result in tree.dispatch_with_prehooks(task):
# Results only from MIDDLE path (proven by types)
assert result.source.trit == Trit.MIDDLE
Files
tidar_cbc.py— Core correct-by-construction implementationtidar_cbc_test.py— Property-based tests (Hypothesis)
Key Properties
| Property | How Enforced |
|---|---|
| GF(3) conservation | Constructor only accepts balanced triads |
| 40-agent count | Tree depth fixed at 3, branching factor 3 |
| Pre-hook ordering | Read/Write phases in state machine types |
| Middle-path collapse | Only MiddleAgent has emit() method |
trit: 0 (ERGODIC)
TIDAR is a coordinator skill — it balances, never sources or sinks.
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