RNAcube · Completeness Proof: 64/64
Tap any cell to inspect its coordinate signature and resolving step.
UUU (CA 0) bottom-left · GGG (CA 63) top-right
Codon Detail
Tap any cell to inspect its full coordinate signature and the step at which it becomes uniquely identified.
Reading the proof (Appendix I, v5): Three-step cascade. Step 1: level, d1, d3 resolve 40 of 64. Step 2: adding flow Phi resolves 20 more, leaving 2 pairs. Step 3: UCA/ACU and CAG/GAC are identical in level, d1, d3, and Phi; separated only by the sign of divergence (sd1, sd3). Outlined in red. Parity is a function of Phi and adds nothing once Phi is present.
Property Definitions
All properties derived from CA = 4×pos₁ + 16×pos₂ + 1×pos₃, UCAG = 0,1,2,3, binary U=00 C=10 A=01 G=11:
Domain: Foundation (CA 0-10), Control (CA 11-31), Chemistry (CA 32-52), Adaptation (CA 53-63).
Level (0-3): val(pos2). Partitions 64 codons into four blocks of 16. Step 1 anchor.
d1 (0-3): |val(pos1) - val(pos2)|. Step 1 anchor.
d3 (0-3): |val(pos3) - val(pos2)|. Step 1 anchor.
Flow Φ (-6 to +6, even): 6 - 2*(one-bits). Resolves 20 more at Step 2. Parity is a function of Φ and adds nothing once Φ is present.
sd1 / sd3 (sign): val(pos1) - val(pos2) and val(pos3) - val(pos2), signed. The four Step-3 codons -- UCA (CA 18), ACU (CA 24), CAG (CA 39), GAC (CA 45) -- share level, d1, d3, and Φ; differ only in sign pattern (-1,+1) vs (+1,-1). The ordered value scale does the irreducible completing work.