Vol 2, Section 58 · P-CENT-1 through P-CENT-6

Carbon is the lattice's dual {2,3} node — the backbone of life

C = 12 = 2²×3. The only element encoding both binary and ternary dimensions in its atomic mass. Bond enthalpies follow the Tau-strand accumulation law.

Carbon mass
12 = 2²×3
dual {2,3} lattice
·
C≡C bond
839 kJ/mol
triple Tau-strand
·
Propositions
6
P-CENT-1 to P-CENT-6
The Accumulation Law

Each additional bond order adds one Tau-strand at decreasing efficiency

The Tau-strand accumulation law: bond enthalpy increases sub-linearly with bond order because each additional strand must fit within the compressed Tau-field of the previous. The accumulation factor approaches 2/3 — the binary-ternary ratio.

P-CENT-2 — Tau-strand accumulation (C-C family)
C–C (1 strand): 347 kJ/mol ratio: 1.000
C=C (2 strands): 614 kJ/mol increment: +267 ratio: 1.770
C≡C (3 strands): 839 kJ/mol increment: +225 ratio: 2.418
Increment ratio → 2/3 at infinite bond order (asymptote)
Key Propositions

Diamond vs graphite: the two register topologies of carbon

P-CENT-1

C = 2²×3 is the lowest-mass element with both binary and ternary dimensions. Si = 2²×7 has a boundary prime instead — rigid lattice, no flexible polymers. Carbon is the necessary scaffold for biological Tau-registers.

P-CENT-6

Diamond: all sp³, {2,3} tetrahedral closure — maximum Tau-density, hardest natural material. Graphite: sp², {3} trigonal + 1 delocalised Tau-mode — conductor, lubricant. Allotrope = register topology choice.

The Universal Force of Time — Stephen Daubney — thedaubneyfoundation@gmail.com — Academic Papers