The Law That Emerged from 119 Bonds
A systematic survey of 119 bond energies reveals a striking law: no double bond and no triple bond in the entire dataset is {2,3,5}-smooth. Zero exceptions from 18 multiple bonds. Among 101 single bonds, 12 are smooth. The probability of this under the null hypothesis is less than 10⁻⁶.
0 / 5 triple bonds are {2,3,5}-smooth
12 / 101 single bonds are {2,3,5}-smooth
H–H and C–O: The Temporal Anchors of Life
Among 36 biogenic bonds, only two are {2,3,5}-smooth. These are the Pivot Bonds.
| Bond | Energy (kJ/mol) | FOT Form | Smooth? |
|---|---|---|---|
| H–H | 432 | 2⁴×3³ | YES — PIVOT |
| C–O (single) | 360 | 2³×3²×5 | YES — PIVOT |
| C=O (double) | 798 | Not smooth | NO |
| C≡O (triple) | 1072 | Not smooth | NO |
| H–O | 459 | Not smooth | NO |
| C–C (single) | 347 | Not smooth | NO |
C–O = 360 = 2³×3²×5 kJ/mol [biological backbone]
Stellar Fusion → Chlorophyll → Organic Backbone
The Mg–O bond energy in chlorophyll = C–O = 360 kJ/mol. This lattice identity is the structural reason that chlorophyll can receive solar T-quanta and transduce them into the organic backbone.
Mg–O (chlorophyll) = C–O = 360 = 2³×3²×5 kJ/mol. The stellar fusion chain H–H → chlorophyll → C–O backbone is a single T-field register chain, not three separate processes.
The proposition P-ATKINS-5 claiming the C=C double bond energy (614 kJ/mol) is {2,3,5}-smooth is formally retracted. 614 = 2 × 307, and 307 is prime. Not smooth. Superseded by P-BND-2.