The 144-Lattice Partition Theorem: How the CTF Framework Found a New Result in Number Theory, and What It Means Inside the Framework

Description: Investigation of the CTF base frequency f0=10373/72 f_0 = 10373/72 f0=10373/72 Hz under the mod-144 power sum framework led to the discovery of a partition theorem for prime power sums. The standalone mathematical result — proven without reference to the CTF Framework — is published separately (Gurwell, 2026b). This paper documents the discovery context and interprets the theorem’s structure within the CTF Framework.

The theorem states that S(p,k)=∑i=1p−1ikmod  144 S(p,k) = \sum_{i=1}^{p-1} i^k \mod 144 S(p,k)=∑i=1p−1ikmod144 is independent of $k$ for all odd $k\ge 3$ if and only if $p\mathrm{mod}144$ belongs to one of 32 residue classes, with lock values in {0, 1, 9, 64, 73, 81}. When the CTF prime set {11, 17, 19, 23, 41, 53} is used as the exponent family, the same 6-value partition emerges.

Within the CTF Framework the six lock values are not arbitrary: 0 corresponds to the static lattice (72 and 144 both lock here), 9 is the spatial generator ($9\times 8=72$, $9\times 12=108$, $9\times 16=144$), 64 = 26 2^6 26 is the pure kinetic power, 81 = 34 3^4 34 is its spatial complement, and 73 = 72 + 1 is the CTF denominator plus unity. The sum $64+9=73$ is exact.

The temporal numerator 10373 = 11 × 23 × 41, tested against its own constituent primes, produces residues 76, 76, 4 with difference 76 − 4 = 72. This self-referential structure is documented as a CTF-specific finding building on the partition theorem, including the 2² (Key of 4) and step difference in the temporal numerator self-residue profile.

The partition theorem provides a formal mathematical basis for the CTF Framework’s spatial/temporal distinction: universal lock classes map to static spatial constants while splitting classes correspond to dynamic temporal elements. All computations are reproducible with the appendix Python code using modular exponentiation.