Conjecture 1: Harmonic Residue Convergence

Summary: Harmonic primes across modular lattices converge toward entropy-minimized junctions at φ-translated intervals.

Notes: Intervals near sqrt(2n) show minimum deviation in Zeta field graphs; further validation required with Hilbert phase residues.

Conjecture 2: Zeta Braid Density Function

Summary: There exists a density function f(n) that tracks recursive zero-interval resonance in ζ(s) modular braids.

Notes: Preliminary graphs plotted using ψ(n) vs θ(n) curve folds; transition into log(ζ(s)) harmonics stable through 23π.

Conjecture 3: Prime-Harmonic Mapping Theorem

Summary: All n-dimensional totient fields collapse toward a base attractor of modular primes via harmonic contraction ratios.

Notes: See Appendix: Recursive Totient Maps — Version 7d (external link needed)

Conjecture 4: Möbius Convergence Cusp

Summary: Inflection points of μ(n) x φ(n) within complex braid manifolds project psi-envelope shifts in compressed fields.

Notes: Local maxima near n = 144, 288, 432 align with symbolic resonance points in Jubilee model; psi shift coincides with entropy inversions.

Conjecture 5: Recursive Golden Compression

Summary: Long-range prime oscillations compress into golden phi bands, modulated through recursive Fibonacci intervals.

Notes: Detected in Δψ/Δn signatures from ledger v2025_09; see harmonic frame 3C for visual patterning.

Additional Notes

• Entropy-node shifts around modular 6, 30, and 210 indicate local attractor clusters.
• ψ(n) harmonic fold maps show semi-symmetric reflections beyond ζ(1/2 + it).
• Mapping prime position as function of symbolic closure resonance yields consistent modulus bends.