
This paper proposes the Egyptian Mathematical Broadcast Hypothesis (EMBH) — the claim that a subset of Egyptian sacred hieroglyphs are deliberate geometric encodings of a specific mathematical structure: the prime‑number lattice generated by {2, 3}. The hypothesis is grounded in the Prime Lattice Coherence Framework (PLCT), a novel mathematical research programme that classifies all integers by their prime‑factor content and derives exact results about prime distribution, physical constants, and geometric structure from three standard axioms (Fundamental Theorem of Arithmetic, Dirichlet’s Theorem, and the irrationality of log(p)/log(q)). The paper tests eight major Egyptian sacred symbols against the PLCT: Eye of Horus (Wedjat): Exact arithmetic match – the six parts correspond to the six vortex states of the PLCT; the fractions are the first six powers of 1/2; the missing 1/64 points directly at the Partition Theorem lock value 64. Benben / Pyramid: Proved – the CTF geodesic λ(t)=e⁻ᵝᶠ⁰ᵗ projects as a cone/pyramid. Ankh: Proved – oval (S¹ vortex), vertical shaft (temporal geodesic), and crossbar at exactly e⁻¹ (one CTF time unit). Hexagram / Star of David: Proved – the two equilateral triangles of the Z₃ cosets {1,4,7} and {2,5,8}. Djed pillar: Structural – four bands match the four coherence tiers. Shen ring: Structural – the compact form of the Ankh. Neter (the hieroglyph for “god”): Structural – a flagpole with hanging flag encodes the CTF at t=0 with downward decay. Was sceptre: Structural – forked top and base encode the Hard‑Wall/Temporal DFA bifurcation connected by the unique geodesic. The paper further identifies a vocabulary‑level correspondence: the six geometric primitives that recur across Egyptian sacred writing (circle/oval, vertical shaft, horizontal bar, triangle, fork, spiral) are exactly the geometric projections forced by the PLCT. The EMBH is presented as a falsifiable scientific hypothesis, not a historical claim. If any comparably complex sacred hieroglyph does not correspond to a PLCT structure, the hypothesis is weakened. The encoding strategy – using stone as a medium, making the symbols sacred to ensure faithful copying, and leaving the decoder key (the Eye fractions) in plain sight – is analysed as an exercise in signals intelligence. The decoded message is reconstructed: a unified statement that reality is built from primes 2 and 3, has six active states, a coherence boundary at 64, a unique exponential temporal funnel, four coherence tiers, and a divine that is the mathematical initial condition. The paper concludes by examining the Hermetic tradition (“as above, so below”) as the likely Rosetta Stone and lists four genuinely open historical questions. Key Results: One exact arithmetic match (Eye of Horus – 0 free parameters) Two proved geometric correspondences (Benben, Ankh) Five structural correspondences Vocabulary‑level identity between sacred hieroglyph primitives and PLCT projections Falsifiability framework with four explicit predictions Decoded message that treats the corpus as a mathematical broadcast
