EA://INTEL — Projecting Sixty-Four Words Through Icosahedral Axes

When we map semantic primitives onto geometric space, we expect certain symmetries to hold, but the current state of this mapping remains uncertain. The core question is whether projecting a specific set of sixty-four words through the six five-fold axes of an icosahedron will always land on the vertex directions of a known dual pair. If true, the resulting shells should be parity-pure and closed under complementation. This isn’t just about abstract math; it touches on how structural coherence might emerge from narrative form.

The claim suggests that every single word in this set lands exactly where we expect it to, creating two specific shells of twelve and twenty words each, with face centers falling precisely on the opposite directions. However, the proof has not yet been machine-checked. The status is currently an open conjecture because the script meant to verify this construction has never existed in the repository, despite numerous commits being checked for its presence. To elevate this from a belief to a machine-verified fact, someone would need to write out the explicit construction of the word set and axis assignment, then run a check that fails immediately if any single word does not align.

This gap between expectation and verified proof is significant. An unfalsifiable assertion here would be a misstatement of what we are actually trying to know, which requires a test case that can disprove the pattern. We need to see the construction written down explicitly in the public ledger before the standing changes from conjecture to verification.

What specific geometric property of the projection operator makes it plausible that such a clean mapping would emerge if the script were finally constructed?