Monna Map Perspective Renderer

A discrete p-adic world, rendered through the Monna map, looks exactly like our smooth Euclidean world — the underdetermination theorem of UMP.010 in motion (naive direct reading: falsified, C3).

Prime p: Depth n: 5 2D grid:

Naive — direct ultrametric reading (C3: FALSIFIED by ordinary vision)

naive: size = 1/|x|_p — discrete staircase

Rendered — through the Monna map (M : Q_p → R, the interface)

rendered: size ∝ 1/(1 + M(x)) — smooth

object at p-adic x = p^k naive size (jumps by p) rendered size (smooth)

Readouts (k = exponent; x_k = p^k)

k	x_k	\|x_k\|_p	naive size	M(x_k)	rendered size

Golden-value gate (verifyMath)

Identity	Expected	Computed	Verdict

Key insight. The naive ultrametric reading predicts apparent sizes that jump by a factor of p — ordinary vision falsifies it (C3). The rendering reading sends the same p-adic scene through the Monna map M(x) = Σ a_kp^−k; the resulting image is smooth, with a vanishing point — indistinguishable from Euclidean perspective. Same world, two metrics; perception measures the interface, not the substrate (§5, UMP.010).
How to verify yourself: switch p and n and watch the naive staircase jump while the rendered row stays smooth; the golden-value gate re-checks the paper's identities (M(−1) = p, M(−p^m) = p^−m+1, …).

How to use

Prime p — the substrate prime (2, 3, or 5); all math is re-derived in base p.
Depth n — objects at p-adic positions x = p^0 … p^n along the line of sight.
2D grid — render grid points (i, j) with 0 ≤ i, j < p^g (g = 4/3/2 for p = 2/3/5; ≤ 729 points) through M onto the right canvas.
Reset — back to p = 3, n = 5, grid off.
Golden values re-run on every change; any FAIL blocks the "verified" claim.