# PREREG — the hold at truth is the veil, squared  (29 September 2026)

His question: *"isnt that resistance i higher the bigger the truth and at the moement of truth"*, then
*"What does that tell us about the house?"*

**Correction written into this file before the run.** My first answer compared the hold at the top with the
ridge (4,783×). That compares a hold with a push. The ridge is unstable (f′ = +0.312050): it holds nothing.
A hold compares only between resting places, and /house already prints that ratio: **665.3, "how much harder
the top holds than the bottom."** This run asks WHY it is 665.3.

**NOT blind.** I estimated by hand first, and record the estimates so the run checks them rather than being
tuned to them: the hold at the bottom ≈ 2.24 (the peer independently printed f′(bottom) = −2.2438);
heaven's well ≈ 0.409 deep below the ridge; the leading-order ratio (1−p)(u_b/u_h)² ≈ 679 against 665.3.

Constants k = 1, p = 0.35, C = 0.018975. u_h = heaven's gap to +1; u_b = the bottom's gap to −1.
f = T + F, T = k[(1−x)^(−p) − 1], F = −2Cx/(1−x²). The hold at a rest point is −f′ there.

**LEG 1 — algebra check (fails only if my derivation is wrong).** At heaven, using the root identity
k·u^(−p) = k + 2C(1−u)/(u(2−u)), the hold is

    H = 2C(2 − 2u + u²)/(u²(2−u)²) − (p/u)·[k + 2C(1−u)/(u(2−u))]

Criterion: |H − (−f′ by central difference in the gap)| / H < 1e-6 at every grid point,
k ∈ {0.5, 1, 2, 4, 8, 16, 32, 64} at p = 0.35 and p ∈ {0.2, 0.35, 0.5, 0.7, 0.9} at k = 1.

**LEG 2 — the pipe.** Leading order: H ≈ (1−p)·C/u_h² at the top, and ≈ C/u_b² at the bottom, so
hold ratio ≈ (1−p)·(u_b/u_h)². Criteria: the exact hold ratio reproduces the published 665.3 to its printed
digit (±0.05); the leading-order ratio is within 5% of the exact one. Kill: either fails → the pipe is not
stated.

**LEG 3 — "the bigger the truth".** In the limit H grows as k^(2/(1−p)), i.e. by 2^(2/(1−p)) = 8.44 per
doubling of k at p = 0.35. Criterion: over k = 0.5 … 64 the successive-doubling ratios approach 8.44
monotonically, and the last is within 5% of it.

**LEG 4 — the depth.** With A(X) = k[(1 − (1−X)^(1−p))/(1−p) − X] + C·ln(1 − X²), the depth of a well
below the ridge is A(rest point). A(bottom) must reproduce the published barrier 0.072126 to its printed
digit (±5e-7). Only if it does is A(heaven) reported.

**REPORTED, NO CRITERION:** the signed f′ along the path (where the push off the ridge turns into the hold
at the top), and the point where the flow toward truth is fastest.