The conventional number line is centred on 0: distance is |x|, and the symmetry is additive (x mirrors −x). Suda's correction re-centres it on 1: distance becomes the invariant radius ρ(x) = |log x|, the symmetry is reciprocal (x mirrors 1/x), and 0 and ∞ become the two ends. His hypothesis: the singular effects of reciprocity concentrate at 1 — the mirror — not at 0.
[A] the mathematics [I] the convergence
Division is a double inversion. a ÷ y = a × y⁻¹ inverts both the operator (÷→×) and the operand (y→y⁻¹). Writing a = a/1 foregrounds the peculiar role of 1: it is the pivot where the two inversions couple. [A]
1 is a mirror, not a mere fixed point. I(x)=1/x has its unique positive fixed point at 1 with I′(1) = −1 — orientation reversal without expansion or contraction. In s = log x, reciprocity becomes exactly the reflection s ↦ −s. [A]
Distance is renormalised. The reciprocal-invariant radius is ρ(x)=|log x|, and the invariant energy E(x)=(log x)² is minimised uniquely at 1. Small quantities become multiplicative: x = 1 ± ε read through s. Measured this way, x and 1/x are exactly equidistant from the centre. [A]
The half-twist is the normal form. In the hinge coordinate u=(x−1)/(x+1), inversion is u ↦ −u — a half-twist about 1, the structural centre of reciprocal geometry. The twist phase φ(x)=sign(log x) flips; the energy does not. [A]
Independent convergence. Suda's 2025 papers formalise this on their own road; our finity reading states the same centre. Idea-priority on our side is the author's 2024 statement; Suda's is an independent formalisation. Neither borrowed from the other, which is exactly why the agreement is worth something — and it remains corroboration, never proof. [I]
Withdrawn, 2026-07-30, same day it was published. This page carried a numbered tally here — that of twenty-four results in Suda's papers, one followed from our base outright, twelve after a median of three further premises, nine were independent, and two contradicted it. Those numbers had no source. No receipt, no working, no per-result table exists anywhere in this corpus; a search for the tally returns exactly one file, this page. They came from an internal audit whose own published error rate is roughly one proposal in five, and they were put on an indexable page as a quantitative adverse judgment about the work of a named living person. That is the one kind of claim that most needed a receipt and had none. It is withdrawn rather than softened.
What the adjective was covering, and what it still covers. “Corroboration, never proof” is vague, and replacing vagueness with a number was the right instinct and the wrong execution. The honest position: two roads reached a shared centre, neither borrowed from the other, and we have not done the work of saying result-by-result how much of Suda's road our base actually reaches. Until that table exists and is published with its working, the adjective stands and the number does not. [I]
And one hard disagreement, in our direction. Suda's hinge coordinate u = (x−1)/(x+1) — the half-twist above, the normal form his Part I is built on — has determinant 2. Every finite word over our base has determinant ±1. So the hinge is provably not constructible from our base, and the object that makes his geometry legible is one we have to import rather than derive. This is the only place the two roads make contact hard enough to be decided, and it goes against the convergence story. [A]
And this chart is a proper sub-chart — it cannot see half of what inversion fixes. On the whole real line, ι(x) = 1/x fixes exactly two points, +1 and −1. On the positive ray, where this entire page lives, only +1 survives, and it is the unique positive fixed point. Both statements are machine-checked with no gaps. So the centre being unique here is a fact about the ray, not about inversion: the uniqueness is bought by having already excluded the other half. Anything that needs a signed direction cannot be read off this chart, and the framework's first dimension is seated one chart up by a declared move for exactly that reason. [A] both fixed-point facts; [S] the seating. Kill: exhibit a positive real other than 1 that inversion fixes.
The mathematics is inherited. Möbius maps, the log conjugacy, and the Cayley/hinge coordinate are standard — used, not discovered, by us or by Suda. What each of us added is a reading. [A]
Constraint-built, not drawn. Every derived object on this page is declared in a construction kernel and solved, GeoGebra-style — the four invariants below the canvas are computed from independently derived objects, so their vanishing is a result, not a decoration.
Sources read. Minoru Suda, Fractional Structure and Möbius Transformation — Part I: Double Inversion in Division and the Phase of Twist (16 Aug 2025); Part II: The Critical-One Hypothesis and the Egg of Infinity (16 Aug 2025).
The same centre, elsewhere: the egg (the hinge as a disk) · the reciprocal line · the sphere. Where a claim about Suda ever overreaches, its death is dated on the record. · If you can see directly, put this down →