Strogatz classifies a planar linear system by two numbers: the trace τ and the determinant Δ. Writing the system in the real normal form for eigenvalues μ ± iω — rotation by ω, scaled by μ — gives τ = 2μ and Δ = μ² + ω², and so
That is negative with no further hypothesis available. The system spirals as soon as ω ≠ 0 (is_spiral), and it is a sink exactly when μ < 0 (is_sink_iff). So “spiral sink” is the entire shared description, and it is very weak: eleven damped oscillators picked at random would satisfy it.
Conjugating by an invertible matrix leaves the trace alone (trace_of_conj) and the determinant alone (det_of_conj). Since τ and Δ are 2μ and μ² + ω², the pair (μ, ω²) belongs to the system and not to the chart.
The corpus's own closest pair is instantiated directly, so nothing is left resting on arithmetic:
Across the eleven bridge rows carrying both μ and ω that is 0 similar pairs out of 55, and 0 again when the clock is allowed to rescale.
Every planar linear spiral sink is topologically conjugate to every other. That is true of all eleven, and it is true of any eleven damped oscillators, so it distinguishes nothing. The claim was true at the level where it says nothing and false at every level where it would say something.
Strogatz, Nonlinear Dynamics and Chaos (2018), sha256 e4c3681c…, 532 pp. §5.2 “Classification of Linear Systems”, printed pp. 129–138; the discriminant on pp. 132, 135, 138; the classification diagram at Figure 5.2.8, p. 138. spiral-pages-verify.py opens the file and finds them, and refuses outright on a sha mismatch — because every page number above then describes a copy the reader does not have.
sorryAx. A clean axiom report is not a reading of the statement: per R20, a theorem can assume its conclusion and still report clean. Follow the link before citing one as evidence.