Initialisation-dependent fixation v1.0.0-candidate

Unrefereed research candidate. Initialisation-dependent fixation in noisy weighted voter models: a resolution of Conjecture 2 of Ganesh, Hauert and Valla. Version 1.0.0-candidate, Anonymous. DOI: https://doi.org/10.5281/zenodo.23687032 · Release page: https://evidencepress.org/releases/initialisation-dependent-fixation/

On the complete graph with bounded, separated rate supports, the fixation limit is governed by the transient mean resident rate, not its equilibrium value.

• Refutes Conjecture 2 as stated (fresh start) whenever resident rates vary: e.g. 0.7842… instead of (3+√37)/12 = 0.7569…, and 0.70203… instead of 2/3 for a constant favourable rate.
• Confirms the conjectured formula under the equilibrium start (as simulated by the source) for a constant favourable rate; for varied favourable rates the equilibrium-start limit is 1 − (E T_B/E T_A)^k.
• The underestimate has supremum 27.3355 percentage points (not attained), below 8.27 points when resident rates differ by at most a factor of three; an explicit burn-in removes it.

Assets: the release ZIP (complete package), the manuscript PDF (28 pages) and RELEASE-SHA256SUMS. Research CI: https://github.com/ipitchford/initialisation-dependent-fixation/actions/runs/40488286762

Assurance: written proofs, exact rational certificates and internal AI-assisted review. Not peer-reviewed, independently reproduced or formally verified. See ASSURANCE.md. Text and data are CC0-1.0; code is MIT.