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Simultaneous amplification beyond fitness three halves — preprint v1.0.0

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@AlecKriebel AlecKriebel released this 08 Aug 14:19
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Simultaneous amplification beyond fitness three halves — preprint v1.0.0

This public preprint proves a strict improvement to the known robust
simultaneous-amplification interval for Birth–death and death–Birth updating.

Main theorem

Let

[
P(R)=R^6-8R^5+22R^4-30R^3+21R^2-6R+1
]

and let

[
R_{\mathrm{hyb}}=1.5028569127905696\ldots
]

be its unique root in (3/2,151/100). The paper constructs one explicit
fitness-independent family of finite connected undirected weighted graphs
that eventually amplifies every fixed 1<r<R_hyb under both update rules.
Consequently,

[
R_{\mathrm{sim}}\ge R_{\mathrm{hyb}}>3/2.
]

This exactly refutes the proposed threshold R_sim=3/2.

Construction and certificates

The family combines a clique core, ordinary hub leaves, and dilute internally
heavy K_2 satellites. The release includes:

  • the complete manuscript and deterministic PDF;
  • exact labelled-chain lumping and transition checks;
  • exact rational coefficient identities;
  • Sturm and tangency certificates for the algebraic threshold;
  • a second independently derived asymptotic proof path;
  • the exact counterexample excluding every graph-independent convex affine
    endpoint separator;
  • hostile-audit and page-by-page PDF QA records; and
  • a one-command replay script, plus a pinned clean-archive bootstrap.

Scope

The value R_hyb is exact for the displayed two-mechanism dilute regime. The
unrestricted exact value of R_sim and a matching universal upper bound remain
open. This preprint is a public research release, not peer-reviewed journal
publication. No journal submission or external contact is claimed.

Assets 4
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