How many different steady states can the same signalling model support under the same conditions? This Evidence Press candidate studies a mathematical model of early T-cell activation. Two kinds of ligand bind to receptors, which pass through a chain of phosphorylation steps. An active phosphatase feeds back onto that chain.

The paper gives one explicit set of positive rational parameters with exactly five positive steady states. It uses a chain with one hundred steps. These are five possible stationary solutions in a fixed conservation class, not five measured states of a real cell.

The proof reduces the equilibrium equations to one scalar equation. Exact evaluations show five separate sign changes, guaranteeing five solutions. A polynomial with two hundred and two integer coefficients supplies an upper bound of five positive roots, counting multiplicity. Together, these bounds give the exact count and show that the scalar roots are simple. The count persists for sufficiently small changes in the model's twelve named continuous parameters.

The evidence includes the written argument, every polynomial coefficient, and an exact-arithmetic verifier. It checks the original concentration equations as well as the reduced formula. Producer checks and internal editorial review remain separate from external validation.

The result does not determine which steady states are dynamically stable. It does not establish biological plausibility or settle the question with only one ligand present. Historical priority remains unclaimed.

Released on twenty September twenty twenty-six, this is an unrefereed Evidence Press candidate. The full paper and evidence are linked on the release page. This is an AI-generated voice summary, not additional mathematical evidence.