Objectivity from Records

This note proves the formal lemma underlying the S₁ stabilization signature: when a realized outcome is redundantly recorded in conditionally independent fragments, optimal observers reading those fragments converge on the same answer at an exponential rate. Under conditional independence and per-fragment Chernoff information bounded below by c₀ > 0, the Bayes-optimal error satisfies P_e(k) ≤ ½·e^(−k·c₀), and pairwise disagreement between two observers reading disjoint k-fragment samples decays at the same rate. Driving disagreement below δ requires only k ≥ (1/c₀)·log(1/δ) fragments.

The note states the theorem, proves it self-contained from Chernoff's bound and a union bound, and identifies the cross-domain empirical signature it predicts: pairwise observer disagreement falling off as a·e^(−b·k) wherever a latent outcome is redundantly recorded in conditionally independent readouts. Its operational pair, Methods-S₁, turns the bound into a deployable agreement-curve audit.

What acceptance commits you to. Acceptance of this note commits the reader only to the conditional bound under its stated independence and discriminability assumptions — not to Universal Collapse Theory, and not to the claim that any particular real-world redundancy is genuinely independent. That is precisely what the paired audit tests.

Keywords: consensus bound; Chernoff information; redundant records; observer agreement; S₁ signature.