theorem_grade_discriminator_sector_count
plain-language theorem explainer
There are exactly three theorem-grade discriminator sectors in the Track 6 package: leading-log entropy, echo damping, and rung phase. Anyone assembling or citing the Fork F sensitivity certificate needs this count pinned. The proof is definitional reflexivity against the Nat constant that enumerates those sectors.
Claim. The number of theorem-grade discriminator sectors equals $3$. Those sectors are the leading-log entropy channel, the echo-damping channel, and the rung-phase channel.
background
Track 6 is the falsifier-sensitivity lane of the Quantum Gravity Discovery Master Plan. This module is its Fork F integration endpoint: it packages existing Lean surfaces rather than adding a new observational lane. The package covers the phi-derived discriminator matrix, dataset attachments on falsifier-register rows, likelihood/status upgrades, and a guarded GWTC-3 ringdown runner.
The upstream definition fixes the theorem-grade sector count at three and names the sectors: leading-log entropy, echo damping, and rung phase. That Nat is the sole dependency of the present equality. Rival-theory rows (LQG, string, CDT/causal sets, Bohmian/Diosi-Penrose) are counted separately and are not part of this claim.
The certificate is intentionally conservative: structural coverage and named channels only, with no claim of empirical confirmation and no upgrade of still-structural PTA, strong-field, or ringdown physics into a discovery statement.
proof idea
One-line reflexivity. The definition sets the sector count to the literal natural number 3, so rfl closes the equality with no lemmas, rewrites, or case analysis.
why it matters
This equality is the first conjunct of the Fork F handoff theorem, which asserts a single integration endpoint: three theorem-grade discriminator sectors, four rival rows on the discriminator matrix, ten falsifier-register rows with dataset attachments, six rows with likelihood/status records, and a guarded GWTC-3 ringdown runner with two supported observable mappings.
It also fills the discriminator_sector_count field of the Track 6 falsifier-sensitivity certificate instance. Without a proved count, the certificate cannot honestly report how many phi-derived discriminator channels are theorem-grade.
In the broader Recognition framework this is verification scaffolding around the gravity discriminator matrix, not a step of the T0–T8 forcing chain. It records structural readiness of Track 6 sensitivity packaging so downstream audits can treat the sector tally as closed rather than aspirational.
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