clockRateBundle
plain-language theorem explainer
Every local recognition horizon context inherits a clock-rate bundle at its surface gravity κ. Holography and exterior-record arguments cite this to reuse the B3 near-horizon rate package without adding KMS, entropy, or curvature hypotheses. The proof is a one-line projection onto the Rindler leg of the shared context.
Claim. For $a,s,b,r\in\mathbb{N}$ and surface gravity $\kappa\in\mathbb{R}$, if a local horizon context joins a one-sided cut model to a near-horizon Rindler form at $\kappa$, then the B3 clock-rate bundle at $\kappa$ holds.
background
This module glues three audited legs on one shared context: a one-sided horizon cut model (horizon record double-posts the seam), exterior posted-record heat with discrete books balance and unit-temperature Clausius as theorems about that record, and a near-horizon rate model. No stress tensor, Ricci tensor, focusing law, Unruh claim, or Einstein equation appears.
A local horizon context packages a horizon record length, a one-sided cut premise, and a near-horizon Rindler form at surface gravity $\kappa$ (presently only $\kappa>0$). Thermality and curvature are deliberately excluded from the context. The B3 rate package is the theorem-side content of that Rindler leg: least positive deficit-free boost return period and related clock-rate data.
Upstream, the shifted cost $H(x)=J(x)+1=\frac12(x+x^{-1})$ rewrites the Recognition Composition Law as a d'Alembert identity; entropy is total defect. Neither is assumed here; the rate bundle is pure Rindler-form inheritance.
proof idea
One-line term wrapper. From the local horizon context $H$, project to its Rindler component $H.\mathrm{rindler}:\mathrm{NearHorizonRindlerForm},\kappa$, then apply the existing lemma that every such Rindler form yields a clock-rate bundle at $\kappa$. No case split, no arithmetic on $a,s,b,r$, and no appeal to the one-sided cut field.
why it matters
Closes the LEG-B attachment for local recognition horizons: once a context is assembled, the B3 rate theorem is automatic. Downstream exterior-record and Clausius arguments in this module can therefore quote clock rates without re-proving deficit-free period minimality or importing KMS. Used_by is presently empty, so this is a leaf export for later horizon-timing and holography assembly.
In the broader Recognition chain it stays local and kinematic. It does not force $D=3$, the eight-tick octave, or the $\phi$-ladder mass formula; those live in the T0–T8 forcing spine. It only ensures that every shared local-horizon context already carries the audited near-horizon rate package, matching the module claim that the boost return period is the least positive deficit-free period with no entropy premise.
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