bitsPerEvent_eq
plain-language theorem explainer
The forced information rate of one recognition event equals $(\varphi+2)\log_2\varphi$ bits (about 2.51), the physical access rate that replaces the artifact $3=\log_2 8$. Anyone citing the rebuilt holographic access bound or the event-capacity certificate needs this closed form. The proof unfolds the bit-rate definition, substitutes the forced-entropy keystone in nats, and finishes by base conversion of the logarithm.
Claim. The forced per-event bit rate equals $(\varphi+2)\log_2\varphi$, where $\varphi$ is the golden ratio (the self-similar fixed point of the Recognition cost).
background
This module rebuilds the holographic access bound after the orbit-count deflation test. A recognition event is weighted by the T9 forced measure: outcome masses $\mathrm{probMass},n=(1-\varphi^{-1})\varphi^{-n}$ (equivalently $\varphi^{-(n+2)}$), normalized with mean depth $\varphi$. The physical content of one event is the Shannon entropy of that measure, not a hard orbit cardinality.
In nats the closed form is $\mathrm{forcedEntropy}=(\varphi+2)\log\varphi\approx 1.741$. Converting to bits gives the rate stated here. The effective outcome count (perplexity) is then $\varphi^{\varphi+2}\approx 5.70$, genuinely different from the spurious eight-state alphabet. Entropy here is average information / channel capacity; it is not a zero-error distinguishability ceiling.
Upstream, the identity rests on the proved keystone that the Shannon tsum equals $(\varphi+2)\log\varphi$, obtained from the geometric mean-depth law and unit total mass via an additive tsum split.
proof idea
Term-mode, three steps. Unfold the definition of the bit-rate (entropy in nats converted by $\log_2$) and the library definition of $\mathrm{logb}$. Rewrite with the forced-entropy closed form $(\varphi+2)\log\varphi$. The remaining identity is pure base conversion of the logarithm; ring closes it.
why it matters
This is the bit-rate face of the forced-measure access law: the number that replaces $3=\log_2 8$ once continuum carriers kill naive eight-state quotients. It is one of four fields of the event-capacity certificate (eventCapacityCert), which packages entropy value, effective outcomes, bit rate, and definitional additivity over $k$ events.
In the Recognition chain it sits on T6 ($\varphi$ forced) and the MeasureForcing geometric law (T9-class outcome quantization). The module framing is explicit: this is mutual-information / channel capacity, not an injection bound, which is why it supersedes the deflated orbit count. Open residual (documented, not faked): the Born bridge from the sub-Gaussian $L^2$ seed to a literal measurement distribution on recognition Hilbert space; the elliptic $U(1)$ phase sector is where residual outcome phase lives.
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