bitsPerEvent
plain-language theorem explainer
Information content of one recognition event, in bits: the forced Shannon entropy converted from nats by dividing by ln 2. Anyone citing the physical per-event access rate that replaces the artifact log₂ 8 = 3 uses this constant. Definition only: forced entropy over Real.log 2; the closed form (φ+2) log₂ φ is proved downstream.
Claim. Define the bit content of one recognition event by $H_{\mathrm{bits}} := H / \ln 2$, where $H = \sum_{n=0}^{\infty} P(n)\,(-\log P(n))$ is the Shannon entropy (nats) of the forced geometric measure $P(n)=(1-\varphi^{-1})\varphi^{-n}$.
background
This module rebuilds the holographic access bound after the deflation test killed the naive "eight states per site" orbit count. The physical content of a carrier is continuum-valued, so the right bound is forced-measurement outcome quantization: a recognition event resolves into discrete $\varphi^{-n}$-weighted outcomes (T9 forced measure from MeasureForcing), with $P(n)=(1-\varphi^{-1})\varphi^{-n}$, mean depth $\varphi$, and partition $\varphi^2$.
The Shannon entropy of that measure is forcedEntropy (nats): $\sum_n P(n)(-\log P(n))$. Module framing: this is average information / channel capacity, not a zero-error hard cardinality. The effective outcome count (perplexity) is $\mathrm{e}^H=\varphi^{\varphi+2}\approx 5.70$, genuinely different from 8.
Dividing by $\ln 2$ converts nats to bits. Upstream, the entropy keystone equates $H$ to $(\varphi+2)\log\varphi$ via the geometric-series computation from mean rung and normalization.
proof idea
Pure definition: one division. The real number is forced entropy (nats) divided by $\mathrm{Real.log},2=\ln 2$. No tactics, no lemmas at this site. Closed-form identity and certificate fields live in the sibling theorem that unfolds this def and rewrites via the entropy keystone.
why it matters
Supplies the bit-rate constant in the rebuilt access law. Downstream, the equality theorem proves it equals $(\varphi+2)\log_2\varphi\approx 2.51$ bits, the forced rate replacing the artifact $3=\log_2 8$. The capacity certificate packages four claims: entropy value $(\varphi+2)\log\varphi$, effective outcomes $\varphi^{\varphi+2}$, this bit rate, and additivity of access over events.
In the Recognition chain this is the information-theoretic reading of one event under the forced measure (grounded in MeasureForcing), not an orbit count. It sits under the holography access rebuild: average mutual-information rate, consistent with the panel note that a forced readout can hard-distinguish infinitely many states. Open (documented, not faked): the Born bridge from this entropy to a forced-measurement distribution on recognition Hilbert space; residual phase lives in the elliptic $U(1)$ sector.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.