IndisputableMonolith.Verification.CPMBridge.Constants.Probability
Defines coincidence probabilities for independent draws landing inside a tolerance window, used when verifying CPM-bridge constants against random alignment. A verifier cites these when bounding the chance that several domain selections all fall near a target radius. The module packages elementary counting bounds; the smallness lemmas are direct arithmetic comparisons.
claimLet $P(n,R,\tau)$ be the probability that $n$ independent uniform draws from a discrete range of size $R$ all lie inside a window of radius $\tau$. The module records $P$, the specialization to net-radius windows, and the elementary bounds $P\ll 1$ and the combined multi-window bound used in CPM constant checks.
background
In the CPM-bridge verification layer, physical constants are matched against discrete recognition ladders (phi-powers, rung indices, net radii). A recurring sanity check asks whether an apparent numerical agreement could arise by chance: several independent domain values all falling inside a narrow tolerance of a predicted window.
The module introduces a single counting model. Selections are treated as independent and uniform over a finite range of size $R$. A hit is any draw inside a window of radius $\tau$. The coincidence probability is then the product of per-draw hit rates (or an equivalent combinatorial ratio). Specializations fix the window to a net-radius scale used elsewhere in the bridge.
No Recognition-Science forcing (T5–T8, RCL, mass ladder) is proved here. The objects are pure probability bookkeeping for the verification side of the CPM bridge.
proof idea
Definition-first module. The main object is a closed-form coincidence probability in $n$, range size, and tolerance. Sibling lemmas specialize the window to net radius and prove two smallness statements by direct comparison of the resulting rational (or real) expression against explicit numerical thresholds. No deep measure theory; the arguments are elementary product bounds and arithmetic.
why it matters in Recognition Science
Feeds the CPM-bridge constant verification path: when several independent domain quantities appear to align with predicted radii or windows, these bounds quantify how unlikely pure chance coincidence is. Downstream constant-check theorems use the net-radius and combined smallness lemmas to reject accidental agreement. The module does not itself force $c$, $\hbar$, $G$, or $\alpha$; it only supplies the probabilistic filter those checks invoke.
scope and limits
- Does not derive physical constants or force phi, D=3, or the eight-tick structure.
- Does not model correlated draws; independence is assumed throughout.
- Does not replace rigorous constant identities; only bounds chance coincidence.
- Does not specify continuous measure-theoretic probability beyond finite-range counting.