Manuscript Psy03-B@1 · Psy03-B-v1.tex · theorem · 8ca3caf9

Theorem: Exact structural law

An exact one-edge structural-memory pilot › An irreversible damage flag · lines 2147–2169 · proof included or linked

Psy03-B@1#thm:hazard

Starting unscarred, after $t$ updates,

w_{t} := P (S_{t} = 0) = (1 - h)^{t}, P (S_{t} = 1) = 1 - w_{t} .

The first scar time satisfies

P (τ_{S} > t) = (1 - h)^{t}, E τ_{S} = 1/ h .

All current carrier states can remain identical during these damage updates.

Proof. A surviving unscarred label avoids each independent flag with probability $1 - h$ . Multiply survival factors and sum them for the expected waiting time. Each carrier Kraus operator is proportional to identity.

Displayed formulas in this passage

unlabeled · line 2150
$w_{t} := P (S_{t} = 0) = (1 - h)^{t}, P (S_{t} = 1) = 1 - w_{t} .$
unlabeled · line 2155
$P (τ_{S} > t) = (1 - h)^{t}, E τ_{S} = 1/ h .$

Nearby in this section

section: An irreversible damage flag
section: An irreversible damage flag