Late Recognition in Streams under Finite Carried Load: No-Go for Load–or–Discard and Information Bounds for Identification

This manuscript formalises a worst-case late-recognition regime in one-pass streams. Inside an unknown window of length B, there exists a unique type that repeats at least m ≥ 2 times while all other types appear at most once, and the identity of the repeated type is uncertifiable before its m-th occurrence. We separate two resources: carried load (unassimilated retained items, constrained by a finite capacity K_max) and intermediate memory (a bounded sketch state not counted as carried load). We prove (i) a worst-case no-go theorem: any architecture restricted to immediate load-or-discard decisions cannot guarantee both bounded carried load and correct identification on every valid instance when K_max < B; (ii) a deterministic intermediate-memory lower bound of log(C(N, B−m)) bits via a one-way communication reduction; and (iii) a randomised upper bound using sampling plus Count–Min Sketch verification, yielding an explicit budget–reliability trade-off. The result provides a second, independent necessity route (via recognisability) complementary to thermodynamic overload in the Synkyria Refusal Stack. Key contributions: No-go (worst case): load-or-discard architectures cannot simultaneously ensure viability (bounded carried load) and identification under late recognition when K_max < B. Lower bound (deterministic): any deterministic one-pass identification algorithm requires intermediate state size at least log(C(N, B−m)) bits (one-way communication reduction). Upper bound (randomised): a sampling + Count–Min Sketch construction gives an explicit budget vs reliability trade-off for identification with probability 1 − δ. Why it matters:Late recognition isolates a regime where correct identification is provably incompatible with “keep-or-discard now” architectures under finite carried-load capacity, motivating intermediate representation layers and (in Synkyria terms) refusal/holding as a viability primitive.