[Bug] PIC addition loses causal state across multiple misses

[morluto]

Observed behavior

PIC addition produces an incorrect final state when one request contains multiple cache misses separated by cached segments.

Each missed segment is currently computed from a zero initial state and combined afterward. A later miss therefore does not see the causally accumulated state of the earlier miss and intervening cache hits.

[miss 1: seed 0] -- add S1 --> [prefix S1]
                                      |
                                      +-- add hit H --> [prefix S1 + H]
                                                             |
                                                             v
                                   [miss 2: seed S1 + H]
                                                             |
                                                             +-- add S2 --> final

S1 and S2 are states produced for missed segments; H is a cached hit state.

Reproduction

A deterministic miss-hit-miss recurrence gives:

expected: [1.0, 7.5]
observed: [6.0, 2.0]

The mismatch is reproducible in both the GDN and KDA PIC addition orchestration.

Expected behavior

Every later missed segment should begin from the state accumulated from all preceding prompt segments, including cache hits between misses. Requests containing zero or one miss should retain their existing single-pass path.

Impact and scope

The issue affects PIC addition requests with more than one missed segment. Single-miss requests do not require causal composition between independently computed misses.