The claim describes a sequence of events (flashing velocity in two spring starts, deload, then ramping up). While the web search results confirm Cole has been pitching and hitting high velocities since surgery, the specific narrative structure—'flashed that higher velocity in his two spring starts before going through a deload process and then ramping back up again, this time for good'—is not confirmed by multiple independent sources. The evidence is suggestive but not fully corroborated.

The web search results confirm Cole's rehab start and his general status, but none of the provided evidence explicitly confirm the specific details: '44 pitches across 4 1/3 innings on Friday night' or that he 'experienced only the normal soreness to be expected.' The evidence confirms he had a rehab start and is progressing, but the precise metrics and subjective feeling are not corroborated by multiple independent sources.

The evidence mentions the Yankees' general plan for Cole's gradual return and the existence of affiliates like High-A Hudson Valley (via Wikipedia), but none of the provided web search results or cross-references specify that the *next* start is *likely* to be at High-A Hudson Valley or Triple-A Scranton/Wilkes-Barre *next week* with both being home. This level of scheduling detail is not independently confirmed.