Gray sweater. Differing from the exact description but acting suspiciously by running in the vicinity of the crime scene.
Ah, a GRAY sweater. Thank you, Mr. Smith
(And could you please give us a source for this detail?)
So! Patrolman Walker sees a guy in a gray sweater running into the library. Perhaps he doesn't even get a good enough look of the top to see that it's a sweater rather than a shirt. Perhaps he just sees: gray top. But even if he does recognize it as a sweater, he understands it's very easy for a gray sweater under a jacket to have been confused by a witness for a white shirt. Well within the normal margin of error. Coupled with the fact of his running in the vicinity of the crime scene, it makes perfect sense for Patrolman Walker to think 'This must be our guy' and to excitedly put out a confident radio dispatch, "He's in the library".
Now compare this with:
A report comes in of a guy in a brown shirt ducking into the Texas Theatre. Very unlikely for a brown shirt to be confused by a witness for a white shirt. Well outside the normal margin of error. It may make sense to send a cop or two to check the thing out, but it makes very little sense to hit the cinema with anything like the fervor with which the library was hit before this.
**
By the way, we know that Patrolman Walker was on high alert in these manhunt minutes for one thing: a man in a white shirt. Makes sense: like other officers, he had heard the description broadcast,
followed by the information that the jacket had been discarded and found. But we have extra confirmation that what he was on high alert for was: a man in white shirt. Because the NEXT man Patrolman Walker confronted was a guy he saw behind a fence. As it happened, the guy was just out walking his dog. But Patrolman Walker didn't know that at first. He saw this man as a suspect for one reason: he was wearing a WHITE SHIRT.
**
Change one detail in the Brewer story and the response of the police to the call from the Texas Theatre makes sense: the man seen by Brewer had on a white shirt. The brown shirt was only 'remembered' later------------------after Mr. Oswald's arrest.