I have not intentionally created a fare break. This was booked direct via UA.com, as a one-way ticket. The LAX transfer (layover) is 1h35. It is not a stopover as per normal usage of the word or as per the definition in the fare rules. I would very much assume that paid checked bags will be checked through (and YYZ has pre-clearance, so Canada-US segment arrives as "domestic") and United email quotes the CAD$30 for the first checked bag for the entire YYZ-HNL journey.

That said, I have saved the fare rules in full. It would appear that the mechanics of the fare construction rely on some kind of add-on combination, as follows:

I normally assume fare class is reflected by the first character of the fare basis code. This is not so here.

• yes, the proper check mark was in the pop up;
• no, the website does not exempt ex-Canada BE from the full-size carry on prohibition [I take WineCountryUA's point that "UA is slow at times getting all the different web pages updated"]
• yes, the "[reservation] processing email" says I can have a full-size carry on;
• no, the "eTicket Itinerary and Receipt email" sent to me, for this specific itinerary, says I cannot take one ("You’re not allowed a full-sized carry-on bag unless you’re a MileagePlus Premier member, primary member of a qualifying MileagePlus credit card or Star Alliance™ Gold member.");
• yes, the endorsement appears consistent with the pop-up, in that it does not include the NOCBBGnotation;
• no, the fare rules which should be the main go to don't sufficiently resolve the issue. In fact, fare basis code KAA4HFBN (used by UA for one-way construction) has the following under Reservation and Ticketing: "BASIC ECONOMY OW/RT UNBUNDLED FARES NON REFUNDABLE FARES NO PRERESERVED SEATS NO CARRYON BAGGAGE UNUSED COUPONS HAVE NO RESIDUAL VALUE". But that same fare rule does not require the endorsement NOCBBG;

I wouldn't mind the futher validation, even though I recognize this may be a rare case of UA-initiated fare construction that was not fully thought out (which UA.com did all on its own--I am discovering this just now, as I am digging further).

KNA5A0BA has no language about carry ons (so permitted). KAA4HFBN has some language prohibiting carry ons. Normal interpretation rules (i.e. most restrictive rule applies to the entire journey) would allow UA to prevail if they denied me a full-size carry on. But of course, the numerous inconsistencies in the booking process would likely undermine such UA argument. I can advocate for myself. But what is a poor, even detail-oriented, passenger to do other than throw their hands up in frustration [or pay up for a non-BE fare]?