The use of Presence Claims in the FOAM Protocol approaches the speed of light. Stale Presence Claims, would not be useful, just as there is not much use for a Movie Theater Ticket stub after you have entered the theater. Proving you were in a place would be a matter of Historical record, although applications that would be written to use such a proof for any other period than NOW is doubtful.
The only one I can think of is Loyalty points related to visitors to a store, and since the Store would account for the interaction with additional data points besides Presence Claims, well then stores should seek to establish a customer relationship. A repeat customer is your best customer. Simply walking into a store does not establish that relationship. Walking into a store a hundred times, less so. (although an interesting exercise in data analytics would be to determine why a customer returned to a store 99 times without buying anything…)
The scenarios you describe require too much latency for a Zone Anchor to approve of. Applications that used historical Presence Claims would most likely not be commanding a volume of users. (and those low volume edge cases could require additional measures) Games are about immediacy and response. Selling a Presence Claim for last week would not be applicable to any casual or high volume application I can think of.
What you describe seems to treat Presence Claims as low-cost to create, yet having a high value thus a secondary market. When in reality FOAM users that interact with FOAM overtime will have a higher trust and stake in the Protocol. Selling that stake’s Private key is not rationale. The architecture will not reward or even recognize lag on interactions with a Zone Anchor that have any latency outside of their geography.
The closest I can get to what I think you are proposing is a system wherein AGENTS with FOAM interacted in specific locales with the FOAM Protocol via a Zone Anchor for a third party, those AGENTS could be contracted to perform that action, under contract or employment. That would be a valid interaction with FOAM. It is a messy scenario, and could show there is an opportunity for new types of work or jobs in the FOAM economy.
I agree that this is largely dependent on the Application written to use FOAM. A badly designed application could be susceptible to the pitfalls you raised, only if they put any credence in Historical Presence Claims. Any application processing Presence Claims NOW would not be susceptible to a market in used Presence Claims.
You obviously are very concerned about this scenario, perhaps a more exhaustive analysis could be made to cover all areas you have raised?