Is there a precise set of rules (e.g., very specific law, or court ruling?) that explains what specifically does - or does not give the US executive branch the right to choose to default on specific portions of debt despite having non-empty treasury?
"non-empty" here has a very precise meaning: they are paying other non-sovereign-debt liabilities but not servicing debt fully.
Please note that I'm NOT at all interested in finance technicalities (e.g. the story line about 3 separate payment systems that are hard to interconnect may be a technical excuse for why the default was possible/likely during prior month, but it has zero impact on legal situation).
I'm also not interested in "separate" accounts, e.g. it's clearly understood that SOME of Treasury's balance sheet is in (supposedly) separate books like Social Security Trust Fund that aren't applicable to debt servicing and are also funded separately. This question only deals with general liabilities that are not being paid from such separate books.
For example, from Forbes article:
Tribe (of Harvard Law School) and Balkin (of Yale Law School) disagree. They think the President would be relegated instead to some sort of "prioritization" process, where he directs those limited funds available to him to making certain that the country honors its outstanding bond obligations -- the most unambiguous focus, they contend, of Section 4 of the 14th Amendment -- and to funding other absolutely essential functions while allowing most other obligations (salaries, entitlements, contracts, etc.) temporarily to go by the wayside, though this would obviously cause enormous pain and upheaval throughout the country.