What exactly are the formal rules around US paying off debt?

Question

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.

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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.

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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.

Answer 1

Per the 14th Amendment:

The validity of the public debt of the United States, authorized by law, ... shall not be questioned.

Given that this is a constitutional mandate, this makes ensuring that the validity of the debt (i.e. whether or not it will be repaid) the top priority for the executive branch. Following this interpretation (and anything is only a personal interpretation until it's tested by the courts), there is no provision to pay any other "general" bill before making debt/interest payments. Thus: Nothing gives the President the right to choose to default on "public debt" in favor of anything else.

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This is slightly more complicated by the section I ...'d out:

including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion

There are two ways to interpret "pensions and bounties for services in suppressing insurrection or rebellion". If it's read as "(pensions and bounties) for services...", then it's not relevant to the discussion. If it's read as "pensions and (bounties for services...)" then pensions are in the same protected category as the debt, adding a second set of bills which must be paid before any others. As far as I know, there's been no legal clarification on which way this should be read.

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As for what "public debt" specifically entails, I refer you to the wikipedia page, which summarizes it as:

Debt held by the public, such as Treasury securities held by investors outside the federal government, including that held by individuals, corporations, the Federal Reserve System and foreign, state and local governments.

Debt held by government accounts or intragovernmental debt, such as non-marketable Treasury securities held in accounts administered by the federal government that are owed to program beneficiaries, such as the Social Security Trust Fund. Debt held by government accounts represents the cumulative surpluses, including interest earnings, of these accounts that have been invested in Treasury securities.