The inventory is a snapshot of a single day, and that day is chosen for reasons that reach well beyond probate. Values are given "as of the date of the decedent's death," which is the same moment the federal income tax rules use to reset the tax basis of inherited property, and the same moment a federal estate tax return values the gross estate. So the appraisals ordered for the inventory generally do double duty, and a valuation that was convenient for the court file can turn out to matter a great deal later, when a beneficiary sells the house and computes a gain. Published step-up in basis covers that consequence; the point here is only that the date is not arbitrary and the numbers are not disposable.
The encumbrance rule is what makes the inventory a poor answer to "what is the estate worth?" The statute requires the type and amount of any encumbrance to be indicated against each item, which means the mortgage appears beside the house rather than reducing the figure written for it. A reader who takes the inventory total as the family's inheritance will be wrong by the amount of the secured debt, and wrong again by the unsecured claims, the administration expenses and the taxes, none of which the inventory reports at all. The document answers a narrower question than people expect of it: what did this person own, and what was it worth on the day they died.
"File or mail" is the provision worth knowing about before an inventory is prepared, not after. Published probate observes that whether inventories are filed publicly differs by state and leaves the question there. Minnesota answers it in its own text: the representative may file the inventory with the court, or mail it, and the second paragraph of the section says who has to receive it either way. Copies go to the surviving spouse if there is one, to all residuary distributees, and to "interested persons or creditors who request a copy thereof," with the clarification that the representative "need not personally receive a copy as a surviving spouse or as a residuary distributee." So the people with a stake see the list regardless. What the choice controls is whether the general public does, and for a family with any reason to prefer that a schedule of accounts and property values not sit in a courthouse file, it is a real choice rather than a formality.
The list is not final, and the statute says so. Section 524.3-708 requires a supplementary inventory or appraisement where property not in the original comes to the representative's knowledge, or where they learn that a value or a description in the original "is erroneous or misleading." The supplement shows the market value as of the date of death of the new item, or the revised value or description, together with "the appraisers or other data relied upon, if any," and is filed with the court only if the original was filed. That last clause preserves the earlier choice rather than quietly reversing it. The forgotten savings bond and the life insurance policy from a former employer are the ordinary reasons this section is used, and using it is the expected course rather than an admission of error.
Two boundaries that stop the inventory being read for more than it says. It lists "property owned by the decedent at the time of death." Whether a joint account or a retirement plan with a named beneficiary belongs on a particular state's inventory form is a question for that state, and nothing here answers it. Separately, the probate inventory is not the federal gross estate. That measure is wider, as published estate tax explains, so an estate can produce two schedules of property that do not agree with each other and have both be correct, because they were compiled to answer different questions.