The mechanism, and what depends on it. In the arrangement the Commission describes, the provider "holds the deposited crypto asset in a manner intended to ensure that, for the Redeemable Wrapped Tokens in circulation, there is an equivalent amount of the deposited crypto asset being held", holds it "for the benefit of the Redeemable Wrapped Token holders", and the deposit "effectively is 'locked up' and cannot be transferred, lent, pledged, rehypothecated, or otherwise used for any reason". Redemption runs the process backwards: the holder sends the tokens back, "who burns (or destroys) the Redeemable Wrapped Tokens and releases the equivalent amount of the deposited crypto asset back to the holder on a one-for-one basis". The right to redeem belongs to whoever holds the token, not only to the original depositor.
Two kinds of provider do this, and they fail differently. A custodian, in the Commission's description, "typically holds the deposited crypto assets in a cryptographic wallet that the Custodian controls", which makes the arrangement a promise by an identifiable company. A cross-chain bridge, which the release defines as code that "programmatically generates and redeems Redeemable Wrapped Tokens without the use of a Custodian", instead "holds the deposited crypto assets in a smart contract". So the holder's exposure is either to an institution and its controls, or to a program and its defects, and neither is the same as holding the underlying asset directly. Smart-contract risk in general is covered on its own page and is not restated here.
The securities analysis has two branches and the second is easy to lose. The Commission's conclusion is that "the offer or sale of a Redeemable Wrapped Token that is a receipt for a non-security crypto asset that is not subject to an investment contract, in the manner and under the circumstances described in this release, does not involve the offer and sale of a security". Its reasoning is that the token "does not have the economic characteristics of a security", that the definition of security "specifically lists 'receipt for' any security" and this is a receipt for something that is not one, and that holders are neither investing in a common enterprise nor relying on anybody's essential managerial efforts, because "the value of such a Redeemable Wrapped Token is derived from the value of the deposited crypto asset and not from the efforts of any third party involved in the wrapping process". The wrapping itself the Commission calls "an administrative or ministerial function".
The other branch is stated in the same paragraph: "In contrast, the offer or sale of a Redeemable Wrapped Token that is a receipt for a digital security or a non-security crypto asset that is subject to an investment contract is an offer or sale of a security". A receipt inherits the character of what it is a receipt for. So the securities question about a wrapped token is not a question about wrapping at all; it is the question of what was deposited, which is the subject of the security page.
The conditions are the part a reader should carry away, because the Commission's conclusion is scoped to a specific arrangement rather than to wrapped tokens as a class. It requires that the token be backed one for one, that it be redeemable one for one, that the deposit be locked up and unusable by the provider, and, in the release's own words, that the provider generate the tokens "without directly or indirectly offering any return, yield, profit opportunity, or additional good or service". A real-world arrangement that pays a yield on the wrapped position, or that is not fully backed, or whose provider lends the deposit out, is not the arrangement the release analyzed, and nothing in the release says how it would come out.
Two boundary notes. A stablecoin is not a wrapped token: it is a token designed to hold a fixed value against a reference asset, usually the dollar, and the Commission treats stablecoins as their own category, whereas a wrapped token is defined by reference to a deposited crypto asset it redeems for. And whether wrapping or unwrapping is a taxable disposal is a genuinely open question: no federal guidance this page could cite addresses it, and the general property rules on the crypto taxes page are where the analysis starts.