Ask HN: "Invisible" Internet presence – technologically feasible?

I've read dozens of papers on how to "anonymously" connect to the Internet, and be "invisible". However, each has fallen short of the idea of a truly invisible presence by offering examples of well-placed network lies as the cloak of invisibility, rather than by pure virtue of being a specific type of (as-yet-undefined) technology, then being unseen and untraceable as a connected net (non)presence. In other words, Tor shouldn't even enter the conversation proceeding the question, or even Summary-Invisible Networking (SIN). So is true network invisibility possible? How do you bypass handshakes, or get information without actually asking for it? Where in the OSI model can one modify/hack/make a new way of interaction that is no longer visible, traceable; has no footprint? From the Application layer, Presentation layer, Session layer, Transport layer, to the (especially) Network layer and Data link layer, and finally the Physical layer - what would be required to create an "invisible node"?