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Thank you for your question!

We are almost there, but I want to reconsider one final component of the definition. That is the phrase "life v non-life"; I'd like to see in your own words what you mean by that. I've been taking it in the sense of 'why are things this way, and not that way' .. in other words, any feature of existence or of reality can be deemed a "feature of life v non-life" in some sense or other. Stated yet differently, everything is life or non-life or some variation/subset/quality thereof.

But, it occurred to me that you may intend to signify something more narrow by this contrast. So, I want to see what precisely you mean by "life v non-life" (and, for that matter, I'd like to know why you generally phrase it "life v non-life/death in nature").

Indeed, I have a narrow construction of the term based on Claude Shannon's mathematical theory of communications which is useful to delineating between "what is life v. non-life/death in nature".

Claude Shannon's theory is the origin of the field of mathematics known as information theory and is used in pharmaceutical and cancer research among other things. The discipline is generally known as "information theory and molecular biology".

Here is my post from another thread:

Information is that which distinguishes life from non-life/death.

Information, paraphrased as “successful communication” is the reduction of uncertainty (Shannon entropy) in a receiver or molecular machine in going from a before state to an after state. It is the action, the communication itself, the arrows on the chart below. It is not the message. The value or meaning of the message being transmitted has no bearing on the model.

Two quick thought experiments for Lurkers:

Consider the difference between a live skin cell and a dead skin cell from the same person, e.g. the DNA and chemicals are as good dead as alive.

Consider what would happen if you dropped a live bird, a dead bird and a cannonball from the rooftop.

Successful communication includes all of the named elements. In biological systems these elements should be interpreted as follows:

source = the inception, beginning or initiation of a communication:

interrupt (e.g. presence of food, heat, radiation, other environmental change)

cycle (e.g. rhythm, timing)

will

involuntary, the “will to live” or “want to live” or “struggle to survive” which characterizes all life, plant and animal, amoebas to whales, collectives of organisms, molecular machinery within organisms integrated cooperatively for the organism to survive, individual cells. Also known as life principle and fecundity principle.

voluntary, “self-will” or "free will" such as intention, abstraction, anticipation, choice. Examples include the will to move a finger, analyze a problem, envision a plan, fly away, etc.
message = genetic message in DNA (including tRNA)
encoder/transmitter = transcription into mRNA
channel (channel code is mRNA code)
decoder/receiver = translation into protein
noise = genetic noise (mutations, viruses), noise in genetic code (tRNA), prions

Applied to the enigmas, this definition would interpret all of the following as living with the following restrictions:

Bacteria - autonomous successful communication

Bacterial Spores – autonomous successful communication

Mycoplasmas – autonomous bacterial model parasite successful communication

Mimivirus – autonomous virus model parasite successful communication

Viroids – non-autonomous virus-like noise/mutation contributing to successful/failed communication (no protein coat)

Viruses – non-autonomous virus noise/mutation contributing to successful/failed communication (feeds genetic data to the host)

Prions – non-autonomous protein noise/mutation contributing to successful/failed communication (protein crystallization)

There is so far no known origin for information (the successful communication) in space/time. This should be visualized as activity represented by the arrows on the above chart. Possible origins include a universal vacuum field, harmonics, geometry.

If you have an alternative mathematical definition, I'd love to see it!