[orgopete]

Note: although alternate resonance forms have been invoked, I do not agree the additional structures are resonance forms. They are oxidation products of a cumulene or dicarbon dioxide.

I'm not sure what you are referring to here, particularly the bold part (bolded by myself).

Since the additional structures did not include curved arrow or charges, I could not be certain whether they should have been resonance structures or not.

If I convert these to compounds, then "C=C=C=C (etc)" can be C4H4  and "-C≡C-C≡C-" can be C4H2. 

Similarly, "O=C=C=O" can be "(+)O≡C-C≡O(+)". I'm a little lazy to draw out resonance structures, but I might have drawn (+)O≡C-C-O(-) as a resonance structure with the carbon a neutral carbene. If the starting structures were uncharged, then the resulting structures should have charges as I understand resonance structures.

[Corribus]

Ah, I see.  I apologize then for the confusion - was intending to speak generally, not a C4 compound in specific, and I was lazy as well and didn't draw any end groups.  In the polymeric limit you tend to see bond alternation rather than all bonds being the same length, as you might expect for a true and equal resonance like benzene.  This is one of the reasons why polyacetylene and other conjugated polymers are semiconductors instead of metallic.

Lacking any experimental data it's hard to know if that is going on in the compound under consideration (available theoretical data is inconclusive) and in any case the rather electronegative end groups (the oxygens) will have big effects in such a short molecule.  The problem is that the molecule is so short-lived that experimental data is almost wholly lacking, which makes it hard to make any compelling argument either way.  All we have to go on is chemical intuition, some scant theoretical work, and comparison to similar molecules.  Spin states almost certainly play a role, but given this is an in undergraduate level forum, the argument I gave in the previous post is the best one I could think of.  Most likely the enthalpic and entropic favorability, plus the kinetic favorability (unimolecular eliminates any need for collision-dependent rates), plays a large role in the short-lived nature of the molecule under consideration.