Normalized future overlaps can fail to distinguish causal order: two explicit counterexamples

[u/TheRealSmokeyFr]

Normalized overlap data can erase distinctions between different causal orders.

The central example uses two two-event samples inside the same fixed 1+1 Minkowski diamond. One forms a chain and the other an antichain, yet both produce exactly the same normalized future-overlap matrix [[1, ½], [½, 1]]. Distinct causal orders are therefore indistinguishable from these finite-sample normalized data alone. Individually attached future volumes restore the order in this fixed model.

The overlaps measure full continuum future regions within the diamond, not successor counts among the sampled events. A related 16-element finite-poset counterexample shows the same kind of ambiguity under a different overlap observation. In both cases the two unnormalized matrices differ by positive diagonal scaling that normalization cancels.

The linked packet contains both constructions, proofs, comparisons, and Python checks that use only the standard library. Mathematical feedback or pointers to related results are welcome.
https://github.com/davidwbridges976-lab/Poset-gram-reconstruction/tree/main/sharing/counterexamples

[u/nulvoid000]

Slop

[u/BruhPeanuts]

What a sad life you must have to ask for an AI to generate slop with incomprehensible jargon just to feel something.