The Lean formalization of carrier rank uniqueness
Original ledger classification: Formal
Recorded statement: Theorem A (carrier rank uniqueness g_car=5) machine-formalised in Lean 4: the Pascal carrier condition 2^(g-1)=C(g,0)+C(g,1)+C(g,2), division-free 2^g=g^2+g+2, has the UNIQUE solution g=5 (theorem carrier_rank_pascal_unique: forall g,…
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
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FORM.CAR.01
Original ledger classification: Formal
Original claim text
Theorem A (carrier rank uniqueness g_car=5) machine-formalised in Lean 4: the Pascal carrier condition 2^(g-1)=C(g,0)+C(g,1)+C(g,2), division-free 2^g=g^2+g+2, has the UNIQUE solution g=5 (theorem carrier_rank_pascal_unique: forall g, 2^g=g^2+g+2 <-> g=5; growth lemma pascal_growth for g>=6; g_car_unique ExistsUnique; carrier_closure_integers N_fam=(2^4-1)/5=3, g+N_fam=8=rank E8). AUDIT: PASS (no sorry/admit, no domain axioms, only propext/Classical.choice/Quot.sound). Complements FORM.P2.02 (P2 carrier algebra)
Original classification detail
Formal [F]
Dependencies as recorded
AX.P2.01; CAR.UNIQ.01; v6; v14
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- Architecture, E8 and the electromagnetic fixed point
- E8 audit and bootstrap
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