A canonical valid active class word

The final single-scale assembly needs one fixed valid active (N,X) word against which the word-independent completed anchor coefficient can be normalized. The labeled-copy cardinal identity supplies a canonical arrangement, and its induced class word is automatically valid.

noncomputable def Anderson4D.referenceHeppArrangement {t : PlaneTree} (mu : t.Multiplicities) : HeppArrangement mu

A canonical labeled arrangement, obtained only from the cardinal ledger for labeled Hepp copies.

Equations

• Anderson4D.referenceHeppArrangement mu = Fintype.equivOfCardEq ⋯

noncomputable def Anderson4D.referenceNXWord {t : PlaneTree} (Nm : t.HeppMarking) (mu : t.Multiplicities) : Fin (totalMultiplicity mu) → ActiveNXClass Nm mu

A fixed active (N,X) word available for every marking.

Equations

• Anderson4D.referenceNXWord Nm mu = Anderson4D.arrangementNXWord Nm mu (Anderson4D.referenceHeppArrangement mu)

@[simp]

theorem Anderson4D.referenceNXWord_mem_validWords {t : PlaneTree} (Nm : t.HeppMarking) (mu : t.Multiplicities) : referenceNXWord Nm mu ∈ validWords (activeNXMultiplicity Nm mu)

The canonical reference word has exactly the prescribed active-class multiplicities.