Heisenberg naturality for the r_R pairing (Lemma 5.6), and the traced-row re-export #
The dévissage χ-layer needs two traced ingredients over the Roe complex:
- the traced Stokes rows
prop_5_8_left_R/prop_5_8_right_R(⟦lem:stokes⟧) — the chain identitiesB^R(d⁰a, y) = ⟨a, L^{A^∨}(y)⟩making theχ-maps well-defined. These are ticket R25's (GQ2/Roe/TrivialSelfDual.lean), landed withtrivialSelfDual_R; this file re-exports them (public import), never re-proving them; - Lemma 5.6 (⟦lem-heisnatural⟧), the coefficient-naturality square of the traced pairing
B^R_{A'}(f∗x, y') = B^R_A(x, f^∨ y'), needed by theχ¹/δ-square rungs. R20 taggedlemma_5_6pure-(A); its wild half (Marking.map_wildValue) is in fact word-coupled, but the port is verbatim — the only change is the finalsimpswappingmixedB/Marking.map_wildValueformixedB_R/Marking.map_wildValueR. R25 does not need it (the trivial module has no coefficient maps), so R26a provides it here (mechanical clone,docs/orchestration/roe-r20-recon.md).
theorem
GQ2.FoxH.lemma_5_6_R
{C : Type u_1}
[Group C]
{A : Type u_2}
[AddCommGroup A]
[DistribMulAction C A]
{A' : Type u_3}
[AddCommGroup A']
[DistribMulAction C A']
[Finite A]
[Finite A']
[Finite C]
(f : A →+ A')
(hf : ∀ (g : C) (a : A), f (g • a) = g • f a)
(t : Marking C)
(x : Fin 4 → A)
(y' : Fin 4 → ElemDual A')
:
Lemma 5.6 (strict coefficient naturality) for the Roe pairing (R-clone of lemma_5_6,
GQ2/FoxHeisenberg/Traced.lean): B^R_{A'}(f∗x, y') = B^R_A(x, f^∨ y'). Verbatim port — only the
final simp swaps mixedB/Marking.map_wildValue for mixedB_R/Marking.map_wildValueR.