axiom Q2Presentation.Induction.q2_trivialCoeff_h2_line {GQ2Profinite : ProfiniteGrp.{0}} : IotaToken GQ2Profinite

H²(G_{ℚ₂}, ℤ/2) is a line — the trivial-coefficient degree-two cohomology of the absolute local Galois group at the single copy of ℤ/2 has dimension exactly 1, consumed here in the strictly weaker cocycle-level token form (dim ≤ 1): two non-cobounding normalized continuous 2-cocycles sum to a cobounding one.

EXACT-CITABLE (audit/CITABILITY_AUDIT_20260708.md §H, verified verbatim against NSW 2nd ed. v2.3, errata clean):

• NSW (7.1.8)(ii): H²(k, μ_n) ≅ (1/n)ℤ/ℤ — at n = 2, with μ₂ = {±1} ⊆ ℚ₂ˣ carrying the TRIVIAL action (so μ₂ ≅ ℤ/2 as G_{ℚ₂}-modules), this is the direct numbered statement h² = 1.
• NSW (7.2.6) at A = ℤ/2, i = 0 (concordant second anchor): H²(k, ℤ/2) ≅ H⁰(k, ℤ/2)* = ℤ/2. The solvability dictionary (CochainSolvable = existence of a locally-constant — equivalently continuous into discrete ℤ/2 — cobounding 1-cochain) is the DEFINITION of continuous-cochain H² at this carrier; the token asserts dim ≤ 1, strictly weaker than the citation's = 1.

LOAD-BEARING GUARDS (§H): SINGLE copy of ℤ/2 only — the token is FALSE already at untwisted (ℤ/2)² coefficients (h² = 2); normalized-cocycle law and local constancy on the Fᵢ are required; Γ is pinned to GQ2Profinite (no open-subgroup or twisted-module quantifier).