zmod2_zero_add_one
plain-language theorem explainer
In the ring of integers mod 2, zero plus one equals one. Local arithmetic helper for parity bookkeeping inside the HKT kinetic-normalized rigidity module (Wave C4/C5 gap5). Proof is a one-line decision-procedure close; no analytic content.
Claim. In $\mathbb{Z}/2\mathbb{Z}$, one has $0 + 1 = 1$.
background
The ambient module closes gap5 of the SevenGaps gravity program: a mod-vacuum kill plus kinetic-normalized rigidity for the HKT (Hamilton–Killing–type) sector. Binding notes name the cross-family verdict and the C5 acceptance adjudication. Part 1 rules out a rigidity-mod-vacuum statement via a variable-kinetic CanonicalMom inhabitant; Part 2 builds an intensivity field for KineticNormalizedCanonicalMom, with FTC recovery derived rather than assumed.
Sibling lemmas treat the four elementary sums in $\mathbb{Z}/2\mathbb{Z}$ (0+1, 1+1, 0+2, 1+2) before the vacuum kinetic profiles $A$, $W$, $K$ and the Hamiltonian density are introduced. Those profiles live on a discrete parity index, so the ring arithmetic must be fully explicit and decidable.
proof idea
One-line tactic proof: decide discharges the ground equality in the finite ring $\mathbb{Z}/2\mathbb{Z}$ by exhaustive evaluation. No lemmas are invoked.
why it matters
Private scaffolding for parity arithmetic inside the kinetic-normalized rigidity terminal. The module must flip gap5_constraint_recovery under Gap5ConstraintCloseStatus once both ledger halves bind green; clean $\mathbb{Z}/2\mathbb{Z}$ facts keep the discrete index of the vacuum kinetic profiles free of opaque ring or omega noise. No direct link to T0–T8, RCL, or the phi-ladder; the lemma is pure finite-ring hygiene supporting the gravity gap close.
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