FlatnessFalsifier
plain-language theorem explainer
FlatnessFalsifier encodes the three conditions that would refute the Recognition Science account of spatial flatness. A cosmologist testing RS predictions would cite it to state the empirical or theoretical rejection criteria. The definition assembles the propositions into a single implication to falsehood with no derivation steps.
Claim. A structure whose fields are the proposition that the measured density parameter differs from unity beyond uncertainty, the proposition that the J-cost function has no minimum at flatness, the proposition that no phi-relations hold among cosmological parameters, and the implication that the disjunction of these three yields falsehood.
background
The module treats the flatness problem: the density parameter satisfies Omega = 1.0000 plus or minus 0.0002, yet deviations grow proportionally to a squared of t, demanding extreme early-time tuning. Recognition Science resolves this by requiring Omega equals 1 as the sole value consistent with ledger structure, with critical density arising from J-cost minimization and phi-constraints locking parameters. The upstream cost definitions supply the J-cost as the derived cost of a comparator on positive ratios from MultiplicativeRecognizerL4 and as the J-cost of a recognition event state from ObserverForcing.
proof idea
As a structure definition it directly assembles three propositions and the implication to falsehood. It references the cost definitions from MultiplicativeRecognizerL4 and ObserverForcing but applies no lemmas or tactics.
why it matters
It supplies the explicit falsification criteria for the RS flatness solution that rests on J-cost minimization at critical density together with phi-constraints. This sits inside the forcing chain from J-uniqueness through the phi fixed point to the eight-tick octave and D equals 3. No downstream theorems are recorded, leaving it as an interface for future tests against Planck-scale observations.
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