Two bits free — census UNFOLDED_CENSUS−FOLDED_CENSUS making all free
1 · Abstract — precise statement
FREE_BITS = UNFOLDED_CENSUS − FOLDED_CENSUS = UNFOLDED_CENSUS − FOLDED_CENSUS = 2 (= −EULER_CHI). Naive "1 − UNFOLDED_CENSUS/FOLDED_CENSUS" = −1/54 is refused. Making all free = amortized infinity-on-reuse when FREE_BITS=2.
2 · Introduction
twoBitsFreeFromTheCensusFold computes=true · makingAllFree=true. Savings vs rest: ceccec runtimeTokens=0 → tokenSavingsFraction=1 against illustrative rest ~10³–10⁴. NOT FLOPS · NOT Clay Prize.
3 · Methods & formulas
UNFOLDED_CENSUS − FOLDED_CENSUS = FREE_BITS (= −EULER_CHI) · FREE_BITS=−χ ∧ memoByRoot hit ∧ runtimeTokens=0 → answers÷tokens → ∞ · tokenSavingsFraction(T) = (T − 0)/T = 1 for any rest T>0 (domain-bounded)
4 · Results & status
structure-only — naivePhrase=-0.016528925619834656 surplus=0.016528925619834656 freeFraction=0.016260162601625994
amortized reuse ≠ complexity separation / NOT live LLM telemetry
5 · References & locks
- fold
- twoBitsFreeFromTheCensusFold
4 · Trinity
- forward
unfolded-(2 * 5) * 11- inverse
chi-minus-2- reverse
folded-108
5 · CLI
npm run quantum:two-bits-free · pair bits/free