Rule for the old pages: anything marked ✗ gets crossed out; the ✓ line beside
it is what replaces it.
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✓ R = 1 − (V − Vmin) / (Vmax − Vmin + ε)
V = this candidate's cost; Vmin/Vmax over the sibling set; ε > 0 tiny.
R = 1 for the best cost, → 0 for the worst.
✓ Floor comes out by itself: Rmin = ε / (s + ε), s = Vmax − Vmin
✗ old hand-set floor 0.01 — cross out, never set a floor by hand again.
✗ old GS-based R — cross out (divide-by-zero at GS = 0).
✓ R_φ = φ^(−2θ/π) θ = 2π·k/(n−1) k = cost rank (0 = best of n)
φ = (1+√5)/2 = 1.618…
Same thing written your notebook's way: R_φ = e^(θ·ln φ / (π/2)) run
inward — resonance decays by one golden ratio every quarter turn.
Best keeps R_φ = 1; the worst of the set keeps φ⁻⁴ ≈ 0.146.
STATUS: beat the straight-line R on BOTH validity and cost,
10 seeds × 300 = 3,000 instances (z = 3.67 and z = 3.05).
In the engine: [config flag]=1 (value-form, partial gain; rank-form is the
full gain and the upgrade path).
✓ χ = clip to [0,1] of ( v / vmax ) v = violation size
✗ old steps {1.0, 0.6, 0.1} — cross out (made an 81:1 cliff).
✓ BEST FORM — CAPX (won its 3,000-instance study):
χ = dip / (repair the remaining future can actually reach)
χ = 1 exactly when the dip can no longer be repaired → gate turns hard
at true irreversibility, stays graded before it.
WARNING (proved by breaking it): the repair bound must be SOUND — never
overestimate reachable repair, or χ < 1 on branches that are already dead.
✓ g(R) = R² / (2 − R) range (0,1], strictly increasing:
g′(R) = R(4 − R)/(2 − R)² > 0. Your first page's R² lives in the top.
✓ Ĉ = g(R) · (1 − χ)² always in [0,1]
Ĉ = 1 only at best-cost AND fully valid; Ĉ = 0 at full violation.
✗ the p in Φ = p×R²×(1−χ) — cross out: same p for all siblings at one
depth, so it never changed a ranking (0 of 2,000). p stays only as the
cross-depth priority.
NOTE, honest: your linear (1−χ) tested equal-validity and CHEAPER on one
family. The square is kept for the clean algebra below, not because it
beat your original.
✓ prune a branch iff Ĉ < θ θ ≈ 10⁻³, or θ = β·(best Ĉ in set)
✗ old dual gate X > θ·Xmax OR P < ε — cross out, one floor covers
both (proved; it prunes slightly MORE — superset, known and accepted).
✓ X = χ·(1 − R) read it, log it, NEVER gate on it.
✓ χ* = 1 − √( g(R_A) / g(R_B) )
A valid-but-costlier branch beats an invalid-but-cheaper one exactly when
the cheaper one's violation exceeds χ*. Costs close together → χ* small →
even mild violations flip the order. Verified on 2,000 pairs, 0 misses.
✓ LAW 1 (redundancy): if violation just tracks cost, sorting by Ĉ IS
sorting by cost — the whole apparatus adds nothing. Know when to not
use your own tool.
✓ LAW 2 (guidance): if violation carries information cost doesn't,
Ĉ makes orderings NO cost-only sort of any width can make.
✓ Association spreads hop by hop, each hop worth 0.7^h of its score,
h = 1…5, default 3. Knob: [config flag].
✓ Answer judged GOOD → chain LTP at dopamine 0.95,
each cell's confidence + 0.05 (cap 5.0)
✓ Answer judged BAD → each chain synapse weight × 0.90,
each cell's confidence × 0.97
Small on purpose: one click nudges, repetition sculpts, decay forgets.
✗ cos(χπ/2) "Born rule" second gate — classical taper, double-counted χ.
✗ τ scaling — a positive constant never changes a sort.
✗ Discrete χ steps — replaced by the continuous χ and the crossover.
✗ Bridge damper mean(Φ_A, Φ_B) / (1 + |χ_A − χ_B|) — REFUTED
(your own margin note called it: "too blunt"). For two constraints
use the joint gate g(R)·(1−χ_A)²·(1−χ_B)² or Deb's rule
(feasible-first); the set-level Bundle(top-k) is still open.
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Every ✓ above has a proof or a pre-registered experiment behind it in
[local path]✗ has the test that
killed it in the same folder. Nothing on this page is old.