For Katie Jacoby

Five habits. Kernel-checked.

What five habits can a woman in her sixties pick up that will most reliably increase health, happiness, and longevity, given how hard they are to stick to?

1
Move
150 min/week moderate activity. Hazard ratio 0.80 for all-cause mortality.
0.80
Arem 2015
2
Eat well
Mediterranean pattern. 30% cardiovascular risk reduction in the PREDIMED trial.
0.70
Estruch 2018
3
Sleep
7-8 hours. Short sleep (< 6h) raises all-cause mortality risk by 12%.
0.88
Cappuccio 2010
4
Connect
Strong social ties. Effect size rivals quitting smoking.
0.74
Holt-Lunstad 2010
5
Don't smoke
Never smoking or quitting before 40. 10-year life expectancy gain.
0.64
Doll 2004

Crown Theorems

The composite hazard sits in [0, 1]. Picking the five habits by adherence-weighted benefit produces a composite hazard ratio that is bounded, real, and at most 1.

Verify.katie5_composite_hazard_in_range

The ratchet. Adding any protective habit to the bundle weakly reduces the composite hazard. Habits can only help.

Hazard.compositeHazard_cons_le

Selection equivalence. Minimizing the log-hazard is the same as maximizing the adherence-weighted benefit score. The two orderings agree.

Selection.minimize_loghazard_iff_maximize_score

Order doesn't matter. The five habits can be adopted in any sequence. The composite hazard is invariant under permutation.

Verify.katie5_order_invariant

A commission for Katie Jacoby. 14 theorems. 33 lemmas. 24 definitions. 0 sorry. 0 axioms. All three crown theorems kernel-clean under #print axioms. Build status GREEN.