So my ti fix gear passes your test. It almost passes the l'Eroica test. (Ti frame - marginal though inspired by a ride I has on a Merlin, 1989, Like that bike, the fork is steel, 1" threaded and quilled. Aero brake levers. (I hated the brake cables in 1977! NOT going back!) Pedals are Shimano 600 semi-platforms. Probably late '90s but fully toestrap, clips and slotted cleats. Fully there on intent. Just easier to get into.

My steel fix gear is actually a bigger stretch of the intent, Same aero levers. And gearing with a triple up front and a 2-sided track hub with a "dingle"on one side. (It's all 1/8" so Surley's version doesn't work and mine is custom made. End result is a 3-speed fix gear that requires stops and a wrench to shift but can run true mountain gearing. (Well, up to a 24 tooth rear, Haven't found an 1/8" cog that's bigger yet.)

Both of these bikes (with sewps; haven't done that yet) could have been the evolution of racing bikes had freewheels had never been invented and rear hubs stayed nutted. The ti bike rides like a full on (fictional) 1980's fix gear racing bike (and is one of the most ear-to-ear-grin fun bikes I have ever ridden.

Oh, both these bikes run extra wide track handlebars that look out of some past era. Fix gear - all day in the drops and comfortable can be very important with headwinds without that 1 cog downshift! Wide on long standing climbs is really good! And wide,non-aero is your friend on high speed, ridiculous RPM descents! The Pista bar "shoulders" are wonderful for seated power climbing. (Seated climbing and spinning just doesn't happen on fix gears.)

Edit: I just realized this bike does have one modern feature - the 12-24 11-speed "cluster". Quite literally. I hang my cogs not being used in order on a bailing wire from hooks. The cluster. When the bike went on Cycle Oregon, the cluster went into my bike tools box.

Ben