SkyAudit: one real helicopter day, decided flight by flight

The traffic is adsb.lol's open globe history for 2026-08-26 (ODbL), pinned by sha256 at the release-tar level and extracted by a calibrated streaming reader (125,746 traces, 0 parse errors, dual-bbox split for NYC and São Paulo). An aircraft seen by both ADS-B and MLAT appears twice in the raw bytes; auditing dedupes to the richest trace per airframe in one place, and public counts always use the deduped number. Flights come from a certified segmentation with a monotonic-time contract — a scrambled trace throws, a 900-second gap splits, 60 seconds of ground contact closes a flight — and every truncation the receiver network caused is flagged on the flight it touched, never smoothed over.

Which aircraft count as helicopters is decided by ONE function, and since the registry joins it answers from authority first: the FAA Releasable Aircraft Database (joined by Mode S hex and N-number) and Brazil's ANAC RAB (joined by registration mark) supply the authoritative type — FAA TYPE-ACFT 6, ANAC class H — with the trace's own type designator deciding only for unmatched aircraft (military serials, one Canadian, a handful of reg-less transponders; each listed in the committed extract). On the pinned day the registries CONFIRM the trace filter exactly: membership changed nowhere, so 82/382/3,056 stand — on authority instead of feeder typing. The two jets squawking helicopter category (an A320 and a BD-500) are now excluded by the registry, not by a hand-kept list.

Each certificate decides: "if THIS observed flight — its distance box, with stated pads — were flown by THAT eVTOL, flying its own published speed box, does the energy used plus the rule's reserve fit inside usable battery, for EVERY parameter point in the boxes?" The eVTOL flies its own speeds over the helicopter's route; it is not asked to imitate a helicopter. Power comes from the momentum-theory model of Kasliwal et al. 2019 (Nature Communications), calibrated in the battery against that paper's own worked examples; physics unknowns (efficiencies, air density, hover budget) are stated boxes, padded outward.

The spec packs are the makers' own published numbers, each quality-flagged at the field level — measured, stated, or assumed. Eve publishes least, so Eve's pack is nearly all assumption and its ledger is nearly all NEEDS DATA: the audit measures ignorance rather than papering over it. Two reserve rules run side by side: the FAA powered-lift SFAR's 20-minute VFR tier, and EASA's 5-minute final reserve — the latter honestly labeled a NECESSARY condition only, since the full EASA energy-management package is not reducible to one number. The São Paulo city pack decides under Brazil's own rule instead: ANAC RBAC 91.151(b) — 20 minutes at normal cruise consumption, quoted from ANAC's pinned text — arithmetically the FAA tier, separately cited, because the jurisdiction is the point.

RE-FLY THE DAY: holding the 100 provable departures fixed and modeling charge occupancy from worst-corner depth against the published charge box, the minimum fleet is EXACT: 9 aircraft are REFUTED by pigeonhole at a witnessed instant, 10 are CERTIFIED by a greedy schedule verified exactly. Zero randomness; the timeline hashes into the record.

The certified thresholds, each proved on both sides of the flip: battery floors for half-day coverage — Joby needs 267 kWh nameplate against a published 130–180, Archer 309 against 120–142, Beta 318 (the only one close to its own number), Eve 304 — the gap between trade-press narrative and provable coverage, priced in kWh. The charge lever, read straight from the certified curve: 6 aircraft at 0–4 min to full, 7 aircraft at 5–22 min to full, 8 aircraft at 23–32 min to full, 9 aircraft at 33–40 min to full, 10 aircraft at 41+ min to full — faster chargers are provably worth 4 aircraft across the published charge box. And the reserve price: Beta's provable legs at 5/10/15/20/25/30 minutes of reserve are 215/195/153/100/14/0 — at a 30-minute reserve NOTHING on this day is provable. That is the FAA docket fight, priced flight by flight.

The day's helicopters burned 56,579–78,610 liters of Jet-A ($73,552–165,081, 141.4–200.5 tonnes CO₂) — from per-type class burn boxes, flagged as estimates. The 100 provable flights are different arithmetic: their energy is the certified used-enclosure sum — decided, not projected — and costs $290–2,056 of electricity against $3,966–9,902 of fuel for the SAME flights. The intervals are disjoint, and the page only says so because the comparison is computed at build — the sentence disappears if the data stops supporting it.

METHODOLOGY V2 (2026-08-27) — the recorded v1 conservatisms were resolved together, in one disclosed move, exactly as promised. What changed: (1) cruise energy is now evaluated V-FREE — at every parameter point t·P(V) = m·g·D/((L/D)·η) and the speed cancels exactly, so v1's independent enclosure of power and time was a sound over-enclosure (up to 34% at the widest cruise box); removing it is a tightness theorem, not a relaxed assumption, and the independent Python verifier re-proves the same identity. (2) Mission mass became an operating-mass box [published empty weight + pilot, MTOW] — Joby publishes empty weight, Archer and Beta publish payload; the strict MTOW corner still decides E-FLYABLE, so the floor only weakens refutations honestly. What was REVIEWED AND REFUSED BY THE DATA: reserve power at "normal cruising speed" — no audited maker publishes a normal cruise (only "up to" maxima), so the reserve keeps the full cruise-speed box; and per-aircraft disk loading — rotor geometry is unpublished for all four (only VoloCity, outside this set, has an official datasheet), so the class boxes stand. THE DELTA, quoted as history (git a07be1f): v1 certified 46 of these 382 flights (12%); v2 decides 100 (26%) — the interval slack was hiding half the provable day, and this paragraph is the disclosure.

One Wednesday is one Wednesday — which is why §7 measures a second, contrasting day instead of assuming stability. The corpus is what the receiver network saw — coverage gaps are flagged per flight, never interpolated. Operation-type labels in the app (tour loop, patrol, shuttle) are heuristics, labeled INFERRED, and judge nobody's mission. Names come from the registries and mean what the registries mean: the FAA publishes the REGISTRANT ("registered to" — often an LLC, not necessarily who operates), ANAC publishes the operador. And nothing here carries airworthiness meaning: every "certified" is a statement about interval arithmetic over published boxes.