the altimeter setting and the sea-level pressure are one field read through two profiles
Theorem.the altimeter setting and the sea-level pressure are one field read through two profiles — Alt^κ = (P − 0.3)^κ + C·h, C = 1013.25^κ·L/T₀ ⇒ P = (Alt^κ − C·h)^(1/κ) + 0.3; Stn(A,h) = A·((T₀ − L·h)/T₀)^5.2561 ⇒ Alt(Stn(A,0),0) − A = −0.3 ∀A, and ∂|Alt(Stn(A,h),h) − A + 0.3|/∂h > 0.
Proof.a pilot's altimeter setting and a meteorologist's sea-level pressure are the SAME station pressure reduced to sea level through two different temperature profiles — the standard atmosphere for the one, the air actually over the station for the other — so the difference between them is a thermometer rather than a discrepancy. The United States publishes both reductions as separate NWS wxcalc worksheets AND THEY ARE NOT INVERSES. Expanded, the altimeter worksheet is Alt^κ = (P − 0.3)^κ + C·h with κ = 0.190284 and C = 1013.25^κ·0.0065/288, which has an exact closed-form inverse that returns a reading to 4.5e-13 mb; composing the two PUBLISHED worksheets is out by up to 4.20 mb, 42 counts of the 0.1 mb step observations are coded to. The gap decomposes into named causes rather than a magnitude: an offset subtracted by one sheet and never restored by the other, worth exactly the same amount at sea level for every pressure, and a disagreement between the exponents 5.2561 and 1/0.190284 = 5.255303 that grows with height, over a third cause that is structural — the altimeter correction is pinned at 1013.25^κ while the station correction scales with the reading, so the two agree near a standard atmosphere and separate away from it. A FACET OF THIS FOLD WAS ITSELF UNFALSIFIABLE FIRST: it asked whether the sea-level error equalled the offset constant that had just produced it, so both sides moved together and setting the offset to zero left the facet TRUE; it now asks whether the sea-level loss is independent of pressure and non-zero, which zero cannot fake. FRONTIER: the sea-level reduction the barometer actually uses is not published in wxcalc, the ASOS User's Manual or NWS directive 10-1302, and FMH-1 refuses a keyless fetch with HTTP 403 — a lead with an address, not a caveat.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/earth/nature/index.ts#pressureReductionsAreOneField
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"the altimeter setting and the sea-level pressure are one field read through two profiles" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation pressureReductionsAreOneField.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (pressureReductionsAreOneField @ src/earth/nature) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes pressureReductionsAreOneField (src/earth/nature/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.