Original ledger status
METROLOGY.CLOSURE.01
METROLOGY.CLOSURE.01
THE FINAL INPUT SET {a, pi, v_geo} CERTIFIED (2026-06-24, Paper D / the scale-modulus closure): 0 dimensionless dials + 1 dimensionful unit, consolidating v153 (No-Unit), v274 (over-determined anchor), v364 (gravity adds no unit), v384 (v_geo is theorem-forbidden, type B). Does NOT 'solve' v_geo (a dimensionless compiler provably cannot output a scale); it CERTIFIES the single declared unit. [E] INPUT SET: a=(1,1,2) -> elem-sym (e1,e2,e3)=(4,5,2)=(|mu4|,g_car,|Z2|), c3=1/(2 e1 pi)=1/(8 pi); the one dimensionful input is v_geo, NO dimensionless dial. [E] DIMENSIONAL BOOKKEEPING (No-Unit, v153): mass~v_geo^1, 1/G~v_geo^2, Lambda~v_geo^4, U_point~v_geo^1, m/mu=e^{3/4}~v_geo^0; under L->lambda L a dimensionless datum is invariant while v_geo^d scales as lambda^{-d}, so a scale cannot be a function of scale-invariants -- v_geo is a forced INPUT. [E] GRAVITY ADDS NO UNIT (v364): 1/c3=8pi and (8pi)^2*48 c3^4=3/(4pi^2) are dimensionless. [N] OVER-DETERMINATION (v274): gravity route (8 pi G)^{-1/2}=2.4353e18 GeV vs cosmology route 2.438e18 GeV agree to 0.11% (conditional on the Lambda-branch). [O] v_geo THEOREM-FORBIDDEN: TOE_strict = TOE_dimensionless + [v_geo], not 'derive the metre' (v384 type B). [2026-08-03 LIII: sharpened to torsor language by v725 (VGEO.TORSOR.01): the input set {a, pi, v_geo} is the calibration point of a rank-1 R+ scale torsor; the bookkeeping table of this row is the machine-verified export table there; no status move.]
Recorded status: Metrology closure [E]/[N]/[O] (Paper D: the final input set {a,pi,v_geo} -- 0 dimensionless dials + 1 unit; dimensional bookkeeping over all dimensionful observables; G-vs-Lambda over-determination 0.11%; v_geo theorem-forbidden). A metrology end-cap, no new derivation
Dependencies, status detail and source
Canonical status: [E] the input-set reduction to {a,pi,v_geo} + the dimensional bookkeeping (mass/1G/Lambda/U_point/(m/mu)=number x v_geo^{1,2,4,1,0}) + gravity-adds-no-unit; [N] the 0.11% G-vs-Lambda over-determination (conditional, v274); [O] the theorem-forbidden typing (TOE_strict = TOE_dimensionless + [v_geo]). A metrology end-cap (consolidates v153/v274/v364/v384); no new derivation, no new number.
Dependencies: RESIDUAL.CERTIFICATION.01; ANCHOR.VGEO.01; v153; v274; v364; v384
Scripts: v401_metrology_closure.py
Location: tfpt_research_contracts
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