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A registered result in its source context

Original ledger classification: Identity [I] (scaling bookkeeping) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration)

Recorded statement: NO-UNIT THEOREM (v_geo re-typed from open gap to CLOSED METROLOGY STRUCTURE -- R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis, v153/v725; external review 2026-06-13 formalised, wave-4 display wording…

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ANCHOR.VGEO.02

Original ledger classification: Identity [I] (scaling bookkeeping) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration)

Original claim text

NO-UNIT THEOREM (v_geo re-typed from open gap to CLOSED METROLOGY STRUCTURE -- R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis, v153/v725; external review 2026-06-13 formalised, wave-4 display wording 2026-08-29): (1) every load-bearing compiler datum (g_car, |mu4|, N_fam, rank E8, alpha^-1, det(Q,K,R,L)=(3,4,8,20) product 1920, c3=1/(8pi), 2pi c3=1/4, phi0) is mass-dimension 0 and INVARIANT under a unit rescaling L -> lambda L [I]; (2) a mass / energy / 1/G carries nonzero dimension and transforms as lambda^{-d}, d != 0, so a map from dimension-0 inputs to a dimension-d output is simultaneously invariant and covariant - impossible unless the unit is introduced => v_geo is a FORCED INPUT, not an output [I]; (3) the three apparent residuals collapse onto the one unit: U_point ~ v_geo (dim 1), 1/G ~ M_Pl^2 ~ v_geo^2 (dim 2, 4d [G]=mass^-2), m/mu = e^{3/4} (dim 0, a pure ratio, v152) [I]; (4) irreducibles stay exactly {one dimensionful unit v_geo, pi} (v78/v68/v152 name the same object). RE-TYPING [A]/[O]: v_geo is a CLOSED METROLOGY STRUCTURE (R_+ unit torsor), not an open-physics gap; display stays [O] as the unit/calibration (no [E] of physics). Legacy stem: 'irreducible metrology primitive' - a declared unit (like choosing a metre), not a missing derivation; a dimensionless boundary compiler provably cannot produce an absolute scale [2026-08-03 LIII: the v_geo interface is now STRUCTURALLY CLOSED as an R+ scale torsor (v725, 21/21, VGEO.TORSOR.01): complete export table O_i = r_i v_geo^{d_i}, dimension matrix rank 1 (conditional [A] on the flavor block, named), all consistency conditions lambda-homogeneous -- the machine form of THIS theorem -- leave-one-anchor-out compatible (G vs rho_Lambda 0.11%), and the CALIBRATION THEOREM stated in torsor language (one external reference selects the point; everything else is prediction). Status unchanged: the closure is the calibration form, not a scale derivation; the one open dimensionless ratio is NAMED, H_EW = ln(Mbar/v_EW) = 37.1776.]

Original classification detail

Identity [I]: No-Unit Theorem; v_geo = irreducible metrology primitive, three residuals collapse to one unit | 2026-08-29 wave-4 display retype: CLOSED METROLOGY STRUCTURE (R_+ unit torsor; one dimensionful calibration necessary by dimensional analysis). No [E] upgrade of physics. WAVE-5 (2026-08-29): unit choice closed; dimensionless hierarchies (M_Pl/v_EW, M_R/M_scal, Lambda_QCD/v_EW, T_reh/M_scal) remain predictive obligations.

Dependencies as recorded

ANCHOR.VGEO.01; FLAV.UPOINT.01; SEAM.EHMODEL.03; v68; v78; v152

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  • v153_no_unit_theorem.pyRegistered verification module · registry
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    No-Unit Theorem (v_geo re-typed): dimensionless data are scale-invariant under L→λL, a mass/1/G is not, so a dimensionless compiler cannot select an absolute scale; the three residuals collapse — U_point ~ v_geo, 1/G ~ v_geo², m/μ = e^{3/4} (a ratio); v_geo is an irreducible metrology primitive, not an open gap; irreducibles stay {one unit, π}

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