# Results — leftover RAR book does not take DE as an ingredient

### KiDS GGL measurement stands · KiDS cosmology not a match · \(H_0\) clothes \(\neq\) expansion theorem · no mill to reopen

**CPT Framework — FT-DE-NO-MATCH / FT-RAR-DE-DECOUPLE**  
**Date:** 2026-09-24  
**Status:** **BANKED** · `PASS_FT_DE_NO_MATCH_RAR_DECOUPLED`  
**Stimulus:** User — if any RAR book depends on DE, revisit immediately and make it DE-free  
**Parents:** `a_geom_ft_de_no_match_freeze.md` · `a_geom_ft_gap_b_outer_results.md` · `a_geom_ft_s3_phi_results.md` · `a_geom_ft_foam_de_results.md` · `a_geom_ft_sparc_astar_results.md`  
**Script:** `scripts/investigations/s3_geometry/ft_de_no_match.py`  
**Data:** `scripts/investigations/s3_geometry/data/ft_de_no_match.json`

Tags: **[E honesty]** · **[Programme]** · **[O residual]**

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## 0. One-line

> **Nothing in the constitutive RAR line *uses* dark energy.** The photon extra-\(\Phi\) kill is KiDS **galaxy–galaxy lensing** published ratios (\(\langle V_{\mathrm{lens}}/V_{\mathrm{BTFR}}\rangle\simeq 1.10\)), not KiDS cosmic-shear \(S_8/w(z)\). SPARC, inner Einstein rings, analytic-\(W\) Newton IR, yield, SS Pythagorean FIRE, and \(c_{\mathrm{gw}}=c\) do not ingest \(\Omega_\Lambda\) or \(q_0\). \(H_0\) appears only as leftover **clothes** (\(R=\sqrt{6}\,c/H_0\), \(cH_0/6\) vs SPARC \(a_0\)), already **[M]**, already not leftover \(\dot R/R\). Two mills *mention* a \(\Lambda\) fluid as a **foil** (FT-S3-PHI \(g_\Lambda\); FT-FOAM-DE scale rhyme): those are “this is not that,” and they are now forbidden as match targets. No RAR mill is reopened. Prize OPEN.

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## 1. Census

| Mill | DE as input? | Action |
|------|----------------|--------|
| FT-GAP-B-OUTER / MA-LONE | No. GGL table | Keep as measurement CAT-EVID |
| FT-RAR-CURVE KiDS IR | No. Same table | Keep; not KiDS cosmology |
| SPARC / FT-SPARC-ASTAR | \(H_0\) clothes only | Still **[M]**; not expansion |
| FT-S3-PHI \(g_\Lambda\) | Foil | Fence: not a RAR board |
| FT-FOAM-DE | Contrast with \(q_0\) | Already not paid; not a target |
| Yield / \(W(E)\) / prize pin / keyhole / SS / GW | No | Untouched |

**Finding D1 [E honesty].** A later reader must not cite KiDS extra \(\Phi\) as “we fitted DE.” The discriminant is stacked shear vs baryon Kepler/BTFR in a published GGL table.

**Finding D2 [E].** If the published \(300\,\mathrm{kpc}\) conversion used a \(\Lambda\)CDM \(D_A\), that is the catalogue’s ruler. The mill does not vary \(w(z)\) or \(\Omega_\Lambda\) to improve the ratio. Dimensionless \(V_{\mathrm{lens}}/V_{\mathrm{BTFR}}\sim 1.1\) is the kill of lone \(m(a)\).

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## 2. Integrity

| Gate | Verdict |
|------|---------|
| RAR DE-free as ingredient | **YES** |
| KiDS cosmology matched | **NO** |
| Reopen leftover mills | **NO** |
| Expansion granted | **NO** |
| Prize closed | **NO** |

**Exit:** `PASS_FT_DE_NO_MATCH_RAR_DECOUPLED`

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## 3. One-line for agents

> **§FT-RAR-DE-DECOUPLE: constitutive RAR has no \(\Omega_\Lambda/q_0\) ingredient; KiDS GGL stays measurement CAT-EVID; do not match KiDS DE cosmology; \(H_0\) clothes \(\neq\) expansion; prize OPEN.**