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This is a raw source document. Integrity tags [E] [M] [O] [F] are coloured for readability. Content is as written in the research file.

Results — leftover’s only scale eliminates other RAR organizers; \(a_{\mathrm{ext}}\) is not eliminated

Isolated well: unique \(y=g_N/a_0\) · \(\Omega\), \(r/R\), \(\Phi/c^2\), \(M\), \(J\) fail the board · disk \(\Sigma\) is \(y\) in disk clothes · EFE same dimension · interpolator unpaid

CPT Framework — FT-H0FREQ / FT-FAT-FORCE / FT-YIELD-GEOM / FT-COV-YIELD-EQ / FT-BULK-ROT / FT-S3-PHI / FT-CONST-PRIZE Date: 2026-09-23 Status: BANKED · PASS_FT_RAR_ELIM_A_ONLY_KIND_NOT_EFE Stimulus: User — opportunity for proof by elimination that acceleration is the only possible variable that organises the RAR Parents: a_geom_ft_hubble_freq_results.md · a_geom_ft_fat_force_results.md · a_geom_ft_cov_yield_eq_results.md · a_geom_ft_bulk_rot_results.md · a_geom_ft_rar_curve_results.md Script: scripts/investigations/s3_geometry/ft_rar_elim.py Data: scripts/investigations/s3_geometry/data/ft_rar_elim.json

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

0. One-line

Yes as dimensional elimination for an isolated leftover well; not as a uniqueness theorem, and not against EFE. Leftover supplies one scale \(a_0=c^2/R\) (clothes). A spherical Newton well is \((GM,r)\). The only local dimensionless argument is \(y=g_N/a_0=GM/(a_0 r^2)\). That is why a winning constitutive law must be a universal map \(y\mapsto g_{\mathrm{obs}}\) with no leftover \(M\) in the EL (FT-FAT-FORCE). Named competitors fail the same board: \(\Omega/H_0\sim 370\)–\(480\) in both MW and dSph (wrong clock, FT-H0FREQ); \(r/R\sim 10^{-6}\)–\(10^{-8}\) (compactness does not pay RAR, FT-S3-PHI); \(\Phi/c^2\sim 10^{-7}\)–\(10^{-9}\) (1PN, not the IR); \(M/M_{\mathrm{crit}}\sim 10^{-12}\); \(j/(cR)\) tinier. Ricci vanishes in the RAR outskirts (FT-COV-YIELD-EQ). Disk \(\Sigma G/a_0\) is \(g_N/a_0\) in thin-disk clothes (Gauss). \(a_{\mathrm{ext}}/a_0\) has the same dimension as \(g_N\) and is not eliminated — that is EFE, still CAT-EVID, Sciama parked. Interpolator not unique (FT-RAR-CURVE). Not a proof of all mathematics. Prize OPEN.

1. What leftover is allowed to spend

Locked leftover \(R\), invariant \(c\). One acceleration \(a_0=c^2/R\). Isolated baryon well: \(G,M,r\). Buckingham:

\[ y=\frac{GM}{a_0 r^2}=\frac{g_N}{a_0}. \]

Any other local argument needs another leftover scale, or fails to split Earth / MW / dSph the way the RAR does.

2. Elimination board

| Place | \(y=g_N/a_0\) | \((a/c)/H_0\) | \(\Omega/H_0\) | \(r/R\) | \(\Phi/c^2\) | |-------|----------------|---------------|----------------|---------|--------------| | Earth | \(8.2\times 10^{10}\) | \(1.4\times 10^{10}\) | \(5\times 10^{14}\) | \(10^{-20}\) | \(7\times 10^{-10}\) | | MW \(8.5\,\mathrm{kpc}\) | \(0.80\) | \(0.14\) | \(370\) | \(8\times 10^{-7}\) | \(2.8\times 10^{-7}\) | | dSph \(10\,\mathrm{km\,s^{-1}}\), \(0.3\,\mathrm{kpc}\) | \(0.090\) | \(0.016\) | \(476\) | \(3\times 10^{-8}\) | \(1.6\times 10^{-9}\) |

Finding E1 [E algebra]. Only the acceleration column (and \(a/cH_0\), which is \(y\) times clothes \(a_0/(cH_0)\)) runs Newton \(\to\) threshold \(\to\) deep IR. \(\Omega/H_0\) is larger in the dSph than in the MW. Finding E2 [E]. \(r/R\) and \(\Phi/c^2\) are tiny everywhere on the RAR. They cannot organise a factor-\(40\) boost at \(300\,\mathrm{kpc}\). \(M\) or \(J\) in the EL is the Ginzburg–Landau wreck (\(\times 500\), FT-FAT-FORCE).

| Competitor | Why it dies | |------------|-------------| | Orbital \(\Omega\) | Wrong clock (FT-H0FREQ, FT-BULK-ROT) | | Radius \(r/R\) | Compactness mill; \(10^{-6}\) | | Potential \(\Phi/c^2\) | 1PN; gravity-of-gravity not a halo | | Mass \(M\), \(J\), mass type | Not universal in \(y\); wrong dSph end | | Ricci / \(f(R)\) | Vacuum in the outskirts; analytic IR Newton | | History \(\tau\), foam | Scatter, not present \(y\) | | Disk \(\Sigma\) | \(g\simeq 2\pi G\Sigma\): same as \(y\) for a sheet | | Fermion spin / Cosserat \(R\) | Compton-small or Gpc |

3. What this is not

- Not uniqueness of McGaugh \(\nu\) versus Pythagorean \(g=\sqrt{g_N(g_N+a_0)}\) (FT-RAR-CURVE). - Not elimination of EFE \(a_{\mathrm{ext}}/a_0\). Same dimension; vector sum \(L_a=c^2/\lvert\mathbf{a}_{\mathrm{int}}+\mathbf{a}_{\mathrm{ext}}\rvert\) remains licensed (FT-WBS-EFE-VEC). Sciama derivation stays parked. - Not a SPARC residual census (literature “no second parameter” is CAT-EVID, not this mill). - Not \(\sqrt{6}\) as SPARC \(a_0\).

4. Integrity

| Gate | Verdict | |------|---------| | Isolated leftover \(\Rightarrow\) unique \(y=g_N/a_0\) | YES (dimensional) | | \(\Omega\), \(r/R\), \(\Phi\), \(M\), \(J\), Ricci organise RAR | NO | | Disk \(\Sigma\) is a second variable | NO (same as \(y\) for a sheet) | | \(a_{\mathrm{ext}}\) eliminated | NO | | Interpolator unique / prize closed | NO | | Proof of all mathematics / promote | NO |

Exit: PASS_FT_RAR_ELIM_A_ONLY_KIND_NOT_EFE

5. One-line for agents

§FT-RAR-ELIM: leftover’s only scale makes isolated RAR a map of \(y=g_N/a_0\); \(\Omega,r/R,\Phi,M,J,\)Ricci eliminated; disk \(\Sigma\) is \(y\); \(a_{\mathrm{ext}}\) not eliminated (EFE); interpolator unpaid; prize OPEN; no promote.
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