Results — evolving leftover \(R\) makes \(a_0\) larger at high \(z\): wrong sign for baryon dominance
Larger \(a_0\) \(\Rightarrow\) more leftover, not more Newton · Genzel disks already sit at \(g(R_{1/2})=(3\)–\(11)\,a_0\) today · \(a_0\sim 4a_0\) at \(z\sim 2\) excluded · compactness, not \(a_0(t)\) · M12 FIRE
CPT Framework — FT-YIELD-GEOM / AST freeze M12 / FT-A0-KIND / R-EFF Date: 2026-09-22 Status: BANKED ·PASS_FT_A0_Z_WRONG_SIGN
Stimulus: User — if \(R\) evolves cosmologically, \(a_0\) should increase at high redshift, matching baryon-dominance of early galaxies
Parents: FT-YIELD-GEOM · M12 · Milgrom 2017 (arXiv:1703.06110) · Genzel et al. 2017
Script: scripts/investigations/s3_geometry/ft_a0_z.py
Data: scripts/investigations/s3_geometry/data/ft_a0_z.json
Tags: [E honesty] · [E algebra] · [Programme] · [O residual]
0. One-line
Wrong sign. If leftover \(R\) was smaller in the past, \(a_0=c^2/R\) was larger. Larger \(a_0\) shrinks \(r_y=\sqrt{GM/a_0}\), raises \(V_{\mathrm{flat}}\propto a_0^{1/4}\), and drops \(g/a_0\) — more yield, more extra \(\Phi\), not baryon Newton. At \(z=2\): \(a_0\times 3\) if \(R\propto 1/(1+z)\), \(\times 5.2\) if \(a_0\propto H_{\mathrm{matter}}\). Milgrom 2017: Genzel et al. disks already have \(g(R_{1/2})=(3\)–\(11)\,a_0\) with today’s \(a_0\), so they look baryon-dominated because they are high-\(g\) and compact, like inner ETG rings; \(a_0\sim 4a_0\) at \(z\sim 2\) is excluded (\(a_0\propto(1+z)^{3/2}\) included). Expanding leftover \(R\) that runs \(a_0\) or \(G\) is M12 FIRE. \(R\) unnamed. No CDM. No \(\mu(x)\).
1. Algebra of the slogan
| \(z\) | \(a_0/a_{00}\) if \(R\propto 1/(1+z)\) | \(r_y\) shrinks | \(V_{\mathrm{BTFR}}\) boost | if \(a_0\propto H\propto(1+z)^{3/2}\) | |------|----------------------------------------|-----------------|------------------------------|----------------------------------------| | 0 | 1 | 1 | 1 | 1 | | 1 | 2 | 0.71 | 1.19 | 2.83 | | 2 | 3 | 0.58 | 1.32 | 5.20 | | 6 | 7 | 0.38 | 1.63 | 18.5 | | 10 | 11 | 0.30 | 1.82 | 36.5 |
Finding Z1 [E algebra]. Yield when \(g2. What Genzel actually is
Milgrom 2017 on Genzel et al. 2017 (\(z\sim 0.9\)–\(2.4\)):
- \(g(R_{1/2})=(3\)–\(11)\,a_0\) with present \(a_0\) - leftover/phantom fraction at \(R_{1/2}\) only tens of percent — agrees without evolving \(a_0\) - \(V_{\mathrm{flat}}\) from baryons is \(0.55\)–\(0.75\) of the inner peak \(\Rightarrow\) declining outer RC, as observed - excludes \(a_0\sim 4a_0\) at \(z\sim 2\), hence \(a_0\propto(1+z)^{3/2}\)
Finding Z2 [E honesty]. Early-disk “baryon dominance” is the high-gradient side of FT-A0-KIND (compact, high \(\Sigma\)), not a larger yield threshold. Same lesson as NGC 6505 / SLACS inner \(\theta_E\).JWST “too big too early” is a formation-time issue (Sanders/McGaugh structure-growth), not \(a_0(z)\) in the RAR.
3. Expanding \(R\)
If \(c\) is fixed and \(a_0\propto 1/R\), Hubble-growing leftover \(R\) runs \(a_0(t)\) and, in Mach clothes, \(\dot G/G\sim H_0\) (M12 FIRE vs LLR). AST freeze: \(R\) static, locked, or present-epoch only. Do not name leftover \(R\) as FLRW.
4. Integrity
| Gate | Verdict | |------|---------| | \(R\) smaller in past \(\Rightarrow a_0\) larger | YES | | That matches baryon-looking high-\(z\) disks | NO (wrong sign) | | Compact high \(g\) with today’s \(a_0\) | YES (Milgrom 2017) | | \(a_0\times 4\) at \(z\sim 2\) | excluded | | Expanding \(R\) licensed | NO (M12) | | CDM / \(\mu(x)\) / name \(R\) | NO |
Exit:PASS_FT_A0_Z_WRONG_SIGN
5. One-line for agents
*§FT-A0-Z: if leftover \(R\) grows, \(a_0\) was larger at high \(z\) — that increases leftover, not baryon Newton; Genzel is high \(g\) with today’s \(a_0\); \(a_0\propto H(z)\) excluded; M12 FIRE.*