Results — leftover foam residual rhymes with the DE scale, not with \(q_0<0\)
Clothes \(cH_0\sim a_0\sim c^2/R\) · wall energy density \(O(1)\times\rho_\Lambda c^2\) · spring-back is \(\dot R\), FIRE against lock · frozen residual is GE-J wall · closed \(S^3\) without \(\Lambda\) decelerates · sky \(z\) TO BED
CPT Framework — FT-FOAM-RESIDUAL / FT-VOL4-MULTIPLIER / FT-R-LOCK / FT-A0-Z / FT-S3-PHI / FT-GEJ-A0-COMPUTE / FT-S3ROT / SFH-1 Date: 2026-09-23 Status: BANKED ·PASS_FT_FOAM_DE_SCALE_KIND_NOT_Q0
Stimulus: User — might moving leftover / memory-foam residual explain dark-energy attributed observations, in full or in part?
Parents: a_geom_ft_foam_residual_results.md · a_geom_ft_r_lock_freeze.md · a_geom_ft_a0_z_results.md · a_geom_ft_s3_phi_results.md · a_geom_ft_s3_rotation_ga_de_consideration.md · a_geom_ft_gej_a0_compute_results.md
Script: scripts/investigations/s3_geometry/ft_foam_de.py
Data: scripts/investigations/s3_geometry/data/ft_foam_de.json
Tags: [E honesty] · [E algebra] · [Programme] · [O residual] · [M packaging]
0. One-line
*In part, the scale. Not in full, and not as \(q_0<0\). Dark-energy attribution is an FLRW kinematic (\(q_0<0\), \(\Omega_\Lambda\sim 0.7\)). Leftover \(R\) is spectrally locked, not an FLRW \(a(t)\) (FT-R-LOCK). A memory-foam spring-back of leftover is \(\dot R\neq 0\), which is that FIRE, and \(a_0(z)\) from expanding \(R\) has the wrong sign (FT-A0-Z). What does rhyme is the acceleration board: \(cH_0\simeq 5.67\,a_0\), leftover \(c^2/R\simeq 2.31\,a_0\), de Sitter acceleration at \(r=c/H_0\) is \(\Omega_\Lambda cH_0\simeq 3.97\,a_0\). Umbilic-wall energy density \(\sigma_B/R\) is \(\simeq 0.32\,\rho_\Lambda c^2\) on the two-ball glue (same \(O(1)\) convention class as GE-J). That is clothes, not a supernova theorem. Frozen residual = leftover wall, acceleration along the leftover normal, not an isotropic 3-acceleration. In-slice \(g_\Lambda=\Omega_\Lambda H_0^2 r\) is \(8\times 10^{-6}\,a_0\) at \(8.5\,\mathrm{kpc}\) (FT-S3-PHI) — not the RAR, not a Hubble diagram. Closed \(S^3\) without \(\Lambda\) decelerates (\(q_0\approx +0.58\), SFH-1). Sky \(z\) stays TO BED. Do not mint \(\Lambda\). Prize OPEN.
1. Split the claim
| Object | What it is | This mill | |--------|------------|-----------| | DE-attributed observations | SN dimming, BAO, CMB acoustic scale, late ISW, growth | not paid (sky \(z\) TO BED; no Hubble diagram mill) | | ΛCDM attribution | \(q_0<0\), \(\Omega_\Lambda\simeq 0.7\) fluid | not identified with leftover foam | | Scale coincidence | \(a_0\sim cH_0\sim c^2/R\) | KIND / clothes (\(\sqrt{6}\) still [M]) | | Foam still recovering | \(\tau\sim R/c\), leftover \(K(t)\) | FIRE if it is \(\dot R\) | | Foam frozen | leftover has not relaxed | GE-J wall rename |
“In part” is allowed only for the scale rhyme. “In full” would be a SN/BAO/CMB theorem. That is not exhibited.
2. Scale board (clothes \(R=\sqrt{6}\,c/H_0\), \(\Omega_\Lambda=0.7\) input not derived)
| Quantity | / \(a_0\) | |----------|-----------| | \(cH_0\) | \(5.67\) | | leftover \(c^2/R\) | \(2.31\) | | de Sitter \(g_\Lambda(r=c/H_0)=\Omega_\Lambda cH_0\) | \(3.97\) | | \(g_\Lambda\) at \(8.5\,\mathrm{kpc}\) | \(7.9\times 10^{-6}\) | | \(g_\Lambda\) at \(300\,\mathrm{kpc}\) | \(2.8\times 10^{-4}\) | | umbilic \(\sigma_B/R\) vs \(\rho_\Lambda c^2\) | \(0.32\) (ratio of energy densities) |
Finding D1 [E algebra]. The cosmic acceleration scale and leftover \(K\) are the same \(O(1)\) board already used for \(a_0\sim c^2/R\). Wall energy density vs \(\rho_\Lambda c^2\) is the same convention class as GE-J’s \(0.18\)–\(2.3\,a_0\). Do not select the cell that hits \(\Omega_\Lambda\) after the fact. Finding D2 [E honesty]. In-slice de Sitter is linear in \(r\) and is negligible on RAR radii (FT-S3-PHI). It is not extra galactic \(\Phi\), and it is not a substitute SN diagram.3. Why foam does not pay \(q_0<0\)
Spring-back. Memory foam recovering is leftover trying to change shape. The only leftover length is \(R\). \(\dot R\neq 0\) is expanding (or shrinking) leftover, FT-R-LOCK FIRE. If \(a_0=c^2/R\) ran, high-\(z\) would see more yield, not baryon Newton (FT-A0-Z, wrong sign). Hubble expansion, if real, is not \(\dot R/R\) of this container. Frozen residual. \(\tau\gg t_H\) so leftover has not relaxed: that is a constant leftover \(K\), i.e. the umbilic wall. Acceleration is along the leftover normal (GE-J), not an isotropic 3-acceleration \(q_0\). Tensor structure does not match (same class as FT-S3ROT: vorticity \(\neq\Lambda\)). Closed \(S^3\) kinematics. SFH-1: no-\(\Lambda\) closed distances give \(q_0\approx +0.58\) (deceleration). Curvature alone does not flip to acceleration. Weber did not free-derive DE (SFH-W). A CPT \(\Lambda\) sector remains shopping. Redshift. SN “acceleration” is a luminosity-distance vs \(z\) fit. Sky \(z\) stays TO BED. This mill does not write a Hubble diagram.4. Integrity
| Gate | Verdict | |------|---------| | Scale rhyme leftover \(K\) / \(cH_0\) / \(\rho_\Lambda\) | KIND, not a \(W\) | | Foam spring-back pays \(q_0<0\) | NO (\(R\)-lock FIRE) | | Frozen foam pays SN Hubble diagram | NO | | In-slice \(g_\Lambda\) pays RAR | NO | | Closed \(S^3\) without \(\Lambda\) accelerates | NO (decelerates) | | DE-attributed observations paid | NO | | \(\Lambda\) minted as a fix | NO | | Sky \(z\) / Sciama unparked | NO | | Prize closed / promote | NO |
Exit:PASS_FT_FOAM_DE_SCALE_KIND_NOT_Q0