# Results — moving leftover water / memory-foam residual is not a \(y\)-map

### Still-water buoyancy already FAIL · currently-loaded mattress is the prize’s time-domain name · leftover clocks make galaxies a fast poke (wrong RAR end) · \(\omega\)-keyed \(\tau\) is a shop · long-lived \(\ell=1\) is cosmic · prize OPEN

**CPT Framework — FT-VOL4-MULTIPLIER / FT-CONST-ROUTE / FT-S3-SPECTRUM / FT-GW170817 / FT-BULLET / FT-P5-CLAIM-FENCE / FT-SCIAMA-FLOOR-PARK**  
**Date:** 2026-09-23  
**Status:** **BANKED / FAIL as RAR derivation** · `PASS_FT_FOAM_RESIDUAL_MOVING_WATER_NOT_YMAP`  
**Stimulus:** User — leftover water may not be still; a very long-lived residual, like a memory-foam mattress springing back  
**Parents:** `a_geom_ft_vol4_multiplier_results.md` · `a_geom_ft_const_route_results.md` · `a_geom_ft_s3_spectrum_results.md` · `a_geom_ft_gw170817_results.md` · `a_geom_ft_bullet_results.md`  
**Script:** `scripts/investigations/s3_geometry/ft_foam_residual.py`  
**Data:** `scripts/investigations/s3_geometry/data/ft_foam_residual.json`

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

---

## 0. One-line

> **The mattress that is *currently loaded* is the constitutive prize in time-domain clothes. The mattress still springing back on leftover’s own clock is the wrong book.** Still water (constant \(\lambda\)) was FT-VOL4: leftover-normal wall, no in-slice boost. Moving water / delayed restoration splits three ways. (A) Equilibrium under present baryons: Kelvin–Voigt creep that has already finished is a static \(y\)-map — unpaid, not derived. (B) Residual on leftover time \(R/c\simeq 34\,\mathrm{Gyr}\) or \(\ell=1\) period \(\simeq 124\,\mathrm{Gyr}\): solar-circle \(\omega\tau\simeq 900\) (a *fast poke*, stiff Newton — wrong RAR end); the ringing mode is leftover-wide, not a kpc well. (C) A dashpot \(\tau\) between Solar-System years and galactic \(0.2\,\mathrm{Gyr}\) would fake “slow outskirts / stiff centres” and is a **new scale**, not leftover \(K\). At fixed \(y\), \(t_{\mathrm{orb}}\propto M^{1/4}\) (MW/dwarf \(\times 4.7\)), so an \(\omega\)-keyed interpolator is not a universal \(y\)-map. History residual lags the Bullet the wrong way. \(b_1(S^3)=0\): no free steady 3-current. Not an L3 resume. Prize OPEN.

---

## 1. Named clocks (clothes \(R=\sqrt{6}\,c/H_0\))

| Clock | Value |
|-------|-------|
| Hubble \(1/H_0\) | \(14.0\,\mathrm{Gyr}\) |
| Leftover crossing \(R/c\) | \(34.2\,\mathrm{Gyr}\) |
| \(\ell=1\) leftover period | \(124\,\mathrm{Gyr}\) |
| MW \(8.5\,\mathrm{kpc}\), \(v=220\,\mathrm{km\,s^{-1}}\) | \(0.24\,\mathrm{Gyr}\) |
| Yield-radius orbit, MW | \(0.28\,\mathrm{Gyr}\) |
| Yield-radius orbit, \(10^8 M_\odot\) dwarf | \(0.059\,\mathrm{Gyr}\) |
| dSph \(1\,\mathrm{kpc}\), \(0.027\,a_0\) | \(0.61\,\mathrm{Gyr}\) |
| MW baryon Kepler at \(300\,\mathrm{kpc}\) | \(69\,\mathrm{Gyr}\) (\(> t_H\): orbits would not have closed) |
| Light time of \(r_y\) | \(2.5\times 10^4\,\mathrm{yr}\) |
| Earth year | \(1\,\mathrm{yr}\) |
| Bullet \(200\,\mathrm{kpc}\) / \(4500\,\mathrm{km\,s^{-1}}\) | \(43\,\mathrm{Myr}\) |
| GW \(100\,\mathrm{Hz}\) | \(0.01\,\mathrm{s}\) |

**Finding F1 [E algebra].** Leftover’s own times are *cosmic*. Galaxy-scale leftover waves cross in \(10^4\,\mathrm{yr}\) and, if they radiate at \(c\), are gone a million times over one rotation. A Gyr memory at kpc is **not** a leftover eigenmode; it has to be a constitutive dashpot.

---

## 2. Three pictures

### A · Currently loaded, equilibrium

Someone is lying on the foam *now*. The dent is held by present baryons. Any viscoelastic transient has died. Quasi-static local rheology with one leftover scale is Newton or a step (FT-CONST-ROUTE Finding R1). A non-analytic equilibrium map \(y\mapsto g_{\mathrm{obs}}\) is the standing prize. Naming it memory foam does not derive the tensor.

### B · Still springing back on leftover time

Residual strain from formation / a past orbit, recovering with \(\tau=R/c\) or the \(\ell=1\) ring.

Kelvin–Voigt polarity (fast poke stiff, long sit sinks) at \(\tau=R/c\):

| Place | \(\omega\tau=2\pi\tau/t_{\mathrm{dyn}}\) | Foam sees |
|-------|------------------------------------------|-----------|
| Solar System | \(2\times 10^{11}\) | instant poke |
| MW \(8.5\,\mathrm{kpc}\) | \(9.1\times 10^2\) | fast poke |
| MW baryon \(300\,\mathrm{kpc}\) | \(3.1\) | borderline |

**Finding F2 [E].** On leftover’s clock the solar circle is a fast poke. Fast \(\Rightarrow\) stiff \(\Rightarrow\) Newton. That is the **wrong end** of the RAR (centres/SS should be Newton *and* the outskirts extra \(\Phi\); leftover \(\tau\) makes the disk Newton too).

**Finding F3 [E honesty].** \(\ell=1\) is a leftover-wide dipole (wavelength \(\sim R\)), translations in the Jacobi mill, not a galactic mattress. Exciting it is a cosmic residual, not extra \(\Phi\) at \(8.5\,\mathrm{kpc}\). A decaying leftover \(K(t)\) is \(a_0(t)\), already the wrong sign if \(R\) runs (FT-A0-Z) and M12 **FIRE**.

History: SPARC is a *present-day* baryon–\(g_{\mathrm{obs}}\) relation (\(\sim 0.13\,\mathrm{dex}\) point scatter). A residual that has not finished recovering remembers assembly, not today’s \(y\). Bullet: ram-pressure offset in \(\sim 40\)–\(200\,\mathrm{Myr}\). A Gyr foam lags; lensing would trail the *past* mass (gas path), opposite to Clowe’s galaxy peaks. Memory does not help the offset; lag hurts.

### C · \(\omega\)-keyed interpolator with a new \(\tau\)

Put \(\tau\) between a year and \(\sim 0.2\,\mathrm{Gyr}\) so SS is stiff and outskirts have time to sink. That \(\tau\) is **not** \(R/c\), not \(1/H_0\), not \(r_y/c\). It is a shop.

At fixed \(y=1\), \(t_{\mathrm{orb}}=2\pi(GM/a_0^3)^{1/4}\). MW vs \(10^8 M_\odot\) dwarf: \(\times 4.73\). An interpolator of \(\omega\tau\) depends on leftover \(M\) at fixed \(y\) — FT-FAT-FORCE class, not a universal \(y\)-map.

---

## 3. Moving water, algebraically

\(b_1(S^3)=0\): no harmonic 1-form. Leftover cannot host a free steady incompressible 3-current. Driven flow is sourced by baryons (then it is constitutive). Decaying flow is an \(\ell\ge 1\) eigenmode (cosmic).

Dent velocity from \(u=(R/c^2)\Phi\): \(\dot u/c=(v/c)(g/a_\star)\simeq 2.5\times 10^{-4}\) at the solar circle. Bernoulli in leftover 4-flow is post-Newtonian, not a factor-\(40\) IR.

Spring-back is **not** P4’s 3-to-4 leak (product \(T^{n\alpha}=0\); Euclidean \(B^4\) has no retarded sink). Different slot.

A memory kernel in the *principal symbol* of the wave operator risks \(c_{\mathrm{gw}}\ne c\) at \(10^{-15}\). Any lingering foam may live only in the quasi-static IR, which is again the prize.

Not an L3 / Sciama resume: 2-seat delay stays killed; cavity Greens stay closed.

---

## 4. Integrity

| Gate | Verdict |
|------|---------|
| Moving leftover water pays RAR | **NO** |
| Long-lived leftover mode is a galactic mattress | **NO** (cosmic) |
| \(\tau=R/c\) has RAR polarity | **NO** (disk is a fast poke) |
| \(\omega\)-keyed response is a \(y\)-map | **NO** |
| History residual tracks present baryons | **NO** |
| Bullet lag helps the offset | **NO** |
| Free steady \(S^3\) current | **NO** |
| Currently-loaded foam | **prize rename**, not a \(W\) |
| Sciama unparked / \(\tau\) invented / promote | **NO** |
| Prize closed | **NO** |

**Exit:** `PASS_FT_FOAM_RESIDUAL_MOVING_WATER_NOT_YMAP`

---

## 5. One-line for agents

> **§FT-FOAM-RESIDUAL: currently-loaded mattress = constitutive prize in time-domain clothes; leftover \(\tau=R/c\) makes the disk a fast poke (Newton, wrong end); \(\ell=1\) residual is cosmic; new \(\tau\) is a shop and not a \(y\)-map; Bullet lag hurts; \(b_1(S^3)=0\); not L3; prize OPEN; no promote.**