Results — S³ defect condensation does not pay aquadratic \(W\)
Dual pages · \(R/a_p\sim 10^{42}\) · analytic EFT \(\Rightarrow\) Newton IR · \(T_{00}\) inventory is CDM-role · P6 no vertex · origin stays PARK as mass mill · prize OPEN
CPT Framework — FT-CLOSE-ROUTE / T23-ORIGIN-SIZE / FT-P6-DOWNCONVERT / FT-PRESTRAIN / FT-LOCAL-L-BARRIER / FT-BULK-ACCUM / FT-PRIZE-PIN Date: 2026-09-24 Status: BANKED ·PASS_FT_MICRO_W_CONDENSATE_NOT_AQUADRATIC
Stimulus: User — get as far as possible; can \(W\) be paid by a microscopic condensation kernel from the topological defect sector on \(S^3\)? Research line should become available as a ruled-out catalog (not a hub dump).
Parents: a_geom_ft_close_route_results.md · a_geom_ft_t23_origin_size_results.md · a_geom_ft_p6_downconvert_results.md · a_geom_ft_prestrain_results.md · a_geom_ft_bulk_accum_results.md
Script: scripts/investigations/s3_geometry/ft_micro_w.py
Data: scripts/investigations/s3_geometry/data/ft_micro_w.json
Tags: [E algebra] · [E honesty] · [Programme] · [O residual]
0. One-line
No named defect condensate pays the constitutive \(W\). \(T(2,3)\)/Hopf live on the electron/proton seat (Clifford \(T^2\)), leftover RAR on the container \(S^3(R)\). Mixing them is dual-pages. Scale: \(R/a_p\simeq 1.5\times 10^{42}\); mean baryon spacing \(\sim 0.57\,\mathrm{m}\) gives \(c^2/\ell\sim 10^{17}\,\mathrm{m\,s^{-2}}\), Compton packing \(\sim 0.8\,\mathrm{AU}\) gives \(c^2/R_{\mathrm{pack}}\sim 10^6\,\mathrm{m\,s^{-2}}\), leftover \(a_\star\sim 3\times 10^{-10}\). London/GP/Skyrme/Higgs kernels are analytic at their vacuum, so the leftover Taylor barrier still yields Newton IR. Treating condensate as extra \(T_{00}\) is CDM-role inventory (FT-BULK-ACCUM). P6: leftover \(\Delta_{S^3}\) has no 3-wave vertex to down-convert defect stress into a leftover modulus. An aquadratic kernel would be the same \(F\) shop at micro scale. Origin line stays PARK as a mass mill. Catalog of kills: a_geom_ft_rar_kills_catalog.md (honesty, chips OPEN; no cpt-physics dump). Prize OPEN.
1. Why a micro kernel looks like a pay route — and is not
A condensate on leftover \(S^3\) could in principle set the prestrain \(K=1/R\). That is FT-PRESTRAIN: leftover vacuum is not \(E=0\). Prestrain does not mint \(\mu(0)=0\). Generic defect EFTs (Gross–Pitaevskii, London, Skyrme, CS mean-field) are analytic at the ordered vacuum; Goldstone kinetics are \((\partial\pi)^2\). Coupled to the 4-metric, that is Hooke in the IR.
| Kernel | Pays \(W\)? | |--------|-------------| | \(T(2,3)\) occupancy as leftover mass | CDM-role \(T_{00}\) | | Hopf/CS helicity mean-field | leftover-wide \(\ell=1\sim 10^{-33}\,\mathrm{eV}\); not a \(y\)-map | | 3-wave downconversion of defect stress | no vertex (P6) | | Analytic condensate EFT | Newton IR (Taylor) | | Hand aquadratic \(\lvert\partial\pi\rvert^3\) | \(F\) shop, not a derivation |
Finding M1 [E honesty]. Dual pages: leftover container \(\neq\) trefoil seat. A kernel on \(T^2\) does not automatically write a leftover-\(S^3\) constitutive tensor. Finding M2 [E algebra]. No named defect length on leftover \(S^3\) is \(c^2/a_0\). Only leftover \(R\) itself is.2. Public catalog
Ruled-out routes for this line are listed in a_geom_ft_rar_kills_catalog.md. That file is the honesty object for a later narrow /status cut. This mill does not update cpt-physics.com. Chips stay OPEN.
3. Integrity
| Gate | Verdict | |------|---------| | Defect condensate pays aquadratic \(W\) | NO | | Origin unparked as mass mill | NO | | Dual pages mixed as a theorem | NO | | \(\mathcal{L}\) written / SPARC \(I\) / promote | NO | | Prize closed | NO |
Exit:PASS_FT_MICRO_W_CONDENSATE_NOT_AQUADRATIC