Results — leftover-locked AQUAL is the 3D reduction of the medium, not a 4D \(W\)
One \(\Phi\) = metric lapse · \(a_0=c^2/R\) clothes · no graph neck · \(P\) not the interpolator · \(F\) unpaid · \(\sqrt{6}\) still [M] · P5 stands · prize OPEN
CPT Framework — FT-SHEET-VS-MEDIUM / FT-LOCK-KEY / FT-PRIZE-PIN / FT-RAR-ELIM / FT-P5-CLAIM-FENCE / FT-S3-SPECTRUM Date: 2026-09-23 Status: BANKED ·PASS_FT_AQUAL_LOCK_3D_REDUCTION_NOT_4D_W
Stimulus: User — once \(a_0=c^2/R\) is the medium’s intrinsic threshold, is the 3D field theory simply AQUAL with a cosmically locked scale, no 4D graph necks, no 10 Gpc projector mismatch, no invented fields?
Parents: a_geom_ft_sheet_vs_medium_results.md · a_geom_ft_lock_key_results.md · a_geom_ft_prize_pin_results.md · a_geom_ft_p5_claim_fence_results.md
Script: scripts/investigations/s3_geometry/ft_aqual_lock.py
Data: scripts/investigations/s3_geometry/data/ft_aqual_lock.json
Tags: [E honesty] · [Programme] · [O residual] · [M packaging]
0. One-line
Yes as the static 3D reduction of tine B. No as a closed 4D theory. If leftover \(K=1/R\) is the constitutive yield of the 4-metric medium, the isolated weak-field EL that is quadratic in \(\nabla\Phi\) in the UV and aquadratic in the IR, with a single potential that photons can see as lapse, is AQUAL with scale \(a_0=c^2/R\). That reading drops the empty-\(B^4\) graph (no neck), does not ask leftover \(P\) to pay kpc RAR (no 10 Gpc interpolator), and does not add a QUMOND auxiliary or a second metric. Compactness \(P\) remains as Poisson solvability on \(S^3\), not as \(\nu(y)\). What is not simple: the join \(F\) is unpaid; leftover clothes \(c^2/R_{\sqrt{6}}\simeq 2.31\,a_0\) is not SPARC \(a_0\); AQUAL does not exhibit the 4D constitutive tensor or \(c_{\mathrm{gw}}=c\); EFE \(a_{\mathrm{ext}}\) is still there; P5 forbids closing Coma/Bullet. Pythagorean remains a distinguished 0-parameter \(F\), not a theorem. Do not pick \(\mu\). Prize OPEN.
1. What this reading correctly drops
| Pathology | Why it is gone | |-----------|----------------| | 4D graph neck | No 3-surface floating in empty \(B^4\); no \(u=(R/c^2)\Phi\) | | \(P\) as kpc interpolator | \(P\) is leftover compactness, not \(\nu(y)\) | | Extra \(\phi\) / QUMOND auxiliary | AQUAL’s \(\Phi\) is the metric lapse (weak field), not a second field | | Second metric / TeVeS | Not this reading | | CDM inventory / dent-share | Not this reading |
That is why it feels clean. It is tine B reduced to three dimensions.
2. What is not “simply” settled
| Remainder | Status | |-----------|--------| | Join \(F\) (or \(\mu\)) | Unpaid family. Homogeneity fixes only the two ends. Pythagorean is distinguished Gauss, not unique. | | Scale | \(a_0=c^2/R\) is kind; \(\sqrt{6}\) clothes give \(2.31\times\) SPARC \(a_0\) ([M]) | | 4D constitutive | AQUAL is the static reduction, not the metric tensor, not GW170817 | | Compact \(S^3\) | \(P\rho\) still required for Poisson; it does not organise the RAR | | EFE | \(a_{\mathrm{ext}}/a_0\) same dimension; AQUAL is nonlinear, so environment remains | | Clusters | P5: leftover \(\Phi\) may claim galaxy RAR, must not close Coma/Bullet |
Finding A1 [E honesty]. “No invented fields” is true of AQUAL \(\Phi\) as lapse. It is false if one then imports QUMOND, AeST vectors, or a membrane field to finish the 4D job. The prize is still a constitutive law of the metric. Finding A2 [E]. Cosmic lock of \(a_0\) is leftover \(K\), not SPARC \(I\). Using SPARC to retune \(R\) or \(F\) is the shop this reading was meant to avoid.3. Integrity
| Gate | Verdict | |------|---------| | 3D reduction is leftover-locked AQUAL | KIND | | Graph necks / \(P\)-as-\(\nu\) / extra AQUAL field | avoided | | \(F\) fixed · \(a_{\mathrm{geom}}=\) SPARC \(a_0\) · 4D \(W\) written | NO | | P5 clusters closed | NO | | \(\mu\) shop / promote | NO | | Prize closed | NO |
Exit:PASS_FT_AQUAL_LOCK_3D_REDUCTION_NOT_4D_W
4. One-line for agents
§FT-AQUAL-LOCK: tine B’s static 3D reduction is AQUAL with \(a_0=c^2/R\) (one lapse, no graph, \(P\) not \(\nu\)); \(F\) and 4D constitutive unpaid; \(\sqrt{6}\) still [M]; P5 stands; prize OPEN; no promote.