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Consideration — The search for a unique \(F\) is withdrawn as the working target

The hunt for one interpolating \(F\) stops · AQUAL stays a conditional shape · the lock is not marked false · the convex set is not emptied

CPT Framework — FT-F-TARGET-WITHDRAWN / FT-AXIS-COMPLETION / FT-AXIS-NEST-F / FT-AQUAL-LOCK Date: 2026-10-01 Status: CONSIDERATION · PLACED_FT_F_TARGET_WITHDRAWN Stimulus: Principal Investigator — close the search for \(F(X)\) and for AQUAL. He holds that a one-dimensional scalar has been proved not to govern the universe, that AQUAL is not a law of nature, and that the Cassini–SPARC overlap has been holding the line on the wrong question. Parents: a_geom_ft_axis_completion_still_family_results.md (§0bn1026, PASS_FT_AXIS_COMPLETION_STILL_FAMILY) · a_geom_ft_axis_metric_act_results.md (§0bn989) · a_geom_ft_axis_nest_join_consideration.md (§0bn988, PLACED_FT_AXIS_NEST_F) · a_geom_ft_aqual_lock_results.md (PASS_FT_AQUAL_LOCK_3D_REDUCTION_NOT_4D_W) · a_geom_ft_lock_key_results.md (PASS_FT_LOCK_KEY_AQUAL_SHAPE_NOT_EMBEDDING_W) · a_geom_ft_parameter_corridor_map.md (§0bn1080) · a_geom_ft_core_frontiers_work_order.md (§0bn1082) · a_geom_compact_core_draft.md Appendix D · a_geom_tf_adm_clifford_distortion_consideration.md (PASS_TF_ADM_CLIFFORD) Algebra: none varied. No new script. No new \(F\). No nested junction written.

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

§0bn1026, §0bn989, §0bn988, the AQUAL lock, the lock key, §0bn1080, §0bn1082, and §0bn1086 stay as written. The sentence in §0bn1082 that the constitutive family stands is historical. Public chips stay OPEN. Phase 2 is not run. No promote.

0. One-line

The search for a unique interpolating \(F\) stops. Do not vary another \(F\). Do not ask a later geometry to return \(\mu=F'(X)\). AQUAL stays the conditional shape of a local scalar of \(\lvert\nabla\Phi\rvert\) with the two ends. It is not the working target. The lock is not marked false. The convex set of §0bn989 is not emptied.

1. What stops

The next task left by §0bn988 was one map from the nest half-line onto the join \(F\). That instruction is withdrawn.

Do not vary another member of \(\mathrm{EH}+F(X)\). Do not ask the nest, the two-cap transmission, a boundary layer, or a hosted core to return \(\mu=F'(X)\). Do not use the unpaid Cassini–SPARC overlap as a veto that sends the work back into the family.

The nest algebra stays. About \(\eta=\pi/4\), \(\lvert H\rvert\) is linear and the Willmore excess is quadratic. The slice fraction \(c=1-\lvert\cos\gamma\rvert\) is not the leaf label \(\eta\). Nothing in that note marks \(x=1\). The note is not rewritten.

2. What Phase 1 banked

PASS_FT_AXIS_COMPLETION_STILL_FAMILY closes the empty-vacuum search for one isolated algebraic formula. The scope of that acceptance is named in §0bn1026. The leftover is the infinite convex set of both-ends members of \(\mathrm{EH}+F(X)\) proved in §0bn989 and left uncut in §0bn1003.

Membership is the two homogeneous ends: \(F\sim X\) gives \(\mu\to 1\) at large \(x\), and \(F\sim(2/3)X^{3/2}\) gives \(\mu\sim x\) at small \(x\), with \(X=x^2\) and \(\mu=F'(X)\). The linear span meets neither pair of ends (§0bn1020). No polynomial meets both. No member is crowned.

An empty set would have been a different exit. The family is the answer to the question §0bn988 asked. The claim that the universe has been proved not to be a one-dimensional scalar is not that exit.

3. What the lock says

PASS_FT_LOCK_KEY_AQUAL_SHAPE_NOT_EMBEDDING_W: the unique homogeneous 3-density with those two kinetic ends is AQUAL, \(F\sim X\) in the ultraviolet and \(F\sim X^{3/2}\) in the infrared. That is Bekenstein–Milgrom 1984. The interpolating \(F\) stays inside the class. Graph, area, and CMC have the wrong ends. PASS_FT_AQUAL_LOCK_3D_REDUCTION_NOT_4D_W: if leftover \(K=1/R\) is the constitutive yield of the 4-metric medium, the isolated weak-field equation that is quadratic in \(\nabla\Phi\) in the ultraviolet and aquadratic in the infrared, with one potential that photons see as the lapse, is AQUAL with \(a_0=c^2/R\). The lock is a conditional theorem about that class. It is not a closed 4D theory. \(F\) inside the class stays unpaid. The lock does not say that every interface condition is a bulk density.

The lock stays on the books. It is not marked false. The Principal Investigator's instruction, recorded here, is that AQUAL is not the working constitutive target and that the search for \(F(X)\) is closed. That instruction is not a new kill token.

4. Cassini and SPARC

§0bn1080 stands. The perihelion gate leaves an infinite fast face, \(n>1.56\). Cassini catalogue evidence asks \(n\ge 6\), and that cut is not applied. The SPARC bend of about \(2\,\mathrm{dex}\) stays a member test. The two tests oppose each other. Their overlap stays unpaid.

They are historical member tests of the class in §3. They do not have to be re-solved before a different question is asked. The overlap is not a reason to resume the search for \(F\).

Do not set \(Q_2=0\). Do not select \(a_{\mathrm{sym}}\) over \(c^2/R\). Do not fit a SPARC catalogue. Do not apply Cassini to finish a cut. \(a_{\mathrm{sym}}=(2-\sqrt{2})c^2/R\) and \(a_\star=c^2/R\) both stay on their own seats.

5. What this note does not write

A nested junction of \(S^3\) seats, asked as its own boundary-value problem and kept off any map onto \(F\), is unwritten.

Appendix D hosts local cores \(I_p\simeq S^3(a_p)\) in a bulk slice. The ratio \(R_{\mathrm{match}}/a_e\) is not derived there. The explicit non-claim is: local host \(=\) cosmic \(S^3\) is not asserted, and no exterior matching theorem is asserted. PASS_TF_ADM_CLIFFORD puts the cone page on the Clifford torus of a local core. The moduli \((\eta,p)\) are local. That page is not leftover cosmic \(S^3\).

Do not fuse a local core with the cosmic container. The two-cap transmission stays \(2n/R\). A linear bulk plus that jump stays linear. \(\alpha\) stays an input (row 3.16, §0bn1042). Leaf \(\eta\) is not slice \(\beta\) (row 3.29, §0bn1055). Do not mint \(\alpha\). Do not hunt 137.

Phase 2 is not run. Public chips stay OPEN. No promote. Do not write a \(z(d)\). Do not rewrite §0bn1026, §0bn988, §0bn989, §0bn1080, §0bn1082, or §0bn1086.

6. Integrity

| Check | Result | |-------|--------| | Search for a unique \(F\) closed as the next task | YES | | Another \(F\) varied | NO | | A later geometry asked to return \(\mu=F'(X)\) | NO | | Lock marked false | NO | | Convex set of §0bn989 emptied | NO | | Cassini–SPARC overlap re-solved | NO | | \(Q_2\) set to \(0\) | NO | | \(a_{\mathrm{sym}}\) or \(a_\star\) selected | NO | | §0bn1026, §0bn988, §0bn1082, §0bn1086, or the lock rewritten | NO | | Nested \(S^3\) junction written | NO | | Local core fused with cosmic \(S^3\) | NO | | \(\alpha\) minted, or 137 hunted | NO | | Phase 2 run | NO | | A \(z(d)\) written | NO | | Promote | NO |

7. First task

Load §0bn1087. The search for a unique \(F\) stops. Do not vary another \(F\). Do not ask a later geometry to return \(\mu=F'(X)\). Do not use the Cassini–SPARC overlap as a reason to return to that search. AQUAL stays the conditional shape of a local scalar of \(\lvert\nabla\Phi\rvert\) with the two ends. It is not the working target. Do not mark the lock false. Do not empty the set of §0bn989. Do not crown a \(\mu\). Do not rewrite §0bn1026, §0bn988, or §0bn1086. Phase 2 is not run. Public chips stay OPEN.

§FT-F-TARGET-WITHDRAWN: the search for a unique \(F\) stops; AQUAL stays the conditional shape and is not the working target; the lock is not marked false; the convex set is not emptied; promote NO.
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