Manuscript IX-Free@1 · IX-Free.tex · section · 33b20e96

Release table, retained boundaries, and final gates

Release table, retained boundaries, and final gates · lines 1638–1755

{}1.12

Object	Provenance	Status	Scope or missing lemma
$B_{f} ⋆_{1} W_{g}$	IX-C, inherited	Constructed	Named first-stage domain
$W_{g} ⋆_{1} B_{f^{'}}$	IX-C, inherited	Constructed	Named reverse domain
Three one-edge outputs	IX-C, inherited	Constructed	Existence and admission
$C_{desc}$	IX-Free F2	Constructed	Evaluated as $R$ ; algebraic test only
$G_{12, 23}$	IX-Free F3–F4	Constructed	Compact scalar kernel; zero metric derivatives
$G_{12, 13}$	IX-Free F3–F4	Constructed	Metric derivative $m + q_{a}$ and descendants
$G_{13, 23}$	IX-Free F3–F4	Constructed	Metric derivative $m + q_{a}$ and descendants
Left scalar map	IX-Free F2, F5	Constructed	Algebraic admitted map; overlap release pending
Right scalar map	IX-Free F2, F5	Constructed	Algebraic admitted map; overlap release pending
Left nonconstant degree-two maps	IX-Free F5	Constructed	Actual-functional block maps
Right nonconstant degree-two maps	IX-Free F5	Constructed	Actual-functional block maps
Degree-four coefficient maps	IX-Free F5	Unresolved	Annihilation of $ker p_{L}, ker p_{R}$
Common-pair and old-product gluing	IX-Free F6	Unresolved	Agreement on intersections and sum intersections
$(B_{f} ⋆_{1} W_{g}) ⋆ B_{f^{'}}$	IX-Free F5–F7	Unresolved	Degree-four descent and overlap agreement
$B_{f} ⋆ (W_{g} ⋆_{1} B_{f^{'}})$	IX-Free F5–F7	Unresolved	Degree-four descent and overlap agreement
Full-sector associativity	IX-Free F7	Unresolved	Conditional proposition only
Full-sector involution	IX-Free F8	Unresolved	Degree-four descent and compatible gluing
F9a, completed families	IX-Free F9a	Constructed	Named fixed-support test domains
F9b, actual-stage continuity	IX-Free F9b	Unresolved	Unclaimed strengthening; no inverse estimates
Normal-topology algebra under (E1)–(E4)	VII-C boundary, inherited	Proved obstructed	Only under the original stated hypotheses
IX-D and G2	Outside this sector	Unresolved	Not begun or opened

Nearby in this section

theorem: Theorem: IX-Free partial construction and release