Manuscript IX-D@3 · IX-D-v3.tex · section · 3ad4586e
D0: the constructed IX-Free-2 sector
D0: the constructed IX-Free-2 sector · lines 585–667
{}1.14
| Object | Entering status | IX-D use |
|---|---|---|
| Object | Entering status | IX-D use |
| on | Constructed in IX-Free-2, relative to its premises | Named free product, not a time ordering |
| Both associations of this word | Constructed through | Scalar and nonconstant coefficients are available |
| Evaluated as zero | Do not reopen degree-four descent | |
| Four degree-four prescriptions | Descended actual maps | Use their established coefficients |
| New-domain and old-domain gluing | Constructed | No live overlap stop in this declared sector |
| Evaluated | Not a causal normalization theorem | |
| Reversal and presentation independence | Constructed on the declared domain | Retain every boundary term |
| F9a | Constructed on fixed-support families | Not F9b or hypocontinuity |
| F9b | Unclaimed | Still unclaimed |
| Closure under unspecified intermediate products | Unclaimed | Higher retarded formulas cannot assume it |
| Complete free domain for a general causal construction | Unclaimed | A separate enlargement problem |
| Absent from the entering construction | Still the IX-D construction obligation |
Thus the earlier free-closure clause is discharged only for , and only as the inherited relative premise in Assumption ass:free2. The earlier future-lift obligations concerning time ordering, causal factorization, anti-time ordering, and old retarded overlaps remain undischarged.
The construction does not establish that
for arbitrary declared pairs or arbitrary . An unclaimed enlargement is not a nonexistence theorem.
Displayed formulas in this passage
unlabeled · line 661