Paper Step 4(A): reuse of the retained outgoing endpoint #
After the paired incoming endpoint has been collapsed, the endpoint-stop driver may start at an arbitrary reachable residual prefix. The retained outgoing shortcut is nevertheless the same last schedule block used in the paper. This file records only the thin geometric adapter needed to feed that block to the already proved outgoing Fourier-defect identity.
In particular, the primitive-block and endpoint integrations below are exact signed complex identities. No norm, majorant, route, or scalar ledger is introduced here.
A shortcut-terminal schedule whose endpoint-stop transport starts at an arbitrary reachable residual prefix. The dependent field makes the equality between the stop terminal and the canonical outgoing terminal literal, so no cast survives in the analytic statement.
- terminalData : R324ShortcutTerminalSchedule pairing
- endpoint : R324WithinHalfEndpointStopAtTerminal self.terminalData.terminal res
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Package an endpoint indexed by an equal presentation of the canonical outgoing terminal.
Equations
- One or more equations did not get rendered due to their size.
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The retained outgoing terminal as the generic one-block context consumed by the paper's exact Step 4(A) Fourier calculation.
Equations
- data.terminalContext = data.endpoint.stop.headContext data.terminalData.terminal [] ⋯
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Reachability keeps the named edge leaving the unabsorbed terminal equal to the free Green kernel.
The singleton retained suffix has exactly the perturbative order of the outgoing terminal block.
The endpoint stop has consumed precisely the proper prefix of the canonical outgoing-shortcut schedule.
The retained terminal is the active part of its ambient interval. This is the schedule fact used in the paper before the final endpoint operation.
The canonical retained terminal ends at the last internal vertex.
Hence its named outgoing edge is the final internal chain-edge slot.
The sparse successor of the retained outgoing edge is the external right endpoint.
In the terminal split, the local successor point is literally the external outgoing variable.
The terminal predecessor is an internal or incoming slot, never the external-right slot; consequently it is independent of the outgoing variable.
The post-coordinate predecessor point used as the fixed left input of the outgoing terminal section.
Equations
- data.terminalPredecessorPoint x v = data.endpoint.stop.headPredecessorPoint data.terminalData.terminal [] ⋯ x 0 v
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The literal ordinary branch produced by the singleton terminal split is exactly the translated raw local section consumed by the existing outgoing Fourier-defect theorem.
Ordinary branch of the singleton terminal split, already rewritten in
the exact raw-local carrier required by the outgoing Fourier calculation.
This is the arbitrary-prefix analogue of the ordinary theorem in
R324PaperEndpointTerminalSplit; no analytic operation is repeated.
Exact signed outgoing-endpoint operation for a terminal retained after
an arbitrary endpoint-stop transport. This is the paper's ordinary-J
defect identity; every endpoint and primitive coordinate is integrated
before the defect is exposed.
The local factor appearing literally in the ordinary singleton split is
fed, without a norm or domination, into the already proved outgoing
Fourier-defect identity. The displayed (gap, first, internal) carrier is
the paper's Step 4(A) order after the standard primitive-tuple reindexing.