Combinatorics / CONCEPT
Two opposite LARGE labels: the complete three-case exchange
The actual two-edge expanding path and two later opposite LARGE labels admit a literal three-case exchange, with every gate and physical inventory derived.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES7
PROOF DEPTH3
DOCUMENT LINKS0
Derive the physical source geometry
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A full exchange retaining every old SMALLtruth-dependency · Closed
- Full exchange through the physical SMALL source halftruth-dependency · Closed
- Full source completion from one actual opposite pairtruth-dependency · Closed
- Reset decomposition of arbitrary legal wordstruth-dependency · Closed
- Same-sign substitution with a compatible suffixtruth-dependency · Closed
- The native repeated one-bit source and its exact striptruth-dependency · Closed
- Whole-suffix boundaries and a negative prefix pairtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A full exchange retaining every old SMALLstructural-affinity · Closed
- A physical doubling packet supplies a three-LARGE exchangestructural-affinity · Closed
- Energy before SMALL count: the physical mixed-suffix exchangestructural-affinity · Closed
- Exact labelled dyadic allocationstructural-affinity · Closed
- Full exchange through the physical SMALL source halfstructural-affinity · Closed
- Full source completion from one actual opposite pairstructural-affinity · Closed
- Isolated SMALL labels with no bound on their numberstructural-affinity · Closed
- Moving one LARGE label across an arbitrary mixed suffixstructural-affinity · Closed
- Native full completion with exactly two physical SMALL labelsstructural-affinity · Closed
- Ordering pairwise compatible steps between two endpointsstructural-affinity · Closed
- Paired completion from actual occurrence countsstructural-affinity · Closed
- Physical exchange by constructive positive SMALL returnsstructural-affinity · Closed
- Physical multiplicities and low-denomination budgetsstructural-affinity · Closed
- Placing two SMALL occurrences across two free gapsstructural-affinity · Closed
- Positive odd penultimate exchanges with genuine SMALL returnsstructural-affinity · Closed
- Reset decomposition of arbitrary legal wordsstructural-affinity · Closed
- Same-sign substitution with a compatible suffixstructural-affinity · Closed
- Single SMALL rigidity and forward cyclic completionstructural-affinity · Closed
- The invariant obstruction of a retained LARGE skeletonstructural-affinity · Closed
- The native repeated one-bit source and its exact stripstructural-affinity · Closed
- Three-small block placement in the sixfold normalizationstructural-affinity · Closed
- Whole-suffix boundaries and a negative prefix pairstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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