trureturingGitHub MATHEMATICAL ATLAS

Arith / CONCEPT

Joint Fresh-Ladder Completion

Several interfaces can jointly repair the complete hole left by deleting a saturated prime chain. The repair uses fixed roots and genuinely fresh numerical labels from the same original family.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH15
DOCUMENT LINKS1
THEOREM

A joint root repair constructs a smaller whole cover

RELATIONSHIP ATLAS

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Direct recorded relationships
Fresh Completion of a Complete Prime ChainFresh Completion of a CompletePrime ChainJoint Fresh-Ladder CompletionJoint Fresh-Ladder Completion
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

None recorded in this release.

RELATED KNOWLEDGE

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None recorded in this release.

LIBRARY / RELEASE VERSIONS

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Authority boundary

Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.