Analytic / CONCEPT
Logarithmic exponential derivative chain
The logarithm of one minus a negative exponential is smooth on the positive half-line and has a strictly positive third derivative.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES5
PROOF DEPTH0
DOCUMENT LINKS1
Three derivatives on the positive half-line
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
- Equality in the Hermite envelopetruth-dependency · Closed
- Hermite upper envelopetruth-dependency · Closed
- Local strict positivity of the actual prime kerneltruth-dependency · Closed
- The coefficient criteriontruth-dependency · Closed
- The general moment envelope and its monotonicitytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Equality in the Hermite envelopestructural-affinity · Closed
- Hermite nodes from two momentsstructural-affinity · Closed
- Hermite upper envelopestructural-affinity · Closed
- Inclusive Mangoldt ramps and complete Mertens transformstructural-affinity · Closed
- Local strict positivity of the actual prime kernelstructural-affinity · Closed
- Series and signed derivativesstructural-affinity · Closed
- The coefficient criterionstructural-affinity · Closed
- The general moment envelope and its monotonicitystructural-affinity · Closed
- Two-point Hermite remainderstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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