trureturingGitHub MATHEMATICAL ATLAS

Observer / CONCEPT

Chronological Signature Group-Like Hopf Laws

Step-two chronological signatures satisfy the group-like coproduct and antipode laws, and the antipode reverses event order with negated values.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH8
DOCUMENT LINKS0
THEOREM

Multiplicative diagonal

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Direct recorded relationships
Step-Two Chronological LogarithmStep-Two ChronologicalLogarithmChronological Signature Group-Like Hopf LawsChronological Signature Group-Like Hopf LawsPrime-Word Antipode, Parity, and Golden-Step BridgePrime-Word Antipode, Parity,and Golden-Step BridgeTime-Ordered Memory Chronology Signature BridgeTime-Ordered Memory ChronologySignature Bridge
Proof dependencyStructural affinityDocument link

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
8
Layer
D5/S3
Domain
Observer
Node ID
D5/S3/Observer/Chronology/ChronologicalSignatureHopf
Repository path
D5/S3/Observer/Chronology/ChronologicalSignatureHopf.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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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.