add(named): the paper measure with machine checked counterexamples to its invariants (M5 metatheory)

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milner committed 2026-09-23 01:30:00 +02:00
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## Graphs
The dependency graph covers the six milestones and every edge runs from a dependency to the result that uses it while the node colour encodes the status proved or stated or planned or blocked:
The dependency graphs are drawn in black and white and split by milestone. Every edge runs from a dependency to the result that uses it. A box is a result named after a paper statement, an ellipse is a supporting result, and a dashed box labelled with a milestone is a result defined in another diagram. The overview gives the shape of the whole development:
![Theorem dependency graph](graphs/dependency.svg)
<p align="center"><img src="graphs/dependency-overview.svg?v=black-white" alt="Theorem dependency by milestone"></p>
The details are then one diagram per milestone:
### M1, binding and reduction
<p align="center"><img src="graphs/dependency-M1.svg?v=black-white" alt="M1 dependencies"></p>
### M2, metatheory and checks
<p align="center"><img src="graphs/dependency-M2.svg?v=black-white" alt="M2 dependencies"></p>
### M3, subsystem
<p align="center"><img src="graphs/dependency-M3.svg?v=black-white" alt="M3 dependencies"></p>
### M4, parallel reduction
<p align="center"><img src="graphs/dependency-M4.svg?v=black-white" alt="M4 dependencies"></p>
### M5, metaterms and the named calculus
<p align="center"><img src="graphs/dependency-M5.svg?v=black-white" alt="M5 dependencies"></p>
The rule sketch gives the transition system generated by the rules B and Gc and R:
![Reduction rules](graphs/rules.svg)
<p align="center"><img src="graphs/rules.svg?v=black-white" alt="Reduction rules"></p>
The reduction graph gives the bounded reduct set of the term that applies the duplicating identity to a variable with every edge labelled by its rule and with the normal form marked:
![Reduction graph of the duplicating identity](graphs/reduction.svg)
<p align="center"><img src="graphs/reduction.svg?v=black-white" alt="Reduction graph of the duplicating identity"></p>