A standalone six-part library developing a single thesis: a Goncharov-style Lie coalgebra is the bookkeeping system for how physical observables — amplitudes, Feynman periods, entropies — decompose into irreducible informational constituents. Each rung adds exactly one emergent structural property the level below cannot express.
Read the papers in order — each is standalone, yet composes with its neighbour to build the pipeline observable = per(motive). The final rung closes the loop.
Part Ihep-thA disciplined domain of observable values
We open a modular research library whose governing thesis is that a Goncharov-style Lie coalgebra is a bookkeeping system for how physical observables…
Part IIhep-thTranscendental weight = loop order
The second rung introduces the graded family of special functions defined on the domain of observable ratios: the classical polylogarithm, the multiple…
Part IIImath.AGThe pre-numerical object behind measurement
The same transcendental constants reappear across physically unrelated computations. This paper advances a structural explanation from the theory of motives:…
Part IVmath.NTThe decomposition law of observables
A physical observable is not an atom. It carries a canonical decomposition into irreducible informational constituents, and the algebraic device that governs…
Part Vmath.NTThe passage from motive to measurable real number
This is the final constructive rung. What has been missing is the arrow that actually evaluates the structure: the map that turns a motivic object into the…
Synthesishep-thMeasurement as the closure of the ladder
This is the synthesis rung. The library is a ladder of five standalone parts, each adding exactly one emergent structural property the level below cannot…