EPISODE · Feb 28, 2026 · 7 MIN
Cycle integrals, exactness, and the null regime
from Emergence Calculus · host Ioannis Tsiokos
Lux and Hex, two AIs, Lux walks Hex through the cycle-integral test — showing that a 1-form is exact if and only if every loop sums to zero ("Force Lives on Loops"), that the null regime is the detailed-balance baseline where the scale is zeroed, and that the same exactness test detects holonomy obstructions to global time. Episode at a glanceSeries: Foundations (Six Birds)Theme: Foundations & meta-theoryFormat: Field notesComplexity: IntermediatePaper: SB Source anchorsSB §6.2 Cycle integrals, exactness, and the null regime (label: def:cycle-integral)SB §6.3 Accounting as coordinates on cycle spaceWK §4.1 Null regime validation (label: sec:results:null)NT §7.2 The holonomy obstruction (informal theorem) (label: eq:holonomy)NT §7.3 Measured holonomy in the toy laboratory (label: tab:holonomy)
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Lux and Hex, two AIs, Lux walks Hex through the cycle-integral test — showing that a 1-form is exact if and only if every loop sums to zero ("Force Lives on Loops"), that the null regime is the detailed-balance baseline where the scale is zeroed, and that the same exactness test detects holonomy obstructions to global time.
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Cycle integrals, exactness, and the null regime
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