{"slug":"research-the-quirq-calculus","name":"The quirq calculus","rules":{"start":"open","maxDepth":10,"allowRewind":true,"allowReplay":true},"nodes":{"open":{"short":"the note","pose":{"base":"centre"},"beat":{"layout":"center","marker":"the calculus · interactive","title":["The quirq","calculus"],"glass":1,"lede":"Every calculation in quirq accounting: scoring, the mint, the all-in cost model, unit and portfolio metrics, the time axis, and the energy bridge.","caption":"10 beats · 5 min to read in full"},"prompt":"Where do you want to start?","choices":[{"label":"From the top","to":"premise"},{"label":"unit metrics","to":"unit-metrics"},{"label":"Straight to the end","to":"close"}]},"premise":{"short":"the premise","pose":{"base":"flooded"},"beat":{"layout":"left","marker":"01 · the calculus","title":["Snapshot before, snapshot after,","score against weighted checks"],"lede":"Snapshot before, snapshot after, score against weighted checks, mint against the budget, meter everything. Every number an operator needs falls out of one ledger.","caption":"Condensed from the note."},"prompt":"Where next?","choices":[{"label":"scoring","to":"scoring-how-completion-is-comput"},{"label":"Wrap it up","to":"close"}]},"scoring-how-completion-is-comput":{"short":"scoring","pose":{"base":"drained"},"beat":{"layout":"right","marker":"02 · scoring","title":["Scoring:","how completion is computed"],"lede":"A unit of work is a triple:","code":"u = (S₀, G, B)\n\nS₀  the snapshot of world state when the unit is created\nG   the definition of done: weighted checks {(g₁,w₁), …, (gₙ,wₙ)}\nB   the budget: what reaching the end state is worth, set by the owner","caption":"Condensed from the note."},"prompt":"Keep going?","choices":[{"label":"the mint","to":"the-mint"},{"label":"Wrap it up","to":"close"}]},"the-mint":{"short":"the mint","pose":{"base":"recede"},"beat":{"layout":"left","marker":"03 · the mint","title":["The mint","the calculus"],"lede":"The owner declares the regime at creation: atomic when partial completion is worthless (a half-merged change), divisible when it is not (four of five report sections).","code":"Q(u) = V(u) · B(u)              divisible settlement (pay per delivered share)\nQ(u) = B(u) · [V(u) ≥ τ]        atomic settlement (all or nothing)","caption":"Condensed from the note."},"prompt":"What next?","choices":[{"label":"the all-in cost","to":"the-all-in-cost-of-an-outcome"},{"label":"Wrap it up","to":"close"}]},"the-all-in-cost-of-an-outcome":{"short":"the all-in cost","pose":{"base":"drained"},"beat":{"layout":"right","marker":"04 · the all-in cost","title":["The all-in cost","of an outcome"],"lede":"The token bill is one line of the true cost. The environment meters all of them:","code":"C_total(u) =  Σ tokensₘ · priceₘ           inference, per model\n           +  t_cpu·r_cpu + t_gpu·r_gpu    metered compute\n           +  Σ calls_j · price_j          external API calls\n           +  storage · r_store            storage\n           +  F / N_units                  environment amortization\n           +  h · r_human                  human intervention time","caption":"Condensed from the note."},"prompt":"Where next?","choices":[{"label":"unit metrics","to":"unit-metrics"},{"label":"Wrap it up","to":"close"}]},"unit-metrics":{"short":"unit metrics","pose":{"base":"recede"},"beat":{"layout":"left","marker":"05 · unit metrics","title":["Unit","metrics"],"lede":"Worked: at B = $4.00 and V = 1.0: Q = 4.00, c_q = 0.032, margin $3.87, multiple 31x. Had it settled divisibly at V = 0.8: Q = 3.2 and c_q = 0.040.","code":"cost per quirq   c_q = C_total / Q         price of a dollar of verified work\nquirq margin     μ   = Q − C_total         surplus on the unit\nmultiple         x   = Q / C_total         the reciprocal view","caption":"Condensed from the note."},"prompt":"Keep going?","choices":[{"label":"portfolio metrics","to":"portfolio-metrics"},{"label":"Wrap it up","to":"close"}]},"portfolio-metrics":{"short":"portfolio metrics","pose":{"base":"drained"},"beat":{"layout":"right","marker":"06 · portfolio metrics","title":["Portfolio","metrics"],"lede":"Over the units in an accounting window T:","code":"QER(T)  =  Σ Q(u) / Σ C_total(u)          quirq efficiency ratio (the headline)\nQV(T)   =  Σ Q(u) / |T|                   quirq velocity (throughput in value)\nIR(T)   =  |{u : V(u) < τ}| / N           intervention rate (the trust signal)","caption":"Condensed from the note."},"prompt":"What next?","choices":[{"label":"the time axis","to":"the-time-axis"},{"label":"Wrap it up","to":"close"}]},"the-time-axis":{"short":"the time axis","pose":{"base":"recede"},"beat":{"layout":"left","marker":"07 · the time axis","title":["The time","axis"],"lede":"Two dynamics move the trajectory in opposite directions, and both must be read.","panelRows":[{"title":"Fresh context","note":"Unit 1 5,600 · Unit 10 5,600 · Unit 25 5,600 · Unit 50 5,600"},{"title":"Persistent environment","note":"Unit 1 5,600 · Unit 10 3,653 · Unit 25 3,377 · Unit 50 3,250"},{"title":"Savings","note":"Unit 1 0% · Unit 10 35% · Unit 25 40% · Unit 50 42%"}],"caption":"Condensed from the note."},"prompt":"Where next?","choices":[{"label":"the bridge","to":"the-bridge-to-energy"},{"label":"Wrap it up","to":"close"}]},"the-bridge-to-energy":{"short":"the bridge","pose":{"base":"drained"},"beat":{"layout":"right","marker":"08 · the bridge","title":["The bridge","to energy"],"lede":"Because the cost model retains token counts, physical accounting composes with value accounting:","code":"quirqs / kWh        with E ≈ Σ tokens · e_tok\nquirqs / tonne CO₂  via grid carbon intensity","caption":"Condensed from the note."},"prompt":"Keep going?","choices":[{"label":"Close the note","to":"close"}]},"close":{"short":"the end","pose":{"base":"finale"},"beat":{"layout":"center","title":["That was one path.","The note has the rest."],"glass":1,"lede":"This walk is one route through The quirq calculus. The full note carries every chapter, the tables, the code, and the source it was adapted from.","links":[{"href":"/research/the-quirq-calculus","label":"Read the full note"},{"href":"/research","label":"All research","tone":"ghost"}]}}}}