Advances variable λ directly. Made the Lyapunov dashboard layer load-bearing.
The problem
We named λ as one of our four thesis variables, but we had no way to measure it. Without multi-week history in the knowledge base, the calculation was not possible. The pitch deck and the editorial briefs all referenced λ as if it existed. It did not.
What we did
With 10 weeks of micro-drama scoring now in the knowledge base, we wrote code that looks at each company’s score in week N and its score in week N+1, computes how much it moved, and stores that as one DecayMetric record. We do this for every pair of consecutive weeks we have. We then aggregate the DecayMetric records into a per-week LambdaSnapshot — the median, mean, and 90th-percentile of how much the whole cohort moved that week.
For micro-drama this produced 180 DecayMetric records and 9 LambdaSnapshot records, derived from the source data and stored in their own labeled section of the knowledge base so we can recompute them anytime without touching the original scores.
The λ trajectory across 9 weeks
| Week |
Median λ |
What was happening |
| W11-2026 | 0.90 | Reporting cadence still ramping; cohort growing from 16 to 17. |
| W12-2026 | 1.85 | Peak volatility. New entrants, calibration in progress. |
| W13-2026 | 1.25 | Mid-volatility as the cohort filled out to 21 companies. |
| W14-2026 | 0.60 | Cohort settling. |
| W15-2026 | 0.30 | Continued settling. |
| W16-2026 | 0.20 | Continued settling. |
| W17-2026 | 0.00 | Structural floor — no movement in the median. |
| W18-2026 | 0.00 | Continued at the floor. |
| W19-2026 | 0.10 | Nudges up on Amazon Prime Video Clips deploy. |
Top movers, W10 → W19
| Company |
Net composite change |
| JioHotstar | +16.80 |
| COL Group / BeLive | +14.45 |
| GoodShort | +6.40 |
| Disney | +6.20 |
| DramaBox | +6.05 |
| Lifetime / A+E | +5.90 |
| Amazon | +3.55 |
These are the brands whose structural position moved the most across the tracked period.
Why it matters
λ is no longer an unmeasured promise. We can quote it in the pitch deck. We can use it to set refresh cadences per vertical (high λ verticals need nightly updates; low λ verticals can hold for a week or more). The Lyapunov layer in the customer dashboard — the part that frames a brand’s “structural basin” and “shock response” — can now read from this derived data instead of from numbers Jonny enters by hand.
What is left
The brand dashboard’s Lyapunov layer still reads hand-curated inputs. The DecayMetric pipeline produces the principled equivalents. Wiring is a small follow-up.
We also have not yet generated λ for the AI-agent vertical. That vertical has 1,672 companies but only one week of scores. We need at least two consecutive weeks to compute λ, and at least four for it to be reliable. The work: run the auto-research cycle for W13, W14, W15 and onward. The methodology is locked; the pipeline exists. What is missing is execution.
Output: λ goes from a guess to a measured rate. The Lyapunov layer becomes load-bearing.