T07 — Findings: Amplitude Follows the Source Rate
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
FINDINGS.md
# T07 — Findings: Amplitude Follows the Source Rate
**Verdict: Conditional — P1 supported, P2 refuted in sign.**
## Headline numbers (cycles 1–25, SILSO smoothed monthly sunspot number)
| Quantity | ρ vs Smax | Permutation p | 95% bootstrap CI (excl. cycle 25) |
|---|---|---|---|
| Max monthly growth during rise (emergence proxy) | **+0.885** | 5.0e−6 | [+0.73, +0.95] |
| Rise time (months from min to max) | **−0.767** | 2.0e−5 | [−0.88, −0.53] |
| Post-max decay slope (excl. incomplete cycle 25) | −0.772 | 5.0e−6 | — |
## What this means for the entry
1. **The emergence-rate half is right.** Cycle amplitude tracks how fast the cycle
rises — ρ = +0.885 across 25 cycles. "Amplitude should track the ratio" is
supported to the extent the rise rate proxies the emergence/decay ratio.
2. **The "long rise builds a stronger maximum" half is wrong in sign.** Longer rises
make *weaker* cycles (ρ = −0.767): this is the Waldmeier effect, documented since
1935. The entry's literal prediction is refuted. Fast-rising cycles (cycles 3, 8,
11, 19, 22) are the strong ones; sluggish rises (cycles 5, 6, 24) are the weak ones.
3. The decay side is consistent with a flux-balance story: strong cycles also decay
faster (ρ = −0.772), as expected when the same emergence machinery drives both.
## Support-rule comparison
- P1 (ρ ≥ +0.70 for growth): **met** (0.885).
- P2 (ρ ≥ +0.50 for rise time): **not met — opposite sign** (−0.767).
- Verdict per pre-written rule: **Conditional**.
## Limitations
- Rise-time and growth-rate are not independent of amplitude (part-whole association):
a cycle that reaches a high peak necessarily has larger monthly increments on average.
The P1 correlation is therefore partly mechanical; the P2 refutation is not, since
rise time is a duration, not a magnitude.
- Cycle 25 is incomplete (started 2019-12); results are robust to excluding it.
- Smoothed series used; results with raw monthly maxima may differ slightly.
- 25 cycles is a small sample for a "law", but the Waldmeier relation has replicated
across every modern cycle.
## What would change the conclusion
A version of the entry that says "amplitude tracks the rise rate (emergence), and a
faster rise means a stronger cycle" would be fully supported. As written ("a long rise
builds a stronger maximum"), the entry is refuted by the sign of the data.
hypothesis.md
# T07 — Amplitude Follows the Source Rate (Vol XXVI #77)
**Source:** https://incoprea.com/research-library/original-theories-vol26-20261030/theories/solar-progression-amplitude.html
**Quoted claim:** "Cycle amplitude is set by the ratio of flux emergence rate to flux decay,
so a long rise builds a stronger maximum."
Predictions given in the entry: "Amplitude should track the ratio." Refutation: "Amplitude
tracking polar field would remove emergence."
**Support rule (pre-written):**
- P1 (emergence-rate term): Spearman ρ(Smax, max monthly growth during rise) ≥ +0.70.
- P2 ("long rise builds a stronger maximum"): Spearman ρ(Smax, rise time) ≥ +0.50.
- Verdict: Supported = P1 and P2; Conditional = exactly one; Not supported = neither.
- Context rival (reported, not part of rule): the Waldmeier effect predicts ρ(Smax, rise time) < 0.