AB=CD and Three Drives: Geometry, Time and Elliott Roles
Two calculated harmonic examples distinguish vertex labels from Elliott waves and separate pattern geometry from observed confirmation.
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AB=CD and Three Drives can be measured directly. Their letters and drive numbers do not supply the missing Elliott subdivisions or evidence of a completed market reversal.
AB=CD measures lengths, not Elliott ABC
Use A=200, B=160, C=184.72, D=144.72 at indices 0,10,15,25. AB=40 and CD=40; BC/AB=0.618 and CD/BC=1.618123 after rounding. Equality is constructed here, while the familiar 1.618 is a rounded reciprocal.
A, B, C, D are vertices. Elliott A–B–C names whole components that need appropriate subdivisions, degree and context. Equal legs cannot provide those facts. Our AB/CD durations are both 10 index units, but that choice is not asserted as a universal price-pattern requirement.
| Measure | Calculated value |
|---|---|
| A (t=0) | 200 |
| B (t=10) | 160 |
| C (t=15) | 184.72 |
| D (t=25) | 144.72 |
| BC/AB | 0.618 |
| CD/AB | 1 |
| CD/BC | 1.618123 |
| AB = CD | 40 |
| Δt(AB) = Δt(CD) | 10 |
Does AB=CD prove a complete Elliott zigzag?
No. Length equality does not establish motive A/C, corrective B or their larger-wave role.
Three Drives: measure the intervening retracements
Use O=200,1=160, A=184.72,2=153.276160, C=172.708453,3=147.990576. O is an added reference origin;1, A,2, C,3 are the five pattern vertices. This example follows the TradingView description: each retracement is 0.618 of the preceding drive and the next drive is 1.272 of that intervening retracement.
The drive durations are 10,10,10 index units; the two retracements last 5,5. Ratios use full precision and the table rounds prices. The author’s site lists other projection variants, which we do not silently merge. Three drives do not establish an Elliott diagonal or prove that a reversal follows.
| Measure | Calculated value |
|---|---|
| O (t=0) | 200 |
| 1 (t=10) | 160 |
| A (t=15) | 184.72 |
| 2 (t=25) | 153.27616 |
| C (t=30) | 172.708453 |
| 3 (t=40) | 147.990576 |
| R1/Drive1 | 0.618 |
| Drive2/R1 | 1.272 |
| R2/Drive2 | 0.618 |
| Drive3/R2 | 1.272 |
| Δt(Drive1/2/3) | 10 / 10 / 10 |
| Δt(R1/R2) | 5 / 5 |
Should drive 2 be calculated as 1.272 times the entire first drive here?
No. Our selected convention measures it from retracement A. The denominator and starting anchor must be stated.
Separate geometric completion from market confirmation
The supplied AB=CD and Three Drives prices complete their numerical constructions only. No later completed closes are supplied for either. Their measured endpoint is not evidence that a real market rejected a PRZ or that a drawing tool automatically detected the pattern.
Use the same declared confirmation question on both examples, rather than importing an Elliott wave label. The first has endpoint 144.72 at 25; the second 147.990576 at 40. Reaction, subsequent structure and execution remain unobserved.
| Measure | Calculated value |
|---|---|
| AB=CD: t=25 | 144.72 |
| Three Drives: t=40 | 147.990576 |
| t > 25 / 40 | — |
Can the final labeled point be called an observed reversal?
No. It is an endpoint in the exercise. A later reaction must be supplied and evaluated under a predeclared rule.
Apply one prospective protocol to both constructions
For a comparison, freeze the exact points and selected ratio convention. An authored test may require two completed closes above the endpoint within five later bars, with completed close below endpoint−2 recorded separately. The deadlines are 30 for AB=CD and 45 for Three Drives.
Keep failure, unresolved cases, revised pivots, costs and fill assumptions in the sample. A geometric match is one input, not a guaranteed entry. No post-endpoint data are supplied here, so the study outcome remains unresolved.
| Measure | Calculated value |
|---|---|
| AB=CD: t(D)+5 | 30 |
| AB=CD: D−2 | 142.72 |
| Three Drives: t(3)+5 | 45 |
| Three Drives: P(3)−2 | 145.990576 |
Does the drawing itself provide a filled trade?
No. Signal definition, order execution and outcome require separate records.