Affine channels as reusable trade hypotheses

How a price channel is stored

A formed price channel can be stored by drawing later parallel lines whose spacing equals the original channel height, so later price may meet those saved lines as support or resistance. In this workflow a price-channel is a pair of parallel support and resistance lines whose width is preserved and reused later as a measured band the market may revisit.

When later price meets a saved parallel line, the expected interaction is a bounce that travels along the line, or a break that continues toward the next parallel intersection. Market-memory is the working premise that a well-formed channel remains relevant later, so later prices may stall, travel along, or break through the saved parallel lines. A half-channel-line is a parallel line drawn at half the original channel height and used as an extra consolidation reference inside the saved band.

Hourly yen reuse of early bands

On the hourly yen, rising-channel height R and falling-channel height F from early 2001 were reused as later parallel bands, including half-channel lines. Those early bands were still treated as active into late 2001 and early 2002.

An affine rewrite is equivalent information

An affine-transformation is a one-to-one rewrite of price by projecting each point onto axes aligned with a chosen channel, so the same data is viewed along the channel rather than in ordinary time and price. The rewrite is defined from a channel line by an origin (t0, P0) and slope angle a, with tg(a) = (P1 - P0) / (t1 - t0). Each ordinary point (t, P) maps uniquely to distances along the channel axes, so the rewrite is equivalent information, not new data.

Folding-rule buys on the rising yen rewrite

On the hourly yen from March 2 to 16, 2001, a folding-rule reversal on the JPY_RIS affine version produced three buy signals that were harder to see on the ordinary chart. A folding-rule is a reversal geometry that becomes easier to mark after the chart is rewritten along a channel.

Fibonacci projection and retracement overlap

After an affine rewrite, fibonacci-retracement levels are percentage pullback and projection levels, including 23.6%, 38.2%, 50%, 61.8%, 100%, and 161.8%, read on the same swing in channel coordinates. On the hourly yen from May 16 to June 14, 2001, a 161.8% Fibonacci projection break on the JPY_FAL affine version coincided with a 61.8% price retracement break. That overlap was treated as extra confirmation of a buy.

Bearish RSI divergence on the falling euro rewrite

A divergence is a mismatch between price extremes and an oscillator such as RSI, which can appear on a channel-aligned rewrite even when it is not obvious on the ordinary chart. On hourly euro around June 2 to 3, 2002, RSI(8) showed a bearish divergence on the EUR_FAL affine version that was not visible on the ordinary euro chart. The archive treats the later euro decline after the January 2, 2002 high, toward a late-January low below 0.86, as the market path that followed that affine-chart divergence signal.

What the archive concludes

The archive conclusion is that saved parallel consolidation lines are the practical result of channel memory, while an affine rewrite is only another equivalent view of the same prices that can make those lines, Fibonacci overlaps, and oscillator divergences easier to test.