Working record

Four versions of one figure, including the one that was wrong.

Chapter seven of the Foundations paper describes a six-stage operating cycle in words and has never carried a figure. This is the record of making one: three directions, four versions, and one direction retired for a reason worth more than the drawing.

The paper already publishes notes on how its text has been revised. This is the same thing for the illustration. A research document that shows how its argument changed and hides how its figure was arrived at is being selective about which working it shows.

v1 Three directions

Three ways of drawing the same six stages, made to be compared rather than to be right. A put the cycle on a time axis as a helix. B plotted distance from the stable core against time. C drew it as a control loop, the way an operations paper would.

At this point A looked the most promising and B looked like a chart.

The operating cycle as an advancing helix The six stages of the operating cycle drawn as a helix advancing along a time axis. Each turn passes through Observe, Interpret, Decide, Adapt, Verify and Learn, and each turn arrives further along the axis than the last, so the cycle repeats without returning to the same state. A horizontal datum marks the stable core, which the coil orbits and never crosses. STABLE CORE TIME Observe Interpret Decide Adapt Verify Learn EXECUTION ADAPTS. THE CORE DOES NOT.
A · Advance
Drift from the stable core, and the cycle that corrects it A plot with time on the horizontal axis and distance from the stable brand core on the vertical. A flat datum line marks the core. Execution drifts steadily away from it and is pulled back sharply at the end of each completed cycle, producing a repeating sawtooth. The six stages are marked along the final cycle, at the points where the correction is decided and carried out. STABLE CORE TIME DISTANCE FROM THE CORE Observe Interpret Decide Adapt Verify Learn DRIFT IS THE DEFAULT. THE CYCLE IS THE CORRECTION.
B · Amplitude
The operating cycle drawn as a control loop The six stages of the operating cycle drawn left to right as a sequence: Observe, Interpret, Decide, Adapt, Verify, Learn. A dashed feedback arc returns from Learn to Observe, closing the loop. A second, shorter arc returns from Verify to Interpret, marking the case where verification changes the reading of the original signal rather than the response to it. Observe 1 Interpret 2 Decide 3 Adapt 4 Verify 5 Learn 6 THE LOOP CLOSES AND BEGINS AGAIN VERIFICATION CAN REVISE THE READING, NOT ONLY THE RESPONSE
C · Control

What was wrong with it

  • A does not read as a helix. It reads as a sine wave, and two of its labels overlap.
  • B runs off the right edge of the canvas.
  • C works and is generic.

v2 Fixing the look, and missing the problem

A got two rendering fixes: the far half of every turn drawn behind the axis, and a sideways oscillation so each turn leans. B stopped running off the edge and its labels were staggered.

Both changes were improvements. Neither addressed what was actually wrong with A.

The operating cycle as an advancing helix The six stages of the operating cycle drawn as a helix advancing along a time axis. Each turn passes through Observe, Interpret, Decide, Adapt, Verify and Learn, and each turn arrives further along the axis than the last, so the cycle repeats without returning to the same state. A horizontal datum marks the stable core, which the coil orbits and never crosses. The far half of each turn passes behind the datum. STABLE CORE TIME Observe Interpret Decide Adapt Verify Learn THE CYCLE REPEATS. IT DOES NOT RETURN TO THE SAME PLACE.
A · Advance
Drift from the stable core, and the cycle that corrects it A plot with time on the horizontal axis and distance from the stable brand core on the vertical. A flat datum line marks the core. Execution drifts steadily away from it and is pulled back sharply at the end of each completed cycle, producing a repeating sawtooth. The six stages are marked along the final cycle, at the points where the correction is decided and carried out. STABLE CORE TIME DISTANCE FROM THE CORE Observe Interpret Decide Adapt Verify Learn DRIFT IS THE DEFAULT. THE CYCLE IS THE CORRECTION.
B · Amplitude

What was wrong with it

  • A still reads as a wave.
  • B’s staggered labels still collide: Adapt with Verify, Interpret with Decide.

v3 A is retired, and the reason is the point

A side-on helix is a sine wave. That is not a drawing failure, it is what the projection produces. And in that projection the coil crosses the axis twice per turn.

The whole argument of the figure was that execution orbits a stable core and never crosses it. The drawing was asserting the opposite of the claim it was made to illustrate, in the document that makes the claim. No amount of polish reaches that, because it was never a rendering problem.

A could only be revived in a projection where the core is a point rather than a line. Seen down its own axis a helix is a circle, and a circle is the form the commercial page already uses, which is the one thing this figure may not be. The direction is closed rather than parked.

B’s labels moved to the baseline under leader lines. Six labels along a diagonal is a spacing problem that no offset solves; the ordinary convention for a plot cannot collide at any width.

Drift from the stable core, and the cycle that corrects it A plot with time on the horizontal axis and distance from the stable brand core on the vertical. A flat datum line marks the core. Execution drifts steadily away from it and is pulled back sharply at the end of each completed cycle, producing a repeating sawtooth. The six stages are marked along the final cycle, at the points where the correction is decided and carried out. STABLE CORE TIME DISTANCE FROM THE CORE Observe Interpret Decide Adapt Verify Learn DRIFT IS THE DEFAULT. THE CYCLE IS THE CORRECTION.
B · Amplitude

What was wrong with it

  • B’s final correction runs through the datum instead of stopping on it, which reads as an error rather than a return.

v4 Where it stands

The correction now stops on the datum. That was checked by parsing the path and asserting that no point falls below the line, rather than by looking at it, because looking at it is how the previous three versions each passed.

C is the figure, locked on 15 August 2026, and it is now in the chapter.

B argued something the prose does not: that drift is the default condition and the cycle is the intervention. That was its strength and, in a foundations paper, its problem. The chapter states that it is not presented as a complete methodology, so a figure making a claim the text has not made is a figure the text cannot support. C states the sequence the chapter actually sets out, and adds only what the prose already says: that verification can revise the reading, not only the response.

B stays here as the direction not taken.

The operating cycle drawn as a control loop The six stages of the operating cycle drawn left to right as a sequence: Observe, Interpret, Decide, Adapt, Verify, Learn. A dashed feedback arc returns from Learn to Observe, closing the loop. A second, shorter arc returns from Verify to Interpret, marking the case where verification changes the reading of the original signal rather than the response to it. Observe 1 Interpret 2 Decide 3 Adapt 4 Verify 5 Learn 6 THE LOOP CLOSES AND BEGINS AGAIN VERIFICATION CAN REVISE THE READING, NOT ONLY THE RESPONSE
C · The control loop — LOCKED, in the chapter
Drift from the stable core, and the cycle that corrects it A plot with time on the horizontal axis and distance from the stable brand core on the vertical. A flat datum line marks the core. Execution drifts steadily away from it and is pulled back sharply at the end of each completed cycle, producing a repeating sawtooth. The six stages are marked along the final cycle, at the points where the correction is decided and carried out. STABLE CORE TIME DISTANCE FROM THE CORE Observe Interpret Decide Adapt Verify Learn DRIFT IS THE DEFAULT. THE CYCLE IS THE CORRECTION.
B · Drift and correction — not taken

On why none of these is a ring. The commercial application of this model is published separately by Digilu, at its own page on the category, and that page carries a concentric figure. These two documents do different jobs: one sets out the model, the other sells the service built on it. Keeping them visibly distinct is deliberate, and a figure is often the most recognisable thing on a page.

On method. Every version here is generated from parameters rather than drawn by hand, so a revision is a readable change rather than several hundred moved coordinates, and any version can be reproduced exactly. The last defect was caught by measuring the path instead of looking at it.

Comp C was placed in Section 7 on 15 August 2026. The lock is recorded in Appendix C, Version Notes.