Our 4QX formal proof of the 2 × 2 scaffold shows that the Instance triangle cannot run BL → TR → TL → BL (the story we’ve repeated since the first holon-mechanism note).
To keep every edge oriented exactly once, Instance must leave BL, pass through TL, then TR, and drop straight back to BL:
TL → TR
↑ ↙
BL (start)That single tweak:
- Aligns the high-level narrative with the formal closure condition.
- Leaves the lived semantics intact (“offer → commit → harvest”).
- Removes the only residual mismatch DeepSeek flagged between prose and proof.
Please update diagrams and documentation accordingly.
1 · Where the old story came from
The early docs pictured Instance as:
- BL → TR “push intention straight to the market”
- TR → TL “market writes pattern back”
- TL → BL “learning trickles home”
Visually pleasing—two loops circulate in opposite directions along the top edge.
2 · What the proof actually fixes
Chain 1 establishes:
- Triangles are ordered triples that start at their private corner (that’s unchanged).
- The shared edge always appears TL → TR in both triangles (this is changed).
– this is how “no unmatched arrow” is defined in § 4 of the proof
Put those together and the only legal Instance sequence is:
| Step | Edge | Plain Meaning |
|---|---|---|
| 1 | BL → TL | surface my offer to the shared shelf |
| 2 | TL → TR | marketplace commits the offer |
| 3 | TR → BL | receipt / metric comes back to me |
No edge reads TR → TL anywhere in the complex.
3 · Why the semantics still work
The intuition stays the same; the waypoint order changes.
| Old Phrasing | Revised Phrasing |
|---|---|
| “Intention rises to market.” | BL → TL posts the intention as a provisional pattern visible to all. |
| “Market writes back to pattern shelf.” | TL → TR means the shelf hands the specific pattern to the burner/market for execution. |
| “Learning flows TL → BL.” | TR → BL sends the confirmed work-order (and metrics) straight to the originator. |
So the agent still “offers → gets scheduled → receives harvest,” but now every arrow matches the scaffold’s objective orientation.
4 · Take-away
The proof didn’t break 4QX; it corrected our diagram.
Getting this detail right means:
- Our teaching material no longer contradicts the finite-ZF scaffold.
- DeepSeek’s next pass will have zero geometry-vs-narrative inconsistencies.
- Future layers (norm holons, stochastic sims) can rely on a single, unambiguous edge map.
Questions or concerns—ping #4qx-core.
Otherwise, flip those arrows and carry on.
— The Formalization Task Force