Combined Feedback

User: In the class loop BR->TL is where local pattern performance metrics feed back to refine the collective pattern. But the individual learns from and uses these local inner metrics too, how is this represented in triangle cycles?

The short answer is: The very same metric packet makes two hops—BR → TL for the collective and (after being stamped into the event stream) TR → BL for the individual—so both triangles absorb the lesson in one turn.

1. Where the metric is born

• BR (inner-flux) logs the raw outcome of an act: reward delta, sensor reading, cost, etc. It is strictly private to the locus that just acted—“what happened on my bench.”

2. First hop: BR → TL (Class loop)

• In the Class triangle TL → TR → BR → TL, the edge BR → TL (h_refine in the formal pseudocode) ships that packet upward to the shared pattern shelf, so the playbook the whole swarm reads is now better tuned.

This closes the pattern ⇆ result circuit for the collective.

3. Interlock at the top edge TL → TR

Because both triangles share the outbound edge TL → TR, the freshly-refined blueprint is immediately the one the Instance triangle will consult next time an agent advertises its capacity (BL → TL). That is already one way the individual “learns” from its own metric.

4. Second hop: TR → BL (Instance loop)

• The metric is also wrapped into the event object that sits in TR.
• The Instance triangle BL → TL → TR → BL contains the edge TR → BL (r_reconcile).
  Here the event—now carrying cost, reward, utilisation, etc.—is reconciled back into the agent’s private ledger.
• That update may debit energy, bump a skill-rating, refresh a cache, etc., so the agent’s latent state (BL) evolves in step with what it just experienced.

Thus TR → BL is the individual-learning leg that complements BR → TL’s collective-learning leg.

5. Why the two-hop scheme matters

Hop	Triangle	Scope touched	What it achieves
BR → TL	Class	Shared pattern (TL)	Keeps the playbook honest—continuous improvement of the collective recipe.
TR → BL	Instance	Private ledger (BL)	Settles accounts and adapts the agent—credit-assignment & habit formation.

Because every cycle executes both hops before it finishes, one metric packet eliminates two kinds of mismatch at once—global blueprint drift and local ledger drift—and the Lyapunov error $H$ can only decrease.

6. Fractal guarantee

Each holon nests another 4QX square inside itself, so the same geometry propagates upward and downward indefinitely. Metrics produced in a deep leaf node climb layer by layer (BR→TL at each rank) while also propagating laterally (TR→BL) within every ancestor, ensuring that learning is always both personal and communal at every scale.

7. Combined feedback

User: TR-BL reconcilisational feedback automatically includes prior BR-TL feedback so it will be inherently factored in to subsequent selection decisions.

Both diagonals pump their own evidence, but the moment that evidence reaches the shared top edge (TL → TR) it is poured into the same outer ledger. Because that ledger is updated by pure set-union—an idempotent merge—every metric from the Class loop and every commitment from the Instance loop lands in one coherent “current snapshot” that any holon can read at once.

From there each loop “listens” only to the aspects that serve its telos:

• Class loop (TL → TR → BR → TL) sifts the merged ledger for pattern ↔ metric gaps. It rewrites recipes so the next burn will tighten blueprint versus outcome.
• Instance loop (BL → TL → TR → BL) scans the same ledger for capacity ↔ commitment gaps. It adjusts private offers so the marketplace never over- or under-books the agent.

Because both loops draw from—and write back to—the identical data pool, any refinement one makes immediately becomes fresh context for the other. The ledger is therefore not a third loop; it is the meeting surface where the two teloi continuously reconcile their distinct concerns while staying in phase with each other’s latest findings.

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Appendix: Edge names

Here are the six arrow names exactly as they appear in the “Appendix D: Kleisli Category of 4QX Cycles” pseudo-code in the formal proof. They cover every edge of the two triangles (note that the top edge is shared by both triangles).

Class triangle edges	Formal name	Rôle
1. TL → TR *	f_exec	Publish / instantiates (starts burn) the chosen pattern.
2. TR → BR	g_metric	Collect the metric packet.
3. BR → TL	h_refine	Fold metrics back into the shared blueprint.
Instance triangle edges	Formal name	Rôle
1. BL → TL	s_offer	Surface private capacity as an offer.
2. TL → TR *	k_commit	Lock the offer into a concrete event.
3. TR → BL	r_reconcile	Settle the agent’s private ledger with the event data.

* Shared edge