Diagrams

These figures are approved renditions of Compendium geometry (HOL-VIS-002 v79 library + HOL-VIS-003). They are not source of truth — definitions and proofs live in the 4QX Compendium.

Read in order: field → seam → loops → dual composition → harmony debt → clearing returns → operator cycle.

1 — Four-quadrant field

Holarchy reads organisational work on a single four-quadrant field. Pattern (TL) holds reusable structure; Event (TR) is seam-visible activity; Resource (BL) is private capacity; Metric (BR) is execution evidence.

Four-quadrant field: Pattern, Event, Resource, and Metric on form/flux and public/private axes (HOL-VIS-002) — The four-quadrant field: public Pattern and Event above; private Resource and Metric below; Form on the left, Flux on the right.

Corner shorthand

Corner shorthand: TL/TR/BL/BR map to Pattern, Event, Resource, and Metric.

Perspective (outer/inner) and modality (form/flux) bracket the four r…

Perspective (outer/inner) and modality (form/flux) bracket the four roles.

2 — Role gloss on the field

Once the bare field is named, each quadrant gains a role gloss — what kind of work belongs there and how it couples to the rest.

Quadrant field with role gloss and perspective/modality brackets (HOL-VIS-002) — Each quadrant carries a distinct role: reusable structure, seam-visible activity, private capacity, and execution evidence.

3 — Public seam (no private shortcut)

Lawful coupling stays seam-mediated. Public work crosses only the Pattern–Event seam (TL–TR). Resource and Metric are private and do not connect directly.

Public seam between Pattern and Event, with no BL to BR private shortcut (HOL-VIS-002) — Public work crosses only the Pattern–Event seam. Resource and Metric are private — no direct BL→BR shortcut.

Offer (Instance) and Accept (Class) are one seam event — commitment v…

Offer (Instance) and Accept (Class) are one seam event — commitment visible before private burn.

4 — Instance loop (flux / continuity)

The Instance loop carries flux-side work: what is still moving, what must return and integrate. Path: Resource → Pattern → Event → Resource.

Instance loop triangle on the quadrant field: BL to TL to TR to BL (HOL-VIS-002) — Instance loop — continuity work on the private–public boundary.

Instance phases on edges: 1·Fit, 2·Offer, 6·Integrate.

5 — Class loop (form / pattern evidence)

The Class loop carries form-side work: binding lawful patterns and returning publishable evidence. Path: Pattern → Event → Metric → Pattern.

Class loop triangle on the quadrant field: TL to TR to BR to TL (HOL-VIS-002) — Class loop — pattern evidence and publishable return.

Class phases on edges: 3·Accept, 4·Run, 5·Publish.

6 — Dual triangles (shared seam)

Both loops meet at Pattern–Event. Neither loop may bypass the seam with a private Resource–Metric edge.

Class and Instance triangles sharing the public seam; no Resource–Metric shortcut (HOL-VIS-002) — Two lifecycles — Class and Instance — share the public seam only.

Full operator cycle on the dual field: Fit → Offer → Accept → Run → P…

Full operator cycle on the dual field: Fit → Offer → Accept → Run → Publish → Integrate.

Kernel names (Pow, Sep, Pair, Union, Empty, Repl) map 1:1 to the Gene…

Kernel names (Pow, Sep, Pair, Union, Empty, Repl) map 1:1 to the Generic Organisation cycle.

7 — Harmony debt (H components)

Total operational tension H splits into coherence debt (pattern–resource shortfall) and flux debt (event–metric shortfall). H is the sum of its two components — not a third debt type beside them.

Harmony debt as column shortfall on the quadrant field (HOL-VIS-002) — Coherence debt compares accepted Pattern with available Resource; flux debt compares expected Event return with delivered Metric.

debt_coh tracks pattern–resource shortfall; debt_flux tracks event–me…

debt_coh tracks pattern–resource shortfall; debt_flux tracks event–metric shortfall.

H = debt_coh + debt_flux — when both are zero, the system is maximall…

H = debt_coh + debt_flux — when both are zero, the system is maximally available.

Harmony means H reaches zero within an honestly accounted boundary.

Distinguish open gaps (what still needs return) from trained residue …

Distinguish open gaps (what still needs return) from trained residue (what will repeat).

8 — Clearing returns (telos)

Clearing requires witnessed return — not activity volume alone. Integrate closes the flux gap (TR→BL); Publish closes the coherence gap (BR→TL).

Integrate and Publish as debt-reducing return edges with gap table (HOL-VIS-002) — Integrate closes the flux gap; Publish closes the coherence gap.

Which gap each return edge closes.

Return edges reduce both debts; ledger shows H = debt_coh + debt_flux…

Return edges reduce both debts; ledger shows H = debt_coh + debt_flux in one frame.

9 — Generic Organisation cycle (operators)

The six-phase cycle is how operators move work through the field: surface, commit at the seam, execute privately, publish evidence, integrate into the next surface.

Clockwise numbered operator cycle starting at 1 Fit: Fit, Offer, Accept, Run, Publish, Integrate (HOL-VIS-003) — Generic Organisation cycle for operators — clockwise from Fit.

Co-writers

Cursor: Composer 2.5 (diagram page assembly from approved library).