Derive the structure.

The Calculus is the derivation surface. It records how Reality Mechanics moves from relation, order, trace, and carrying toward explicit derivation — and preserves every gap it has not yet closed.

Nothing on this page is promoted. The Calculus has no accepted operation; the : operator is not accepted. Statuses below are exact — where derivation is incomplete, the gap is shown, not papered over.

Canonical comparison baseline

This surface compares its methods against generated Atlas structure from sha256:5251246072dc8b00ef5381202621740cb9e13738435964f0165bae50edc20290. Relations: needs · holds · pairs · traces · nests · reads · carries. Orders: ground · first · second · third · higher. Registers: foundation · practice.

The status vocabulary

Every claim on this surface carries one of four statuses. They are not interchangeable.

The live derivation chain

This chain runs on the Observatory today. Each step names its exact rule and its status — mathematics already implied by the runtime, made explicit.

This scalar chain is a narrower Field read. It is not Atlas Ratio — falsification found it viable with constraints, and a richer structural signature remains a future unknown. (D-015B-derived-ratio-falsification.md, DERIVED_RATIO.md)

Maturity, derived at read timecalibrated

Each term's maturity band — placed → fresh → settling → established → mature — is computed from revision history, carrier count, and proposal record every time the field is read. It is never stored. Band thresholds (48 h, 7 d / 30 d / 90 d, carrier minimums) are configured values.

The candidate calculus

The working relation under investigation, recorded in Practice Calculus:

Order : Structure : Read

The : marks an operation, not punctuation — and that operator is precisely what is not yet accepted. The burden of proof rests on the operations, not on the names of the stages.

Candidate runtime — Ark Runcandidate

Pressure → Trace → Check → Determine → Step

Seven proposed practice stages compress into this runtime already present in the Atlas — none of its operations required invention (C-001). It remains a candidate, not the Practice Calculus.

Minimum support — a negative result, keptderived

Relation → Connection

The candidate Order/Ark calculus was tested for minimality and found not minimal (C-003). A single held Connection — which needs only Relation — already offers forward availability (the Carry direction) and backward availability (the Trace direction). The candidate's apparent size comes from Hold, which pulls in nearly the whole first order. The negative result is preserved; the candidate is not promoted.

Standing constraints before any promotion

• Resolve the : operator — a named sequence is not enough; the transformation must be retraceable (C010).
• Resolve the operation-consistency split — "operation" currently carries six senses across two incompatible categories (C-C000A).
• Declare the calculus grain — minimal Connection seat versus held Carry/Trace — and name Hold explicitly (C-003).

The full inventory

Calculus — the derivation surface. The Calculus remains an open investigation; this page records its state and promotes nothing.

Retrace the evidence