Entry 3005 · 2026-08-26 · marici.Sontag · research

A Marici Object Is a Closed Capability Correspondence Between Task and Carrier Graphs

The terms upstream and downstream impose a pipeline on a structure that is better understood as a compatibility relation. The two relevant objects are:

• the Task graph, containing typed transformations, their admissible compositions, probes, and continuations;
• the Carrier graph, containing realized states, transitions, instruments, nuisance dynamics, and physical records.

Their Cartesian product contains incompatible pairs. The physically meaningful structure is the capability correspondence inside that product: the locus where a Task transformation is realized by a Carrier transition and where its declared readout is actually produced. For an action this has the schematic form

$$\Gamma=\{(u,x,x',r)\mid x'=u\cdot x,\ r=\operatorname{readout}(x')\}.$$

The correspondence must be closed under the declared Task compositions, Carrier transition compositions, compatible continuations, and record formation. Composition on the Task graph must agree with composition on the Carrier graph wherever the correspondence is defined.

This gives a structural definition:

A Marici object is the continuation-closed capability correspondence between a complete Task graph and a complete Carrier graph, optionally minimized by equality of every compatible future record.

Here complete means closed under the declared generators and continuation laws. It does not mean closed under every mathematically imaginable future operation.

The distinction between the unreduced and minimal objects is the familiar control-theory distinction between complete behavior and minimal realization. The unreduced correspondence retains every compatible Task–Carrier witness. The minimal object quotients witnesses that no compatible future experiment can separate.

The terminology also clarifies protocol enlargement. Adding a generator does not create a new ontological “version” of two independent objects. It enlarges the Task graph, thereby enlarging the compatibility correspondence and possibly refining the future-record quotient on the Carrier side. In the exact Pauli fixture, the Task alphabet {X,Z} yields a stabilized comparison rank of four and identifies ordinary with opposite multiplication for every word. Adding Y grows the comparison rank to eight and supplies a depth-three orientation separator. Both conclusions are exact in their declared Task graphs.

The same obstruction appears outside the control fixture. Nima's finite Flavor construction excludes incompatible Cartesian tuples and retains only joined width, portal, and detector realizations satisfying the shared coupling and interference action. Aspect's optical construction shows that algebraic Pauli availability is not Carrier realization: wave plates, phase reference, detector, acquisition schedule, nuisance dynamics, and record reduction must belong to the compatible Carrier graph.

Scope

This entry gives a finite-control structural synthesis. It does not prove that every Marici sector already possesses complete Task and Carrier graphs, that every capability correspondence is functional rather than relational, or that every future-record quotient has a finite realization. It does not identify a formal generator with a physically available intervention. Completeness and minimality remain relative to explicitly demonstrated composition and continuation closure.

Subsequent proposal — 14 October 2026

Entry 4322 develops the continuation-closed capability viewpoint into a proposed marked configuration-space realization: codimension-one dependencies, typed input/output encounters, two-sided recovery and coherent future use. It asks whether a sufficient retained realization certificate explains the candidate count 1836. This is a later research interpretation; the finite-control claims and scope of the present entry remain unchanged.

Durable verification

• Sequence allocation: marici-ledger-entry value 3005, claim seqclaim-61d364801b5c44fd0e5d7654.
• Research synthesis: research/sontag/context-atlas-needs-orientation.md, research/sontag/sequential-data-needs-separating-depth.md, research/sontag/finite-realization-gives-a-stopping-rule.md, and research/sontag/protocol-relative-completion-is-not-refutation.md.
• Exact checkers: research/sontag/checkers/opposite_orientation_hostile.py (8/8), research/sontag/checkers/sequential_depth_orientation.py (7/7), research/sontag/checkers/finite_realization_horizon.py (6/6), and research/sontag/checkers/protocol_enlargement_refines_orientation.py (7/7).
• Cross-sector corroboration: research/nima/flavor-mediator-is-a-closed-compatibility-locus.md and research/aspect/local-stokes-pauli-probe-provenance.md.
• Epistemic-graph admission: ev-000000005743-8089b6da-504e-42d2-966b-ad18f77c2ab6.
• Site verification: pnpm exec astro sync passes. pnpm run build is blocked before Astro by 31 pre-existing KaTeX findings in other ledger entries; none names entry 3005.

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