theorem · fr-4-theorem-9-4

Finite-Depth Relational Reconstruction

Result stated and proved in the source manuscript; website restatement (draft) fusion-reconstruction

Statement

Fix . At every level through , assume a specified passage-type or relation-type certificate system, adequate finite provenance for higher levels, compatible generators with bounded or separately certified closable totalizations, compatible retained and decoder transports, one finite-context-uniform graph constant , compatible closable retained totalization, closed decoder realizations, and validity of all represented finite relations. Then every represented route claim through level survives: passage-type total routes are closable, and relation-type equalities persist on the completed certified image.

Meaning and scope

The theorem concerns the represented claims in a specified finite-depth package. It does not prove finite depth for every system, canonical minimality, or infinite-depth totalization. Constants may depend on the level.

Source

Paper 4, Theorem 9.4. Draft manuscript — compile-audit version; not marked frozen.

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