DRCT: when is an observation enough, and what must be added?

When is a partial observation of a system enough to predict its future, what exactly must be added when it is not, and can a machine find that addition unaided?

DRCT v1 redefines the programme's D0, first an intuition of truth, as zero unresolved predictive information, so each proposed new coordinate becomes a testable requirement.

1. Independently checked

   Step 1

   What was built. DRCT v1 (saved 23 August): the coarsest predictive refinement of an observation, the predictive deficit H(C*|Z), a missing-bit bound and a closure spectrum.

   What was found. Deterministic re-expression cannot recover erased distinctions, and in some systems no amount of observed history repairs the projection; genuinely new observables are needed.

   What it opens. The question of what a new observable must distinguish.

   • Dimensional Relational Closure Theory (DRCT) v1 Public

2. Independently checked

   Step 2

   What was built. v2–v3: a closure-defect graph (repair as graph colouring, library repair as set cover), then a semantic-free bridge to executable measurements and active probes.

   What was found. Exact pairwise measurement specifications and impossibility certificates, without naming the hidden coordinate; semantic meaning is optional for closure.

   What it opens. v4 names the remaining reliance on hidden-state labels as the next wall.

   • DRCT v2 — Closure-Defect Geometry and Observable Synthesis Public
   • DRCT v3 — Semantic-Free Operational Observable Bridge Public

3. Independently checked

   Step 3

   What was built. v4–v5: blind reconstruction from observable histories and future tests (a saved log reports an exhaustive pass on 5,832 small Moore systems), then statistical closure on one noisy stream.

   What was found. Failure of closure can be certified locally; in general, sufficiency cannot be proved from a finite passive corpus. v5 calls exact future equality 'the wrong primitive' for physical data.

   What it opens. The next readable record tests the calculus on a small trained transformer; packages for versions 7 and 8 are listed in the file catalogue, but their contents are not hosted.

   • DRCT v4 — Blind Predictive Closure Reconstruction Public
   • DRCT v4 exhaustive blind-reconstruction verification output Public
   • DRCT v5 — Statistical Closure From One Noisy Continuous Stream Public

4. Independently checked

   Step 4

   What was built. v6 black-box transformer stress test (all 780 contexts), v9 intervention closure depth with hashed predictions, v10 module tomography, v11 gauge and port theorems.

   What was found. Logits fix the function but not the weights; module-level probes recover all 1,428 parameters; identifiability is always relative to the experimental interface.

   What it opens. Choosing the next experiment automatically.

   • DRCT Black-Box Transformer Stress Test v6 Public
   • DRCT v9 — Predict-Before-Reveal Causal Query Complexity Public
   • DRCT v10 — Exact Module Tomography and the Observability Ladder Public
   • DRCT v11 — Gauge, Measurement Ports, and Identifiable Subspaces Public

5. Independently checked

   Step 5

   What was built. v12–v13: information-per-cost experiment planners, first finite, then continuous along the principal-eigenvector experiment direction.

   What was found. An exact cost lower bound of 9 in a 5,760-mechanism gauge laboratory; closure is stated relative to a declared experimental resolution.

   What it opens. Synthesising the sensor itself.

   • DRCT v12 — Autonomous Experimental Scientist Public
   • DRCT v13 — Continuous Model Manifold and Invented Experiments Public

6. Independently checked

   Step 6

   What was built. v14–v16: symbolic sensor-equation synthesis, invention of an unknown binary operation as a Cayley table, and minimum-arity relation discovery.

   What was found. Each step removes one supplied assumption but keeps a meta-language: relations, arity, affine composition.

   What it opens. Whether invented relations become reusable concepts.

   • DRCT v14 — Symbolic Sensor Equation Synthesis Public
   • DRCT v15 — Operator Invention From Closure Residuals Public
   • DRCT v16 — Ontology / Arity Discovery Public

7. Independently checked

   Step 7

   What was built. v17–v21: concept promotion with negative controls, a learned sameness rule, generator invention from anonymous worlds, morphism-type selection and morphism-ontology induction.

   What was found. Labels such as 'bijection' arise only as readings of learned anonymous classes, and D4 is recognised after reconstruction; row and column degree predicates remain the supplied prior.

   What it opens. The open wall named by v21: inventing the structural predicates themselves.

   • DRCT v17 — Transferable Concept Invention Public
   • DRCT v18 — Learning the Equivalence Relation Between Concepts Public
   • DRCT v19 — Transformation-Generator Invention Public
   • DRCT v20 — Morphism-Type Invention Public
   • DRCT v21 — Morphism Ontology Induction Public

The next question. Can the structural predicates used to describe relations be invented rather than supplied, so that no primitive predicate language has to be assumed?

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