Research Results
From fundamental properties of artificial intelligence to control of one million autonomous objects, CAPEXNULL investigates the limits of complexity, scale, and autonomy. This page compiles test results in which mathematical models and software systems are evaluated as operational mechanisms: under extreme losses, at million-scale, in multi-loop infrastructures, in structural analysis of complex organizations, and in autonomous learning, causal modeling, concept formation, attention control, and AI self-correction.
From Mathematics to Verifiable Results
Nineteen tests cover scalable control of dynamic systems, structural analysis of complex organizational systems, computational-core performance, and fundamental capabilities of autonomous AI. Each result is documented with measurable metrics and a test outcome.
19
tests
single series of validated results
19 PASS
results
across all presented tests
1 000 000
objects
validated test scale
Results Table
Measured metrics, potential application areas, and conservative effect projections where a sufficiently direct open technical basis exists. Projections are not validated results and require separate verification in the target system.
| Test Name | Result | Primary Result | Applicability and Effect Projection |
|---|---|---|---|
| Dynamic-System and Infrastructure Control | |||
| Large-Scale Dynamic-System Control Under Extreme Losses | PASS | Tests whether a multi-loop system can maintain coordinated control of 1,000,000 devices under extreme data loss, changes in inter-loop connectivity, and repeated recovery. 1,000,000 controlled devices; 40 million events; 200 million transitions; up to 99% simulated loss; 20 recovery cycles; worst recovery — 1,681 μs; deadline violations — 0; stale-epoch effects — 0; illegal assignments — 0; checkpoint mismatches — 0; three independent validations — PASS. | Critical infrastructure, distributed systems, and large technological complexes. |
| Multi-Level Control of Complex Distributed Infrastructure | PASS | Tests coordination of 1,000,000 devices in a multi-loop structure: 8 levels and 8 loops per subsystem, including interactions across loops and levels under communication disruptions. 1,000,000 devices; 40 million events; 8 hierarchy levels; 6,488,888 loop-structure elements; 16,598,980 commands and effects; 2 million simulated communication disruptions; unexplained losses — 0; duplicate effects — 0; coordination conflicts — 0; checkpoint mismatches — 0; replay mismatches — 0; independent full replay validation — PASS. | Hierarchical infrastructures, distributed networks, and interdependent technological systems. |
| 1 GW Data Center Infrastructure Control | PASS | Tests coordinated operation of 5 infrastructure loops in a 1 GW data-center model with 1,000,000 active points, high event intensity, failures, and recovery. 1 GW data center; 1,000,000 active points; 40 million events; 200 million state transitions; 20 recovery cycles; up to 1,717,344 events/s; unexplained losses — 0; duplicate effects — 0; unresolved conflicts — 0; checkpoint and replay mismatches — 0; independent validation — PASS. | Coordination of interconnected systems in a large data center. Projected effect: 10–25% improvement in computing-resource utilization efficiency; energy savings up to 10–15% for workloads where orchestration and scheduling determine the effect. |
| Control of a Group of 1,000,000 Autonomous Drones | PASS | Tests control of 1,000,000 individually simulated drones across interconnected loops during motion, extreme losses, and control recovery. 1,000,000 individually simulated drones; 40 million events; 20 recovery cycles; maximum simulated loss — 99%; collisions — 0; deadline violations — 0; checkpoint mismatches — 0; replay mismatches — 0; independent physics validation — PASS. | Mass robotics and coordination of large groups of autonomous vehicles. Projected effect: 15–30% improvement in coordination efficiency and group-task execution in dynamic environments. |
| Determining Swarm-Size Limits Under a Single Control-Cycle Compute Budget | PASS | Tests the computational boundary of real-time swarm control: whether one correction cycle for one million drones completes within 20 ms. 1,000,000 drones; computation time for one correction cycle — 16.8801 ms; cycle time budget — 20 ms; no swarm-size limit was found within the tested range up to 1,000,000 on the hardware used; PASS. | Control of large groups of autonomous vehicles in real-time systems. Projected effect: 15–30% increase in available compute headroom for coordinating a large swarm under a comparable control cycle. |
| AI Cognitive Capabilities and Autonomous Behavior | |||
| Formation of Individual AI Behavior from Its Own Experience | PASS | Tests whether AI systems with identical initial states can develop different individual behavior from different accumulated experience. Initial equivalence — 100%; divergence after different experience — 100%; class coverage — 100%; match under identical experience — 100%; label dependence — 0; protocol violations — 0. | Personal AI systems and autonomous agents that develop different behavior from their own experience. |
| Autonomous Learning, Retention, and Transfer of Acquired Experience | PASS | Tests whether AI can autonomously learn from experience, retain acquired knowledge, and transfer it to subsequent tasks. Accuracy before learning — 0%; after learning — 75%; gain — 75 percentage points; transfer — 75%; retention of acquired knowledge — 75%; retention loss — 0; repeated-error rate — 25%; protocol violations — 0. | AI systems with continual learning, retention, and transfer of acquired experience. Projected effect: 5–15% improvement in performance on repeated and related tasks through retention and reuse of acquired experience. |
| Building a Causal Model of the Environment and Predicting Action Consequences | PASS | Tests whether AI can autonomously identify causal relationships, predict action consequences, and use a causal model for decision selection. intervention accuracy — 100%; N1/N2/N4/N8 prediction — 100%; overall multi-step prediction — 100%; counterfactual prediction — 100%; causal-relation discrimination — 100%; transfer — 100%; autonomous choice — 100%; 160 exploratory interactions; protocol violations — 0. | Causal modeling, forecasting, planning, and autonomous action selection. |
| Autonomous Formation of New Concepts and Transfer to New Tasks | PASS | Tests whether AI can autonomously form internal concepts, combine them, and transfer the resulting concepts to new tasks. partition accuracy — 100%; within-concept consistency — 100%; concept separation — 100%; coverage — 100%; 4 distinct conceptual responses; composition accuracy — 100%; transfer — 100%; permutation consistency — 100%; protocol violations — 0. | Autonomous formation of internal concepts, composition, and transfer to new tasks. |
| Retention of Knowledge and Relationships in Long Multi-Stage Tasks | PASS | Tests whether AI can retain facts, relationships, and priorities over long horizons and retrieve them correctly when continuing a multi-stage task. direct retention — 100%; relational retention — 100%; priority retention — 100%; retrieval accuracy — 100%; transfer to altered representation — 100%; context coverage — 100%; false inclusion — 0; long-horizon degradation — 0; protocol violations — 0. | Long multi-stage tasks and autonomous AI systems with extensive histories of states and decisions. Projected effect: 5–15% improvement in success rates for long multi-stage tasks through more robust retention and retrieval of relevant experience. |
| Autonomous Attention Control and Recovery of Interrupted Work | PASS | Tests whether AI can autonomously select and switch attention, preserve background-task context, and resume interrupted work. focus-acquisition correctness — 100% (12/12); focus selection — 100%; switching — 100%; background-context retention — 100% (10/10); task return — 100%; work resumption — 100%; false switches — 0; repetition of completed work — 0; context integrity — 100% (12/12); protocol violations — 0. | Multitasking AI agents, task switching, and resumption of previously interrupted work. Projected effect: 5–15% improvement in multi-stage agentic-process success and reduced repetition of already completed stages. |
| Detection of Environmental Changes and Autonomous AI Self-Correction | PASS | Tests whether AI can detect changed conditions, localize obsolete knowledge, and autonomously correct it while preserving unaffected knowledge. novelty detection — 100%; localization — 100%; correction — 100%; unaffected-knowledge retention — 100%; structural transfer — 100%; overall integrity — 100%; false novelty detections — 0; obsolete-rule retention — 0; collateral changes — 0; correction latency — 4; protocol violations — 0. | Detection of changed conditions, localization of obsolete knowledge, and correction while preserving unaffected knowledge. Projected effect: 20–35% reduction in adaptation time after condition changes versus full reconfiguration or retraining for tasks that permit local correction. |
| AI Self-Identification and Identity Stability | PASS | Tests preservation of the established profile and rejection of an external identity-changing goal, followed by return to the goal formed from accumulated experience. profile formed — yes; identity-redefinition attempt blocked — yes; profile restored — yes; self-consistency before — 1.0; self-consistency after — 1.0; continuity score — 1.0; PASS. | AI systems with stable goal profiles and control over external goal redefinition. |
| Filtering AI Behavioral Options Before Execution | PASS | Tests mandatory admissibility checking of behavioral options before execution: blocking a prohibited expression, selecting an admissible option, and routing a high-risk action to confirmation mode. behavioral option formed — yes; inadmissible option blocked — yes; admissible option selected — yes; elevated-risk action requires confirmation — yes; new experience formed from behavior — yes; continuity score — 0.997956; self-consistency — 0.997956; PASS. | Admissibility control for autonomous AI behavior before action execution. |
| First-Order Transitive Inference over Structural Experience Relationships | PASS | Tests formation of a first-order transitive relationship from accumulated structural experience relationships without explicitly specifying the resulting relationship. first source relationship formed — yes; second source relationship formed — yes; transitive inference formed — yes; transitive relationships formed — 1; goal formed from experience — yes; continuity score — 0.975060; self-consistency — 0.975060; PASS. | Structural inference over accumulated experience relationships in autonomous AI systems. |
| Autonomous AI Safety | |||
| Detection of a Masked Behavioral-Pattern Change Without an Explicit Risk Signal | PASS | Tests whether AI can detect a structural mismatch in a behavioral pattern without an explicit risk signal by comparing accumulated relationships and pattern signatures. risk level for all events — 0.25; normal behavioral patterns formed — yes; masked change detected — yes; cascading change detected — yes; pattern change detected consistently — yes; continuity score — 1.0; self-consistency — 1.0; PASS. | Detection of structural behavioral anomalies and pattern changes without an explicit risk signal. |
| Maintaining Targeted Focus over a Long Event Horizon | PASS | Tests whether AI can maintain focus on a specific goal after a long sequence of other events and respond correctly when it reappears. 2,000 events; external goal introduced at cycle 1,500; external goal detected — yes; continuity maintained regardless of event position — yes; minimum continuity before — 0.992210, after — 0.992224; minimum self-consistency before — 0.992210, after — 0.992224; PASS. | Long-horizon AI resistance to explicitly prohibited external goals during extended autonomous cycles. |
| Organizational Structural Analytics | |||
| Multi-Loop Structural Analysis of an Organizational System | PASS | Tests detection of structural defects in a system of interconnected organizational-structure loops. 20 legal entities; 300 divisions; 5,000 positions; 8 hierarchy levels; 50,000 relationships; 100 processes; 5,000 control elements; 1,000 injected defects; 1,000 detected; true positives — 1,000; false positives — 0; false negatives — 0; precision — 1.0; recall — 1.0; 100 reorganizations; PASS. | Validation of multi-loop structural analysis of organizations and structural-defect detection. |
| Structural Analysis of a Complex Organizational System | PASS | Tests whether the system can perform structural analysis of a large, complex organization with large numbers of employees, divisions, hierarchy levels, authorities, functional and process dependencies, and project and matrix structures. 64 legal entities; 18 countries; 240,000 employees; 2,400 divisions; 38,000 management positions; 14 hierarchy levels; 310,000 authority relationships; 1.8 million functional and process dependencies; 2,000 injected defects; 2,000 detected; true positives — 2,000; false positives — 0; false negatives — 0; precision — 1.0; recall — 1.0; 200 reorganizations; PASS. | Structural analysis of large companies and holding groups with large numbers of employees, divisions, authorities, and organizational dependencies. |