Designing a leading-edge chip has become dramatically more expensive. The Semiconductor Industry Association reports that the cost rose from about $30 million at 65 nm in 2006 to more than $540 million at 5 nm in 2020—an increase of more than 18-fold in fourteen years—through a process that can span years and involve thousands of engineers.
Yet the deeper problem is not only how to optimize a chosen design. It is what happens before conventional optimization begins.
Modern computing systems are no longer simply chips. They combine compute dies, HBM stacks, advanced packages, high-speed links, power delivery, cooling, and rack-scale infrastructure.
Choices about where computation lives, which state is stored or recomputed, how data moves, where ownership resides, and where system boundaries fall can eliminate entire families of possible implementations.
Downstream tools can optimize the design space they receive. They cannot recover a valid implementation path erased before their search began. It is like choosing one route across a city and deleting every road not taken.
Since Rent’s rule entered the public literature in 1971, the field has developed powerful theories and tools for interconnection, memory traffic, performance, architecture exploration, and physical design. What was still missing was a general formal map of the valid realization choices that exist before one architecture becomes definitive.
We developed A Communication Theory of Computation Realization to provide that map.
The theory’s central object is Computation–Realization Geometry, or CRG: the valid ways a computation can become physical, together with the joint demands each realization places on movement, state, work, latency, replication, ownership, and hierarchy.
The order is the point.
- the computation states what must remain true;
- the rules define which transformations and trades are valid;
- the geometry records what can be achieved jointly;
- technology chooses last.
This ordering separates the computation itself from the many physical forms it may legally take. Instead of committing prematurely to one architecture, CRG preserves the realization information needed for the decisions that remain ahead.
At the center of the theory is the Safe-Commitment Law:
Discard an option only when the decisions still ahead could not tell that it was gone.
This is not an argument for retaining every possible design. Keeping every alternative is usually impractical.
For a declared class of future decisions, CRG identifies the information that must survive. When a premature reduction removes something a later decision needs, CRG can construct a concrete regret witness: a future decision showing exactly how the discarded option would have changed the outcome.
Rent’s rule is not replaced. Within CRG, it becomes one observable projection of a larger realization geometry—an important measurement taken after a particular family of realization choices has already been made.
Shannon’s work illustrates the power of finding an abstraction that makes previously hidden limits expressible. CRG applies that methodological lesson to the step between a computation and its physical realization.
From theory to an operational system
We did not stop at theoretical formulation and controlled validation.
Alongside the publications, we built and are releasing CRG System: a standalone, embeddable, and integrable realization-control platform that implements Computation–Realization Geometry in operational software.
CRG System:
- registers valid implementation alternatives under declared rules;
- computes their joint obligations;
- preserves the geometry required by future decisions;
- incorporates changing technology, evidence, and uncertainty;
- determines what may safely be selected, retained, or removed;
- identifies whether a change requires repricing, re-embedding, or reopening;
- and issues auditable, independently verifiable certificates governing commitment and change.
It is designed to sit alongside—not replace—compilers, optimization systems, EDA tools, physical simulators, laboratory systems, databases, and existing engineering workflows.
Organizations can use CRG System directly as a standalone engineering environment, embed it within another application, or integrate it through documented interfaces into an existing toolchain.
Today we are releasing the complete CRG program through three connected bodies of work:
- the theory and complete technical manuscript corpus;
- the public benchmarks, validation studies, negative controls, and reproducibility materials;
- and CRG System software, documentation, verification tools, integration interfaces, and deployment packages.
The research corpus and operational system are distributed separately by design. The research repository preserves the public scientific and validation record. The CRG System package provides the standalone and integrable vehicle through which the theory can be evaluated, adopted, and applied in operational workflows.
CRG System is source-available at no charge for permitted academic, public-research, personal, and other noncommercial use with attribution. Commercial use requires a separate license.
Human-led and AI-enabled
This work was human-led and human-accountable, with material research and engineering assistance from GPT‑5.6, Claude Fable 5, and coordinated AI systems.
Those systems contributed to mathematical exploration, theorem formalization, implementation, verification, adversarial review, literature synthesis, and exposition. Human project leadership retained responsibility for research direction, acceptance or rejection of claims, validation standards, release decisions, licensing, and scientific accountability.
We believe this contribution can help establish a new abstraction layer for architecture–technology co-design—and demonstrate what becomes possible when human direction, scientific accountability, and advanced artificial intelligence are brought together against difficult, long-standing problems.
Communication before commitment. Preserve the options the future may still need.
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