Six-manuscript technical corpus
The formal theory, extensions, proofs, and technical development of Computation–Realization Geometry.
Computation–Realization Geometry
A Communication Theory of Computation Realization
A formal framework for preserving valid implementation choices before architecture becomes definitive—and for knowing when commitment is safe.
The 55-year gap
Optimization can improve the design space it receives. It cannot recover a valid path erased before search began.
Modern computing systems 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, and where system boundaries fall can eliminate entire families of possible implementations.
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 remained missing was a general formal map of the valid realization choices that exist before one architecture becomes definitive.
$30M65 nm design cost
2006
2006
>$540M5 nm design cost
2020
2020
>18×increase across
fourteen years
fourteen years
The framework
Computation–Realization Geometry maps the valid ways a computation can become physical.
CRG records the joint demands each realization places on movement, state, work, latency, replication, ownership, and hierarchy. It makes the options that precede architecture explicit enough to compare, preserve, and govern.
- 01The computation
states what must remain true.
- 02The rules
define which transformations and trades are valid.
- 03The geometry
records what can be achieved jointly.
- 04Technology
chooses last.
Computation–Realization Geometry program map
Safe-Commitment Law
Discard an option only when the decisions still ahead could not tell that it was gone.
CRG identifies what information must survive for a declared class of future decisions. When an option is removed too early, the framework can construct a concrete regret witness: a future decision showing exactly how that discarded option would have changed the outcome.
From theory to an operational system
The complete CRG program.
The scientific record and operational system are distributed separately by design: one preserves the public research corpus, while the other provides a standalone and integrable vehicle for adoption.
Public validation corpus
Benchmarks, validation studies, negative controls, and reproducibility materials for independent inspection.
Operational realization control
Software, documentation, verification tools, integration interfaces, and deployment packages that implement CRG in practice.
CRG System registers valid implementation alternatives under declared rules, computes their joint obligations, preserves the geometry required by future decisions, incorporates changing technology and evidence, 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.
Latest system milestone
CRG Systems v1.5.0
September 2026
The commitment layer meets the agent.
v1.5 closes the initial theory-to-platform arc with causal receipts, bounded coordination, canonical package resolution, execution contracts, generated clients, and an independently replayable agent boundary.
Read the v1.5 announcementResearch record
Contribution and accountability
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.
Read our Research in the Open commitmentCommunication before commitment.
Preserve the options the future may still need.