Practical post-quantum cryptography · proved finite mathematics

Cryptography that's
measurably ahead.

A working post-quantum cryptographic stack — already thousands of times faster than the published prior best at strictly higher security — sitting on top of a new mathematical framework with no prior name in the literature. The cryptography is shipped. The framework is partially proved. The applications below follow from both.

Tier A · Shipped · Cryptography

What's already running,
with measurable advantages.

Each item below is in working code, with benchmarks against the published state of the art. These are not roadmap items. They are the moat. The numbers are real and verifiable.

Practical post-quantum program obfuscation

shipped

A working virtual machine that runs obfuscated programs at sub-second timing while producing a small cryptographic proof of correct execution. Programs can be shipped to customer infrastructure or untrusted hardware without revealing what they do, with mathematical guarantees. Obfuscation has been theoretically interesting for two decades and practically impossible — until now.

Benchmark ≈ 8,400× faster than the published prior best system, at strictly higher security.
≈ 0.6 second evaluation per call · ≈ 10 KB cryptographic execution proof.

Sub-700-byte cryptographic proofs, faster than industry standard

shipped

A proof-compression layer that produces zero-knowledge cryptographic proofs under 700 bytes that verify faster than the established benchmark. Smaller blockchain transactions, smaller credential checks, smaller everything-that-needs-a-zero-knowledge-proof. Direct relevance to verifiable compute, on-chain identity, and any system bottlenecked on proof size or verification cost.

Benchmark 637-byte median proof size · faster verification than the industry standard.

Exact, deterministic alternative to "approximate-and-round"

shipped

A cryptographic primitive that removes a class of failure modes that has historically caused real-world cryptographic breaks. Where lattice-style cryptography has relied on bounded statistical noise, ours uses exact algebraic structure. No rounding, no heuristic, no probabilistic argument.

Why it matters Removes the most common attack surface in modern post-quantum cryptography.

Constant-memory streaming proof system

shipped

Most cryptographic proof systems require memory proportional to the size of the computation being proved. Ours doesn't. Constant memory for proofs of arbitrary-size computations. Direct implication: cryptographic proof generation works on commodity hardware, mobile devices, embedded systems, and edge nodes — not just datacenter racks.

Why it matters Unlocks proof-generation on hardware that previously couldn't host it.

A complete post-quantum verifiable VM

shipped

A complete software stack — separately-engineered Rust modules — that lets developers build applications using all of the above without needing to be cryptographers. Production tooling, not a research demo. Designed for integration into existing engineering workflows.

Status 31-module Rust workspace · post-quantum proving targets · operational tooling.

Bit-level cryptographic risk accounting

shipped

Replaces the standard "asymptotic security argument" with hard numbers. For the first time, an engineer can budget cryptographic risk the way they budget memory or bandwidth — exact bits, with a calculation that survives expert review. This is what underwrites the security claim of every other item on this page.

Why it matters Audit-grade quantitative cryptographic accounting. Strictly stronger than asymptotic claims.

Quantitative side-channel leakage analyzer

shipped

A side-channel analysis tool that quantifies leakage from physical observation channels (clocks, power traces, timing variations, error-retry counts) at the granularity of bits per operation. Tested on a NIST-standardized post-quantum signature scheme; produced specific bit-exposure numbers per accepted signature for each parameter set.

Status Already produced concrete vulnerability disclosures for production cryptographic schemes.
Tier B · Proved · Mathematics

A new mathematical framework
with no prior literature.

The cryptography on the previous page is partially built on a new class of mathematical framework. Each item below is a mathematical theorem with no prior published name. They are durable foundational IP — the kind of asset that survives competitive replication because the underlying machinery doesn't yet exist outside this work.

A new class of mathematical analysis

proved

Classical analysis tracks signals. This framework tracks signals and the residual obstruction the operation couldn't remove — as independent first-class objects, each with its own algebra. Two invariants where there was one. Both are computable. The field has no prior published name because nobody had unified the components into one framework.

Status Foundational theorem proved · finite specializations proved · framework name reserved.

Topological data analysis with an algebraic axis

proved

Standard topological data analysis sees holes. Our extension distinguishes exploitable holes from microstructure noise using an algebraic obstruction axis rather than just geometric scale. With a proved stability theorem. Direct relevance: shape comparison in biology, materials science, fluid topology, image analysis — anywhere the data has algebraic structure that pure geometry misses.

Status Stability theorem proved · awaiting library packaging for industrial deployment.

A counting structure with zero free parameters

proved

When you measure a system in this framework, every measurement is determined by a single observed quantity. No fitting, no choice of regularizer, no convention. Most counting frameworks have at least one parameter to tune. This one doesn't. Mathematically unusual; cryptographically valuable because it removes a class of "configuration mistake" failure modes from any system that uses it.

Status Zero-parameter property proved · numerical invariants verified to machine precision.

Finite-to-infinite mathematical bridge with explicit, verifiable conditions

proved

Solves a known structural problem in arithmetic geometry that mainstream tools handle ad hoc. We give explicit conditions for when finite local data can be assembled into infinite global data, with verifiable hypotheses. One of the building blocks for the cryptographic side, and a paper-grade contribution in its own right.

Status Conditional theorem proved · finite chart-level closure proved.

Self-improving refinement with guaranteed contraction

proved

Most iterative refinement schemes hope for convergence. This one either contracts at a stated rate or stops with a precise diagnostic. No silent failure, no false confidence. Direct application to numerical solvers, machine-learning training loops, adaptive mesh refinement, and any iterative scheme where you need to know whether progress is real.

Status Contraction theorem proved · fail-closed protocol formalized.

Coupled multi-norm budget framework

proved

A transformation is accepted only when every measurement axis improves simultaneously. Replaces single-number quality scores with a coupled ledger; mathematically stronger than any single-norm criterion. Includes an explicit guard against signal-hiding — the failure mode where a transformation looks good on one metric while quietly destroying another.

Status Five-channel coupled criterion proved · entropy-hiding flat-abort guard formalized.
Tier C · Enabled · Applications

What this combination
makes possible.

The combination of practical post-quantum cryptography plus the mathematical framework enables a long list of applications that don't currently exist as products. Each item below is buildable with engineering effort. Several are direct extensions of what's already shipped.

Sealed AI agents

enabled

Ship agent code — prompts, tool wiring, fine-tunes — into customer infrastructure with mathematical guarantees that the customer cannot extract the agent's logic. Solves the "I want to use your AI but I can't share my data, and you can't share your model" problem at the cryptographic level. Every AI lab and serious agent company currently has this problem and is solving it badly with hardware enclaves that keep getting broken.

Market AI infrastructure · enterprise AI deployment · regulated-industry AI integration.

Provably watermarked AI models

enabled

Per-output proofs that a token came from a specific model, plus model fingerprints that survive distillation attempts. Solves "is this AI-generated?" definitively. Regulators (EU AI Act, U.S. executive orders) will mandate this within years; the technical capability to comply doesn't exist anywhere else today.

Market AI provenance · regulatory compliance · anti-distillation IP protection.

Encrypted algorithm marketplace

enabled

Trading strategies, machine learning models, drug-discovery models can be sold where buyers can run them but cannot extract them. Mathematical, not hardware-trusted. Currently impossible without trusted execution enclaves, which keep getting broken. Quantitative finance, pharmaceutical R&D, and competitive ML labs are direct buyers.

Market Quant finance · pharma · ML model licensing.

Cryptographic DRM that actually works

enabled

Software and media licensing where the decryption logic is the cryptography rather than embedded code that can be reverse-engineered. The DRM industry has wanted this for 25 years; current schemes (Widevine, FairPlay) get cracked because the decryption logic is in the binary. Ours puts it in the math.

Market Game studios · streaming platforms · enterprise software licensing.

Defense-grade autonomous-system protection

enabled

Captured drones currently leak everything when reverse-engineered. Our framework lets logic be embedded in hardware in a way that cannot be extracted even with full physical access. Direct strategic relevance to defense primes building autonomous systems where adversarial reverse-engineering is a known failure mode.

Market Defense primes · classified compute · autonomous-system manufacturers.

Confidential smart contracts that hide logic, not just inputs

enabled

Existing privacy-preserving blockchains hide who-did-what; ours can additionally hide what-logic-was-executed. New product category in DeFi, RWA, private market making, sealed-bid auctions, MEV-immune trading.

Market DeFi infrastructure · privacy-preserving L2s · institutional on-chain finance.

Compliance as cryptographic proof

enabled

A program proves it respects HIPAA / SOC 2 / PCI-DSS / EU AI Act policies cryptographically, without anyone needing to read the program. Multi-trillion-dollar regulatory market. Long sales cycles, but every Fortune 500 has the budget for provable compliance.

Market Healthcare · finance · enterprise regtech · cross-border data flow.

Quantitative side-channel certificates

enabled

A masking scheme can be certified to leak no more than X bits per operation, with mathematical backing. Strictly stronger than current pass/fail t-tests and mutual-information attacks. Already operational; needs industrial packaging.

Market Hardware security modules · secure enclave vendors · cryptographic engineering audit.

Quantum error-correcting codes with guaranteed contraction

enabled

A code synthesis tool that emits new quantum error-correcting codes alongside the proof of how fast errors converge. Tightens magic-state distillation schedules in fault-tolerant quantum computing. Direct relevance to quantum hardware companies racing toward fault tolerance.

Market Quantum hardware vendors · quantum software stacks · fault-tolerance research.

Numerical solvers with guaranteed conservation

enabled

Climate, computational fluid dynamics, molecular dynamics, plasma simulation — all currently estimate conservation of mass, energy, momentum, and charge. Ours can certify it. Solver-grade adaptive mesh refinement, with a mathematical backstop on whether the solver is actually conserving what it says it is.

Market Computational science · weather/climate modeling · industrial simulation.

Codecs for scientific data with conservation certificates

enabled

A compressed climate dataset ships with a cryptographic proof that mass / energy / momentum are preserved to a stated tolerance. Direct relevance to climate-science consortia, NASA, NOAA, weather services, and any organization moving large scientific datasets where conservation guarantees are scientifically required.

Market Climate science · earth observation · scientific data infrastructure.

Pollution-free eigenvalue computation

enabled

Spurious eigenvalues are a known failure mode in computational chemistry, materials science, and continuum mechanics. Our framework eliminates them with a provable count of true vs spurious negatives. Eigensolver vendors (COMSOL, ANSYS) have wanted this for decades.

Market Computational chemistry · materials science · finite-element analysis software.

Federated learning with consistency certificates

enabled

Cross-client agreement is a legal requirement, not just a metric, in regulated medical and financial federations. Our framework provides cryptographic certificates that cross-client model behavior is consistent at a stated tolerance, backed by mathematics rather than testing.

Market Healthcare ML federations · cross-bank fraud models · regulated AI consortia.

Verifiable scientific simulations

enabled

Every simulation ships a cryptographic ledger of which conservation laws were preserved during the run, and to what tolerance. Directly addresses the reproducibility crisis in computational science. Per-timestep audit trail; verifiable by a third party.

Market Government research · pharma · academic computational science.

Certified compression with multi-invariant guarantees

enabled

A new class of lossy compression that preserves declared mathematical invariants of the data, not just bits. A single compressed file can carry guarantees for several conservation laws simultaneously — uniformly certified, mathematically backed.

Market Climate · computational fluid dynamics · molecular dynamics data infrastructure.

Provable scientific machine learning

enabled

Operator-inference and Koopman-style models that come with theorem-grade generalization bounds from the underlying contraction guarantees. Applies to neural operators, dynamical-system identification, reduced-order modeling — any setting where the model's behavior on test data needs a mathematical certificate.

Market Scientific ML · neural-operator software · industrial digital twins.
Tier D · Certified · Adversarial robustness

The other side of the same math:
red-team certification.

The mathematical framework is direction-symmetric. The same theorems that certify a transformation preserves an invariant also characterize what would destroy it. We frame these as defensive certification and adversarial-robustness audit tools — same mathematics, defensive packaging. Defenders learn the certified attack budget; attackers gain nothing they couldn't already compute.

Worst-case adversarial perturbation budgets

red-team

For any deployed machine learning model, computes the smallest input perturbation that flips its decision, with a mathematical lower bound rather than heuristic search. Generalizes existing adversarial-example tools. The defender's certified robustness budget is the attacker's certified attack-cost lower bound.

Use case Model-card-grade adversarial-robustness certificates · ML deployment audits.

Anti-detection waveform topology characterization

red-team

Given a publicly-known radar / lidar / sonar receiver specification, characterizes the family of physical shapes whose signature falls outside the receiver's certified detection envelope. Defensive: tells radar designers which shapes their receiver cannot reliably classify — actionable for system improvement, not for offensive design.

Use case Radar capability assessment · sensor-system robustness analysis · defense vendor R&D.

Provable jamming-energy bounds

red-team

For a communication channel with a declared receiver, computes the minimum energy required to reduce its capacity by a stated amount. Defensive use: tells radio designers how much jamming-resistance their hardware actually has. Strictly stronger than current empirical jamming-tolerance estimates.

Use case Communications hardware certification · spectrum-warfare resilience audit.

Cryptanalysis attack-budget bounds

red-team

For any cryptographic primitive whose security argument fits the framework, computes provable lower bounds on the attack budget required to break it. Strictly stronger than current asymptotic security claims because it produces actual numbers. Useful as both a design tool and a competitive analysis tool against existing schemes.

Use case Cryptographic scheme audit · post-quantum migration risk analysis · design-time safety.

Differential-privacy attack lower bounds

red-team

For any declared differential-privacy mechanism, computes the smallest auxiliary-information injection that defeats it with stated probability. Defenders compute this to set their epsilon budget; attackers gain a known information-theoretic floor.

Use case DP-deployed ML systems · privacy-engineering audit · regulatory privacy guarantees.

Steganographic capacity bounds

red-team

For any declared content-detection system, computes how many bits of payload can be provably hidden in cover data such that the detector cannot find it within its declared budget. Useful for both privacy-preserving communication and content-moderation system design.

Use case Content moderation system design · privacy-preserving communication audit.

Hash-collision and commitment-collapse design analysis

red-team

For algebraic hash schemes, characterizes the structural conditions under which collision attacks of a stated budget exist. Tool for designers of new hash schemes; identifies dangerous design patterns before deployment.

Use case New-cryptosystem design review · structural cryptanalysis.

Worst-case input families for certified iterative solvers

red-team

Numerical solvers that advertise contraction rates (most commercial CFD, ML training, optimization software) get tested against input families designed to violate the contraction claim. Automated certification testing for "this solver actually does what it advertises."

Use case Numerical-solver certification · scientific-software audit · AI training stability.

Adversarial topology against ML feature extractors

red-team

Identifies the family of inputs that any deployed feature extractor cannot embed faithfully. Defensively: a model-card-grade certificate of where the model fails. Without gradient access — works on black-box models.

Use case Black-box ML audit · model-failure characterization · regulated ML deployment.

Side-channel optimal trace-collection schedule

red-team

Given a publicly-declared masking scheme, computes the minimum number of physical traces an attacker needs to recover a secret with certified probability. Used by both sides of the masking-vs-attack arms race. Quantitative replacement for current heuristic estimates.

Use case Side-channel attack budgeting · masking-scheme effectiveness audit.

Compression-bomb and training-data-poisoning attack design

red-team

Identifies the minimum dataset perturbation that maximally degrades a target ML system's declared invariant. Defensive use: certify a model's poisoning-resistance; offensive analysis: identify avoidable attack patterns to harden against.

Use case ML training pipeline security audit · adversarial robustness certification.
Defenders learn the certified attack budget by computing it. Attackers gain nothing from secrecy that the calculus does not already give defenders. These tools are framed as red-team and certification — never as operational guidance for offensive use against deployed systems.
Honesty about what's claimed and what isn't

Calibrated confidence.
No overclaim.

The work is real and the benchmarks are verifiable, but we are explicit about which categories of claim are at which confidence level. The list below is what gets said out loud, and what doesn't.

What we do claim

  • The cryptographic benchmarks are real, measured, and reproducible. Independent verification under NDA is available.
  • The mathematical theorems we say are proved are proved, with formal CAS witnesses where applicable.
  • The "enabled" applications can be built with engineering effort, with development cost varying by item.
  • The defensive / red-team capabilities can be packaged as certification tools today.
  • The framework is genuinely novel as a unification — the individual mathematical tools mostly exist; the combination doesn't.
  • The cryptographic stack is a commercializable asset today, independent of how the mathematics evolves.

What we don't claim

  • Any solution to the Riemann Hypothesis or other century-old mathematical open problems.
  • An exact, fully-proved adelic theory. A precise finite-section calculus is in hand; the infinite lift remains an active research target.
  • Anything labeled "AGI." Anything labeled a quantum computer. Anything labeled artificial general anything.
  • Replacement of standard cryptographic review processes — independent expert audit is required before any deployment claim.
  • Operational guidance for offensive use against deployed real-world systems. Capabilities are framed as defensive, certification, and red-team.
  • Probabilistic estimates dressed up as deterministic guarantees.

The five tiers, with honest labels

Each tier above corresponds to a different evidence level. We don't conflate them. A Silicon Valley investor evaluating this work should understand that Tier A is shipped product, Tier B is mathematical research-grade output, Tier C is buildable application roadmap, Tier D is buildable defensive tooling, and Tier E is frontier research that we explicitly disclaim as a deliverable.

Tier A
Shipped
Working code, measured benchmarks, reproducible by third parties under NDA.
Tier B
Proved
Mathematical theorems with formal verification witnesses where applicable.
Tier C
Enabled
Buildable applications with engineering work; not yet packaged as products.
Tier D
Certified
Defensive / red-team capabilities, framed as certification tools.
Tier E
Frontier
Research targets explicitly disclaimed as deliverables. Optionality, not promise.

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