VICIFOLD · BUILT ON CAS+ THEORY
Top-tier strategic war-gaming,
made enterprise infrastructure for the AI era.
Run each of your candidate plans thousands of times in the same simulation environment, and understand the likely outcomes of each plan before you decide.
01 · A decision that cannot be calculated
At a product review, the team must choose between two pricing options and two launch channels.Both plans have met their test targets.Yet the previous product, which also met its targets, fell short of expectations within three months of launch.The load on a bridge can be calculated.The market performance of a new product cannot,because the people in a market influence one another.
02 · Forward problems, inverse problems and simulation
FORWARD PROBLEM
When the rules are clear and the relationships between variables can be expressed as equations, the result can be calculated directly, as with the load on a bridge. A product launch is different. Consumers, competitors and channels influence one another, and the same market situation never occurs twice, so no such equations can be written.
INVERSE PROBLEM
BI reporting, data mining, big data, machine learning and large language models all infer rules from historical results. When applied to a new decision, these methods have three limitations: new products have no history to learn from, the same data can often support several explanations, and small changes in the input can lead to very different conclusions.
SIMULATE
Simulation starts from your candidate plans. We translate each plan and its assumptions into simulation rules, place them in an environment of thousands of digital consumers, and run the same plan thousands of times under the same conditions. Before you decide, you can see the outcomes the plan may lead to, the probability of each, and the points at which results begin to diverge. Several plans can also be compared directly under the same conditions.
03 · A historical precedent
Sources: Wikipedia, “Western Approaches Tactical Unit”; GOV.UK / Dstl, “Women winning battles”, 2018; Simon Parkin, A Game of Birds and Wolves, 2019.
The Atlantic, 1942.
Escorts struggled to detect German U-boats, and Allied merchant shipping suffered heavy losses.
In Liverpool, a grid was drawn across the floor of a room.
A team of young Wrens used combat reports and ship data to simulate convoy battles on it, again and again.
Through repeated simulation, the team identified the U-boats' tactics: surfacing at night and entering the convoy from behind.
By 1945, the counter-tactics developed from this work had been taught to some five thousand officers.
Patterns found in simulation were tested at sea, and the methods that worked became standard tactics.
More than eighty years later, ViciFold has developed this approach into software.
04 · Our goal
The work in Liverpool required a dedicated team. Today, strategic war-gaming of this kind is still mostly commissioned by governments from specialist institutions, and few companies have access to it.
Large language models make a new approach possible. They allow thousands of digital consumers to make choices in their own words and for their own reasons, and they can translate a business plan into rules for a simulation environment. Simulation that once required many experts can now be delivered as software. Our goal is to make simulation a standard step before major business decisions: record the judgement before the decision, review it against actual results afterwards, and give every team the same method.
SIMULATION
You provide the candidate plans. We translate them into rules for one simulation environment, run each plan thousands of times, and group the results into a small number of outcomes in a report that supports your decision.
05 · How it works
We work with you to break each candidate plan into simulation rules, including price, channel, launch audience and likely competitor responses. Anything that cannot be determined is clearly marked as an assumption.
The simulation environment contains thousands of digital consumers with different backgrounds and preferences, who exchange information and influence one another. Each run of the same plan can produce a different result.
Thousands of worldlines converge into a small number of outcomes. The report shows the share of each outcome, the main events that lead to it, and which assumptions would change the result.
The judgement and the simulation basis are recorded before the decision. Actual results are then reviewed item by item to find whether any gap came from the plan, its execution or the market, and the findings calibrate future simulations.
06 · What you receive
Each simulation delivers an outcome map that shows the possible outcomes, the share of each, and where results begin to diverge.
After a plan is simulated thousands of times, the share of runs that end in each outcome represents its likelihood within the model.
Each outcome can be traced back to a few turning points, such as a product review or a stock shortage.
Adjust the price or change the launch audience, then simulate again to see how the outcomes shift.
07 · Before you start
Each simulation supports one specific decision, so the first step is to define that decision clearly.
Plans do not need to be complete. Any options you are still considering, such as pricing, channels, launch audiences or timing, can be written up as a plan.
Define the results that matter most and the conditions that cannot change. These determine the questions the simulation needs to answer.
One person is accountable for the decision and records their judgement before the simulation begins.
When results are available, a person who was not involved in designing the plans reviews them, so that the assessment stays objective.
08 · Determinism
The basis of every simulation, and every output from the language models, is recorded in full. Simulations can be paused and resumed at any time without repeating completed steps, and replaying a simulation from its record produces an identical report. Every simulation can therefore be reviewed afterwards.
CAS+ THEORY
CAS+ is ViciFold's theoretical framework. Built on complex adaptive systems, it incorporates Dr. Gen-Hua Shi's work on fixed points, the numerical manifold method and contact theory, applied to artificial intelligence by Dr. Max Y. Ma. CAS+ determines whether a simulation converges and groups thousands of runs into comparable outcomes.
09 · Complex adaptive systems
A market consists of many individuals, each acting by its own rules, influencing others and adapting over time. No single participant controls the whole, yet the market as a whole shows clear trends. This is known as emergence. A flock of birds changing direction is one example; a product that suddenly becomes popular is another.
The Santa Fe Institute, founded in 1984, advanced research in this field. In business decision-making, however, the approach has long faced four challenges. Large language models address the first. The other three require mathematical methods.
In traditional models, researchers define individual behaviour by hand, often with only a few rules that cannot represent real consumers.
Small differences in initial conditions can lead to completely different results. A single run shows only one possibility; many runs are needed to see the distribution of results.
When word of mouth passes a certain threshold, purchases rise sharply. The overall direction is often decided by a small number of factors.
The results of thousands of runs must be consolidated into a few comparable, reproducible outcomes before they can support a decision.
10 · Two scientists
The mathematical foundation of CAS+ comes from two scientists. For more than forty years, Dr. Gen-Hua Shi has studied how rock blocks make contact, slide and lose stability, and has developed a complete set of methods for analysing such systems. Dr. Max Y. Ma, who studied under Dr. Shi, has applied these methods to artificial intelligence.
Chair of Fundamental Mathematics
Co-founder & Chief Scientist
Since 2024, the two scientists have collaborated on deep manifold research, applying this mathematics to neural networks. Two preprints have been published.
In a continuous system, change is smooth and can be calculated step by step with differential equations. A discontinuous system consists of separate units that interact through contact or connection: connections can break, form or slip, and the state of the system can change abruptly. Most mainstream tools in mathematics and mechanics assume continuity and smoothness.
Business systems are also connected, discontinuous systems. Buyers, sellers, products and influencers form a network, and a single negative review or stock shortage can suddenly change the relationships within it.
11 · Three tools of CAS+
Responses generated by large language models are treated only as candidates. Which behavioural rules apply, and what values the parameters take, are tested and fitted against actual observations and known constraints, so that an approximate model can be reconstructed and computed. Three tools then refine the model: they analyse stability near equilibrium, combine local models into a whole, and identify the boundaries at which relationships switch.
F(x*) = x*When a simulation reaches a state that no longer changes, that state is called a fixed point, a form of equilibrium. CAS+ uses fixed points to test whether a simulation converges and which decisions the equilibrium is most sensitive to. If a simulation enters a cycle, the system reports the cycle.
Ω = ⋃ UᵢA single model can rarely describe an entire market. The numerical manifold method uses several overlapping covers, each describing one region, and combines them by weight into a whole. CAS+ uses this method to connect local models of different customer groups and channels.
gₙ ≥ 0Two blocks can be separated, in contact or sliding, as determined by a set of inequalities. Discontinuous Deformation Analysis (DDA) expresses these relationships in a solvable form. Relationships in a market switch in a similar way: when word of mouth passes a threshold, purchases rise sharply.
When the same plan is simulated many times on the refined model, thousands of worldlines converge into a few comparable, reproducible outcomes. The share of each outcome is a probability estimate within the model and must be calibrated with actual data.
12 · System architecture
At the base is a deterministic kernel, which ensures that the same inputs always produce the same results. Above it, large language models simulate each consumer, complex adaptive systems simulate how consumers influence one another, and CAS+ determines whether the simulation converges and groups thousands of worldlines into a few outcomes.
Each digital consumer is given a background, preferences and views, so it can understand your plan and respond to it.
Simulate how consumers exchange information and influence one another, so that individual choices add up to group trends.
Determines whether a simulation converges and groups thousands of worldlines into comparable outcomes.
The same inputs and records always produce the same results, with support for pausing, resuming and full replay.
Actual results are used to calibrate the whole system, so future simulations reflect your market more closely.
USE CASES
Any field in which many participants influence one another, and relationships can change suddenly, can be simulated before a decision is made. We are starting with new product launches.
13 · New product launches
Before a new product launches, a company needs to decide on pricing, channels, the launch audience and the communication schedule. These decisions are interrelated and are affected by the responses of consumers, competitors and channels. In the past, such reviews relied mainly on commissioned research and experience, and their accuracy could only be confirmed after launch.
Questions you can simulate before launch
Record the judgement before the decision and review it after launch, so that the next review has a clear reference point.
14 · Other fields
These fields consist of many connected participants. Relationships can switch, and local changes spread along the connections. Supply chains, clinical trials and financial markets all share this structure.
Planning, sourcing, production and delivery are closely linked, and the effect of a single disruption is amplified along the chain.
Recruitment, enrolment and adherence depend on the choices of many individuals. Different trial designs can be simulated in advance to compare how resilient they are.
Participants observe and react to one another, and local fluctuations can spread and grow through their connections.
MORE USE CASES
Reactions to a price change pass through dealers, platforms and consumers.
Every move a company makes prompts a response from competitors. Several rounds can be simulated in advance.
Simulate how information spreads, and where it is amplified or subsides.
Merchants, users and platform rules are interconnected, and a single change can shift the whole system.
Assess whether a new policy is adopted across teams or worked around.
Anticipate how affected groups will adjust their behaviour after a policy takes effect.
ABOUT
Our Chinese name, 一波万绪, means “one ripple, ten thousand threads”. When a drop falls into the sea, its ripples spread in every direction, and the effects of an important decision spread in the same way. We help companies understand those effects before they decide. ViciFold is based in Shanghai and Singapore and serves companies across North America and Asia-Pacific.
15 · Our principles
All assumptions, illustrations and simulated data on our website and in our reports are clearly labelled.
Every simulation can be replayed in full from its record, so all reviewers see the same report.
The accuracy of a simulation is ultimately tested against actual results. Reviewing results is a standard part of every engagement.
We provide the possible outcomes and their causes. The final decision is always yours.
Begin a simulation
If you are preparing an important decision, contact us with your candidate plans. We will help you test each of them in simulation.
Shanghai · Singapore
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