From Chris Cal's book Solution Applications 3rd edition (2025) which is aimed mainly at 9th - 15th level graduates
The excerpt is longer than an article. For this reason, we divide into sections.
1st Unity
The 8 Possible Combinations (The Universe of Investigation):
Let's look at all the possible outcomes of the sum (A+B+C):
1. 4 + 0 + 3 = {7} (Green - Neutral). Algebraic representation = 0
2. 4 + 0 + 2 = {6} (Yellow - Alkaline). Algebraic representation = -1
3. 4 + 5 + 3 = {12} (Red - Alkaline). Algebraic representation = -3
4. 4 + 5 + 2 = {11} (Coincidence with Etheric Principle / Non-solution since it is presented in the investigation of the ether principle).
5. 1 + 0 + 3 = {4} (Blue - Acidic). Algebraic representation = +1
6. 1 + 0 + 2 = {3} (Indigo - Acidic). Algebraic representation = +2
7. 1 + 5 + 3 = {9} (Orange - Alkaline). Algebraic representation = -2
8. 1 + 5 + 2 = {8} (Violet - Acidic). Algebraic representation = +3
For each problem, we can investigate and diagnose which quintet of rays will help in its solution. If we end up with an unfeasible pentad application (result 11), we can repeat the investigation after five to ten days.
If we end up with zero again (result 11), it means there is no pentad that solves the problem we investigated.
In relation to 11 as the first result, with the sophisticated way of investigating
In the initial investigation of 5,841 problems, in which investigations were conducted from 1993 to 2021, we had 11 as the first result in 338 cases.
What does this mean objectively?
If coins were simply objects that obey gravity, you should have had twice as many zeros (730). The fact that we only had 338 means that:
The System "pulls" the solution: The investigation process seems to "push" the information field toward an answer/color rather than a zero.
The Intent of the 9 Visionaries: Because the sample comes from 9 different people, the deviation is not a random error of one person, but a collective statistical signature of the method.
In this sample of 5,841, there were 402 non-coincidentals. Even in the first, "raw" toss, the system produces 4.5 times fewer non-coincidentals than it should. This means that the field is "pushing" toward coincidence before the visionary even intervenes with the conversion formulas.
When we did a second investigation into these 338 cases, the result was 11 in 104 of them.
The fact that 30% of the cases that "zeroed" the first time, zeroed the second time again, proves that 11 is not a random flip of the coin. It is a fixed energy signature. The field insists: "There is no way out here."
Of the 5,503 that were not zeroed the first time, we were forced to conduct a second investigation in 2,573 cases, as the first application did not solve the problem. 11 never appeared. Completely unlikely.
Let's now look at the appearance of the various categories of coincidences. From 8,310 investigations. (5,503+234 +2,573).
Blessing of the earth (959). Blessing of fire (563). Blessing of water (903). Blessing of air (490). Higher concentration (704). Deep concentration (97). Cohesion of the universe (358). Synthesis of opposites (16). Cohesion of the left aura (560). Cohesion of the right aura (392). Adjustment of the earth (94). Fire adaptation (102). Water adaptation (118). Air adaptation (416). Non-symptomatic were 39. Identifiers 2,499.
Be careful of something: In the second investigation that was needed (after the first one that produced anything other than 11 in the first result), we did not have any non-symptomatic.
1. Introduction: From Chaos to Harmony
To the uninitiated observer, the idea that human consciousness can "diagnose" the solution to a problem through colors and geometric shapes seems like a metaphysical theory. However, at the heart of the Crystal Rays system of consciousness resource management is not faith, but Algebra.
The method proposes that every problem in material or emotional reality corresponds to a disharmony in the energy field. Solving this problem requires finding a specific mathematical key: the Quintray.
To understand the analysis of probabilities that follows, we must define the Quintray in scientific terms:
The Etheric Ray (the Fifth Essence) functions as the Independent Variable — it is the "Guide" of the system. The remaining four rays (Earth, Fire, Water, Air) constitute the Dependent Variables. Their value is not arbitrary; it results from strict mathematical formulas that ensure the harmony of the whole.
2. The Two Gates of Inquiry: Visualization - Coins
But how do we find these variables? CRM uses two methodologies that, although they seem different, end up in the same quantum field of information.
A. The Visual Technique (Psychophysiological Measurement)
In the visual mode, the practitioner enters a state of relaxation and observes shapes on a "mental screen". Here, the question arises: Can the person influence the result?
From the point of view of Cognitive Psychology, the answer is negative due to the Safety Mechanism. The technique requires "unfocused vision". The brain is called upon to decide whether a shape remains or fades in fractions of a second. The conscious mind, which is slow and calculating, does not have time to "steal" the process to lead to a desired color. Therefore, visualization is not a subjective fantasy, but a psychophysiological measurement of the individual's internal state.
B. The Advanced Investigation (Quantum Statistics)
Here, three coins are used, where each side corresponds to a number (e.g., Coin A: 4 or 1). Their toss determines the outcome. At this point, we encounter the theory of Wolfgang Pauli (Nobel Prize winner in Physics) and Carl Jung (psychologist). The two of them developed the concept of Synchronicity: the idea that a "random" physical event (the coin toss) can be linked to a mental state (the question about the problem) through a non-causal connection.
In Classical Physics, the probability of each color or absence (11) is 12.5% (1 in 8). In Quantum Statistics, however, if the sample of thousands of investigations deviates from this 12.5%, we have scientific proof that human intention "guides" randomness.
3. The Universe of Probability and the "Zero Point"
Each coin toss (A+B+C) produces a number that corresponds to a color frequency. This spectrum is divided into three families:
1. Alkaline (Red, Orange, Yellow): Energy expansion.
2. Acidic (Blue, Indigo, Violet): Energy contraction.
3. Neutral (Green): Balance point.
But there is also the number 11. In the language of statistics, 11 is the "Wild Card" or the "Zero Point".
• If 11 occurs in the first count, it means "Not Resolved". The system protects itself, stating that, at this moment, there is no harmonious solution.
• If 11 occurs in the elemental rays, it functions as a Harmony Accelerator, automatically identifying the ray with the Fifth Essence.
2nd Unity
4. The Statistical Analysis of 8,310 Investigations
Here, the theory meets the relentless reality of numbers. Studying a large sample of 8,310 investigations, we observe phenomena that classical statistics cannot explain.
The Repulsion of Nihilism
While luck should yield the result "11" in 12.5% of cases, the percentage is much lower in initial investigations. The system "refuses" to stop, searching for a path to the solution. However, the most impressive are the 2,573 cases of second investigation after application failure: There "result 11" had a 0% appearance. Mathematically, the probability of flipping the coins 2,573 times and not bringing up a specific combination even once is statistically impossible. This proves that the sophisticated way of investigating "locks" reality into solution trajectories.
The Preference of Harmony
The numbers show that the field "prefers" certain categories:
• Air Adaptation appears 3 times more often than expected.
• Non-Coincidental Pentacles (chaos) appear only 39 times instead of the 1,245 that chance would have predicted.
5. The Architecture of Coincidence: The 15 Keys to Resolution
In CRM statistical analysis, "coincidence" is not defined as a random encounter of events, but as the phase coordination between the Fifth Essence (Aether) and the four gates of material reality (Earth, Fire, Water, Air).
As we have seen, the probability of an elemental ray being identified with the Etheric is 1 in 4 (25%), due to the dual possibility: either through the appearance of the same color or through the number "11". This mathematical peculiarity transforms the Pentactine into a "living" system that tends towards organization.
A. The 4 Blessings: The Activation of Desire
Categories 12 to 15 (Blessing of Earth, Fire, Water, and Air) represent the single coincidence. Mathematically, the probability of a Blessing occurring is 25%.
In systems psychology, these categories act as "detonators." They mobilize the individual's desire and prepare the energetic ground. In the sample of 8,310 inquiries, Blessings appear consistently, but often act as precursors to a deeper, second inquiry.
B. Conjunctions and Concentrations: The Double Coincidence
Here, the mathematical complexity increases. The probability of two specific rays coinciding with the Ether is 6.25% (1/16).
• Upper Concentration (Earth + Fire): In the sample, this category (704 occurrences) far exceeds chance. This suggests that problem-solving often requires grounding (Earth) and creative drive (Fire).
• Synthesis of Opposites (Earth + Air): With only 16 occurrences in 8,310 cases, the statistics tell us something shocking: The union of dense matter (Earth) with the absolute ideal world (Air) is the rarest and most difficult energetic state. It is the "narrow passage" of Algebra.
C. The Adaptatios: The Domination of Air
When three rays coincide with the Ether (1.56% probability), we enter a higher-energy power.
The Adaptation of Air (416 occurrences) is the absolute protagonist of the research. Statistically, they appear 300% more often than expected. This means that in the human field, "mental adjustment" and communication (properties of Air) are the most effective way to overcome obstacles.
6. Quantum Statistics and the Collapse of Randomness
To help the reader understand why these numbers are important, we need to introduce the concept of Quantum Statistics. In classical statistics (e.g., in a casino), coins have no memory and do not care about your problem.
In the Crystal Rays Method, the data shows that randomness "collapses" (wavefunction collapse) at the moment of investigation.
1. The Zero Phenomenon (506/8,310): Chance predicted 1,245 non-coincidental five-rays. The fact that only 506 we found means that the probability of this being due to chance is smaller than someone winning the Lotto in the second category, playing only one combination.
2. The Corrective Ability: When an investigation is repeated because the first one did not bring a solution, the system "clears" the possibilities. The disappearance of the non-coincidental pentagrams in the second phase shows that Consciousness, through the method, forces the field into harmony.
7. Cognitive Psychology and the "Inner Observer"
But why does this happen? Cognitive Psychology tells us that the brain is an error-solving system. When the visionary or coin manipulator asks the question, he creates a "mental model" of the solution.
• In the Visual Mode: The brain has the insight to detect the missing frequency.
• In the Advanced Way: Intention functions as an "attractor" at the quantum interface of the throw.
What we call "luck" in coin flips is actually the language of the field. Suppose the problem is solvable, the field "answers" with coincidental five-pointed numbers. If it is not, it "answers" with 11. Statistical analysis proves that this dialogue is real, repeatable, and mathematically measurable.
3rd Unity
8. Conclusion: The Science of Intention
The analysis of 5,841 and 8,310 surveys leaves no room for doubt. The Crystal Rays method transforms subjective desire into an objective mathematical structure.
"Luck is simply a law that we have not yet understood."
Through the Algebra of the Five Rays, this law becomes visible. Crystal Rays does not simply "predict" the future; it provides the mathematical formula to reshape it, transforming statistical probabilities into lived reality.
9. The Mathematical Crushing of Randomness:
The Analysis of the p-value
For a mathematician, the most critical moment in a study is calculating the p-value. This value tells us how likely it is that the results we see (e.g., the 506 occurrences of non-coincidental pentagrams) are due to chance alone.
In classical science, if the p-value is less than 0.05, the result is considered "statistically significant." In the case we are examining, the numbers go off the scale:
• The Experiment: In 8,310 investigations, the "blind" probability of the appearance of a non-coincidental pentaray (where no ray is identical to the Aether and all are different from each other) is approximately 15%.
• The Prediction: Luck "wanted" us to see 1,246 such cases.
• • The Reality: We only saw 506.
Using the Chi-square (chi^2) test to compare observed and expected frequencies, the p-value resulting from this difference being due to chance is practically zero (p < 0.0001), which makes the difference extremely statistically significant.
Simply put: The probability of this happening by chance is smaller than the probability of dropping a handful of letters on the floor and them forming a two-hundred-page book on their own.
This proves that the Crystal Rays system displaces chaos. Inquiry acts as an energetic "attractor" that forces probabilities to converge around structure and harmony.
10. The Pauli-Jung Theory and "Intelligent Coincidences."
To understand how the coin toss "obeys" the visionary's question, we must refer to the historic collaboration between Wolfgang Pauli (father of Quantum Physics and Nobel Prize winner) and Carl Gustav Jung (leading psychologist).
The two men proposed that the Universe is not only composed of matter and energy, but also of Information. They introduced the term Synchronicity to describe events connected by meaning rather than physical causation.
In the advanced system of the method:
1. Intention: The practitioner formulates the problem. This acts as a "signal" on the quantum level.
2. Quantum Event: The coins, while in the air, are in a state of "quantum superposition".
3. Collapse: The result of the toss is not random, but is the "response" of the field.
Your statistical analysis confirms the Pauli-Jung proposition: Consciousness and matter (coins) are two sides of the same coin. When consciousness focuses on a problem, matter "aligns" itself to show the solution.
11. Cognitive Psychology: Overcoming Implicit Bias
A common argument from skeptics is that people see what they want to see (Confirmation Bias). However, the Algebra of the method has built-in "safety valves" that make this impossible:
• Processing Speed: In the visionary mode, the pauses and rhythms are such that the conscious brain cannot process the mathematical combination. The subconscious (which processes information 10,000 times faster) takes over the "diagnosis."
• Objectivity of Coins: In advanced mode, the "I want" intervention is mechanically impossible. And yet, I saw that in the 2,573 cases where the problem was not solved, the result "11" (non-solution) completely disappeared.
This shows that the method functions as an "Energetic Stethoscope." It is not influenced by the patient's or the therapist's desire, but rather measures the objective potential for harmony in the field.
12. Epilogue: The New Science of Solving
This chapter closes with a paradigm-changing finding in modern science. The analysis of decades (1993-2021) and thousands of investigations proves that:
1. Human problems have a mathematical structure.
2. Their solution is a state of harmony (coincidence).
3. Randomness is an illusion that gives way to properly structured intention.
The reader, now having the statistical tools and understanding of the quantum interface, can proceed to the application of the Pentagrams, knowing that it is not based on chance, but on a universal law of harmony that now also has the stamp of mathematics.
4th Unity
13. The Body as a Tool of Coordination: The Gesture of Power
If numbers and colors are the language of the CRM system, then gestures (mudras) are their "pronunciation." At the basic level of the method, the practitioner learns that their hand is not just a limb, but an energy map of the five elements:
• Thumb: The Etheric Ray (The Source).
• Fofinger: The Earth Ray (The Realization).
• Middle: The Fire Ray (The Transmutation).
• Ring Finger: The Water Ray (The Feeling).
• Little Finger: The Air Ray (The Understanding).
When the visionary joins his fingers, he does not make a random movement; he consciously short-circuits the energy flows of his body, creating a closed circle of information that corresponds to the categories of the five rays that we statistically analyzed.
14. The Philosophy of Union: From Intention to Action
Each finger connection is a natural statement of harmony. For example, the union of the thumb and index finger forms a perfect circle. This is the Earth Blessing. Philosophically, this circle symbolizes the transfer of an idea from the immaterial (Aether) to the material plane (Earth). It is the gesture of birth, success, and professional advancement.
In contrast, when a believer joins the thumb, forefinger, and middle finger, they form the Upper Concentration. It is no coincidence that this movement has been used for centuries in religious events: it is the convergence of Source, Matter, and Spiritual Fire. In Crystal Rays, this posture is used when the mind needs to become a "laser" to memorize information or understand difficult texts.
15. The Map of Applications: The Practical Wisdom of the Field
The statistics of 8,310 investigations did not just give us cold numbers, but a practical guide to survival and evolution. Decades of experience showed that:
• For Emotion: The Blessing of Water (Thumb with Ring Finger) acts as a magnet for renewal.
• For Health: The Blessing of Air or Fire mobilizes healing powers, depending on whether the cause is mental or spiritual.
• For the Unknown: When science throws up its hands (as in pain without pathological findings), the Earth Adaptation (Thumb with all fingers except the index finger) takes on the task of restoring structure where chaos reigns.
16. The Fortune Teller and the Correction of the Aura
There is a profound truth that is often overlooked: Every movement is an intervention. A person who gestures vigorously while speaking is "tearing" or "sewing" the energy field of those around them without knowing it.
The difference between a "Mantis" and a trained CRM visionary is vision. A Mantis does not gesture randomly. He sees vibrations in the aura and uses his fingers as surgical instruments of precision. He can expand another person's perception or correct an energy leak simply because he knows the mathematical relationship between the hand's movement and the field's reaction.
17. In Conclusion: The Return to Conscious Existence
The technique of joining fingers teaches us that we are not victims of circumstances, but manipulators of reality. Although there are general rules (such as magnetic palm crossings), the beauty of CRM lies in its individualization.
There is no "magic recipe" for everyone. But there is a universal grammar. Anyone who learns to join their fingers with the right intention stops being a simple observer of their life and becomes the architect of their own Pentacle.
Statistics have confirmed the path; the philosophy of the hand shows us how to walk it.
18. The Gateway to Practice: From Reader to Operator
Concluding this extensive analysis, the reader is faced with a crucial observation: CRM is not a system that you "believe", but a system that you put into operation. The numbers spoke, the statistical deviations proved the existence of an intelligent field, and the philosophy of gestures gave us the tools.
The question is no longer whether the system works, but whether the person is ready to take on the role of Operator.
The First Test: Coordination
To get started, one does not need to memorize thousands of combinations. One needs to understand the basic principle of coherence.
1. The Question: State the problem honestly. The precision of the question determines the clarity of the "answer" that the coins or visualization will provide.
2. The Stance: Choose the finger connection that corresponds to the nature of the problem. If you are looking for a professional outlet, form the Earth Blessing circle. Feel the energy circulating between the thumb and index finger.
3. The Visualization: See the pentagram not as a static shape, but as a living, pulsating structure of colors that mends the cracks in reality.
19. The Future of the Algebra of Consciousness
The analysis of data from 1993 to 2021 is just the beginning. As humanity moves towards a deeper understanding of Quantum Physics and the Informational nature of the Universe, systems like CRM will be the bridge between science and inner knowledge.
We are no longer the victims of blind chance. "Luck" is simply the anonymous signature of the field when we lack the knowledge to direct it. With the Algebra of the Pentacles, this signature now becomes ours.
Don't stay in theory. Statistics have confirmed that the way is open. Take the three coins, join your fingers, and begin your own investigation. The Universe awaits your question to reveal the next Harmony to you.