NOTICE FROM THE FOUNDATION RECORDKEEPING AND INFORMATION SECURITY ADMINISTRATION.
This is an automated message re: SCP-4656. Due to its anomalous effects, all personnel receiving this message must confirm its receipt to ensure SCP-4656's continued containment. In accordance with the Special Containment Procedures, some segments are highlighted in blue for your convenience.
Thank you for your cooperation.

Item #: SCP-4656
Object Class: Keter
Special Containment Procedures: This document will be sent to all Foundation personnel with Level 2 Clearance or higher by email every week. Personnel should then (re)read the document to reinforce the mnemonic device used to contain SCP-4656: there is no connection. Any information about SCP-4656 must be rendered as plainly as possible while still keeping with the standard format. Due to its otherwise self-containing nature, knowledge of SCP-4656 and its properties is harmless and available to any relevant personnel.
However, Foundation webcrawlers are to monitor any academic communities for instances of SCP-4656-2 or other signs of infection. Any individuals found in the infection's early stages are to be passively observed. Any groups displaying widespread infection will be infiltrated by Mobile Task Force Delta-6 (“Grifters”) and disbanded from the inside. Methods of doing so may even include defaming SCP-4656-1 instances or their work. If any SCP-4656-1 instances reach Stage 4 or 5 anyway, personnel may directly interfere to prevent them from progressing to Stage 6. This may even include directly informing instances that the connections do not exist.
Should Stage 6 occur, containment personnel must use all available measures to prevent its completion, including lethal force. During this time, SCP-4656's assigned Senior Containment Specialist must identify the foci of the SCP-4656-1 instance(s) and gather as much information about them as possible. They must then take copies of this information to the nearest Metaphysical Isolation Chamber in case of failure to prevent the completion of Stage 6. This is to prevent the nonexistent connections from affecting anything critical.
If Stage 6 completes, then the resulting damage to reality must be repaired using the preserved information. In the case of Stage 6a, little further action is necessary. Since the connections do not exist, SCP-4656 relation to the damaged concepts can be exploited to recontain it. In the case of Stage 6b, the acting Senior Containment Specialist will meet with the O5 Council to decide the next course of action about any damaged/erased concepts. This is to ensure that the imperative justifies the heavy use of Foundation resources necessary to repair such damage.
Only individuals who have a known proficiency in mathematics may conduct testing involving SCP-4656. This is to both control the resulting effects of Stage 6a and to reduce the chances of an unintentional Stage 6b. Currently, the Department of Analysis is the group managing potential candidates. All questions regarding SCP-4656 and its applications should be directed to either them or the onsite RAISA liaison.
Personnel not involved with testing are to be thoroughly reminded that there is no connection. This is to ensure that there is no uncontrolled spread of SCP-4656 outside of testing. Under no circumstances are any instances of SCP-4656-2 to be created without direct supervision from testing personnel. Personnel found making connections that do not exist will be dealt with on a case-by-case basis.
Any mention of The Sefirot Guild outside of internal Foundation documentation should be reported immediately to O5-10.
Description: SCP-4656 is an abstract concept that exhibits an anti-infohazardous effect.1 Specifically, SCP-4656 is the concept of a process designed to establish causal/thematic connections between several unrelated entities by analyzing coincidental patterns. The anomaly surrounding SCP-4656 is that despite testing proving otherwise, no system exists for this purpose. Indeed, conventional mathematics could not support such a system. In all senses, SCP-4656 does not exist, and, therefore, it cannot establish real connections. There are no connections.
However, systems based off SCP-4656 always return evidence of connections. Further, once a sentient mind contains SCP-4656, it alters the behavior of the affected subject (hereafter referred to as SCP-4656-1) to account for this information. Their attempts to actualize this concept (the resultant systems designated SCP-4656-2) and display it to others is what propagates SCP-4656.
The spread of SCP-4656 occurs through the following mechanism:

Stage 1 (Speculation): An unaffected subject becomes aware of SCP-4656, whether through viewing the results of a SCP-4656-2 system or by pondering SCP-4656 itself. Strangely, infection only occurs if the unaffected subject truly believes that SCP-4656 exists. This risk can be mitigated entirely if an unaffected subject is informed/reminded that there is no connection. If the concept does not take root in the subject's mind, then they will remain unaffected.

Stage 2 (Notation): Once infection occurs, however, they will become acutely aware of random trends in large data sets. In addition, they will become unshakably convinced that these trends are due to connections between these data sets, even though those connections do not exist. Both the type of matching data and the pool from which data is gathered appear to be irrelevant. Nothing is too broad or too specific to trigger the effects. This awareness only applies to random relationships; qualities that are either inherently similar or identical cannot be charted using SCP-4656.2 This awareness also denotes their conversion into SCP-4656-1. In this stage, they will fixate upon several entities, typically ones holding personal significance, and record any instances of the noted trend.

Stage 3 (Actualization): Once an instance has gathered enough raw data, they will then begin to develop a mathematical formula based on their recordings (SCP-4656-2) and attempt to solve it.3 No consistent elements have been identified for SCP-4656-2, as the system is looking for connections that do not exist. Therefore, the elements of SCP-4656-2 are dependent on the SCP-4656-1 instance creating them and will often contain nonsensical mechanics as a result.4 Depending on the complexity of SCP-4656-2, Stage 3's duration may vary widely. Past durations have taken anywhere from 30 minutes to 7 years.

Stage 4 (Realization): Stage 4 is marked by the instance reaching a solution and returning a single value. Due to the nature of SCP-4656-2, this value could be anything from a number to a name to a physical object. The meaning assigned to this value seems to be dependent on how many degrees of separation there are between the observed entities. More degrees of separation typically results in values that are more esoteric. Without fail, this value is an underlying causal marker in every piece of data used. However, the connection is only obvious if divined through the created SCP-4656-2. This value will even indicate connections that are non-obvious or even impossible. This is, of course, because the connections do not exist.

Stage 5 (Proliferation): The SCP-4656-1 instance will then attempt to share their discovery and their SCP-4656-2 with as many other people as possible. Any unaffected subjects who ponder the validity of the results risk SCP-4656 infection unless they already know that the connections do not exist. However, due to the nature of SCP-4656-2, the instance will be incapable of explaining it in a way that unaffected subjects will be able to understand. This usually leads to the instance's work being dismissed as fraudulent, hampering the spread of SCP-4656. If an instance is discouraged from sharing, the compulsion grows dormant as they realize that the connections they made do not exist. The instance's behavior then gradually returns to normal as SCP-4656 fades from their mind. If they continue this endeavor, however, they will become more and more devoted to relaying SCP-4656-2. This will lead to one of two possible outcomes.

Stage 6a (Alteration): The SCP-4656-1 instance's efforts will result in the creation of a version of their SCP-4656-2 that expresses its premises as an axiomatic proof. This duration usually lasts about as long as the duration of Stage 3. If they are successful, this creates a paradox. Since SCP-4656-2 is a visual depiction of a nonexistent concept, it has been theorized that the reason Stage 6 is so volatile is that these systems technically don't exist. Further, they are enforcing connections that also don't exist. By incorporating methods that do exist into their formulas, they override the principles on which the SCP-4656-2 is founded. This paradox causes a sort of 'informational effervescence'.5 This corrupts the framework of the created SCP-4656-2 and retroactively alters its nature. The nonsensical operations become those that are rational in order to resolve the ontological paradox. Thus, reality itself changes to match the rational version of SCP-4656-2, which is by default a CK-Class Reality Restructuring Scenario.

Stage 6b (Disintegration): However, if an SCP-4656-1 instance is unsuccessful, this creates a further paradox. A proof that speaks against the validity of their results negates the connections that they made and reinforces their nonexistence. Since the metaphysical framework of the system is already unstable, the conceptual bulk of SCP-4656-2 collapses altogether. All information about entities observed through it fuses with the information of SCP-4656, virtually erasing them from existence. The only known method of salvage/reification is manually remaking the entity using preserved information. Preservation of information has been achieved in the past through metaphysical isolation (storage in alternate dimensions, alternate universes, Scranton boxes, etc.).

That method of storage, while exorbitant, is absolutely necessary to see the results of any alterations. For example, an instance of SCP-4656-2 created during testing uses through the following steps:

Taking the square root of a truck symbol multiplied by 4(lm)

The value of the previous step being divided by a lamp symbol

Adding a heart symbol to the result of the previous two steps

This series of calculations would equal the Foundation's insignia. At this stage, no alarm was raised as the connection did not yet exist. However, after the SCP-4656-1 instance was able to define the symbols (thus completing Stage 6a), the equation was found to correspond to a Foundation front company. This company – Sconces, Candelabras, and Photography – is a widespread chain store that offers electrical and lighting equipment.
All of the variables can be made constant by taking measurements on a unit sold by the company. The truck symbol refers to the distribution of a unit sold by the company and its distance from the store. The lamp symbol refers to the composition and dimensions of the unit. The heart symbol refers to the satisfaction of the customer. For clarification, these values were undefined before the completion of Stage 6a. Before then, the equation literally operated on the objects that the symbols represented. As such, there was no connection.
The meaning of this was unknown until the Senior Containment Specialist exited the Chamber after testing had concluded. Their compiled records showed that the lamp in question was originally purchased from a mundane lighting equipment manufacturer. Further, they showed no existence of Sconces, Candelabras, and Photography before the testing session. This was especially concerning due to its well-recorded existence since 1956 and high number of customers.
The Department of Analysis conducted an investigation as part of testing protocol. Notably, they discovered that any appliance sold by the company demonstrated a passive anomalous effect. Exposure to an appliance's light instills a subconscious alignment with the Foundation's directives. As a result, locations with high concentrations of the company's products were found to have faster item recovery and cover-up times due to the civilians' unconscious cooperation.
No special plans to exploit the connection that shouldn't exist have yet been made, although they have been considered.
Addendum 1: Discovery
SCP-4656 was discovered after a routine sweep of Site-01's archival servers. Due to their isolated nature, personnel stationed on-site were able to observe a possible discrepancy. Further examination showed that the existence of a Group of Interest known as The Sefirot Guild had been erased from all other records.
Based on information lingering in Site-01, The Sefirot Guild was a group of occult mathematicians. Their ‘guild' was devoted to a modification of Gnostic teachings. These teachings stated that numbers hold the truest significance over all other things. Further, they held that through numbers, anything could be divined. They even believed that the nonexistent could be charted.
Members would show this belief through ritually developing mathematical proofs stating the validity of such practices. According to remaining records, they made heavy use of equations indicative of SCP-4656-2. This would explain their relative obscurity before their erasure. The nonsensical connections they made would likely have kept them from being perceived as credible.
In an effort to ascertain what it was that they did, SCP-4656 itself was discovered. Through analysis of their last recorded communications, it was determined that their usage of SCP-4656-2 was the cause of their erasure. Currently, it is theorized that The Sefirot Guild had attempted to use SCP-4656-2 on other instances of SCP-4656-2. In doing so, they ‘stacked' the paradoxical nature of SCP-4656-2 on top of itself. The resulting completion of Stage 6b erased them from existence instead of what they observed.
After observing the fate of The Sefirot Guild, SCP-4656's true nature was established. Projections suggest that even one uncontrolled Stage 6b could result in either an OK-Class Metaphysical Collapse Scenario or a ZK-Class Reality Failure Scenario.
Therefore, it is imperative that you remember that there is no connection.

Click Here to Confirm Receipt.

Receipt Confirmed. Inoculation Complete.

Thank you for your cooperation, and remember:
There is no connection.
Secure. Contain. Protect.

Footnotes
1. An anti-infohazard is a rare kind of information-based anomaly that functions through non-awareness. Whereas a normal infohazard manifests itself by knowledge of or references to its locus endangering subjects, an anti-infohazard manifests itself by lack of knowledge endangering subjects.
2. Currently, the reason for this is unknown.
3. Though the number of monitored entities varies, the number of (nonexistent) connections established will never be less than four. Thus, it seems that the maximum number of similarities that may exist in a system before SCP-4656 may be applied is three. The reason for this is also unknown.
4. Notable examples include raising 'meals that remind you of home' to exponential powers, multiplying imaginary numbers by 'the color black', and taking the square root of 'Former Vice President Joe Biden'.
5. A term defined as two distinct concepts losing cohesion and adopting traits of each other.

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