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properties of knots
in the genesis sequence

The knot has long acted as a topological analog to the material universe. Just as there are no finite number of unique numbers, the knot has been a mental construct to speculate that there can be no finite number of unique objects. A discriptive geometry realized through a framework proven out in creating the Genesis Sequence yields the set of properties for knots, demonstrate here, that conceptualize the core elements of this unique claim to an infinite number of unique knots.


Animations are made to run through all the linearities created up to now. In the origin sequence knots that cannot be connected to another have been termed — “Primes” — and are the highest value of knot because they will never be identified in a combination.


Well over half the origin sequence have characteristics that make them linkable with each other. The animation running here shows those with a single linking feature.

A Single Link Combination Example

The distribution of the system's artworks is made up of a progression of single and linked forms and combinations of one to another of them. The animation here shows an example with all the single link linearities in the origin sequence in combination with the last one in the sequence shown at the top of this page.


The potential that an infinite number of totally different knotted circuits with no two alike is ever more apparent with each two and three link linear circuit found to exist. The animation here shows those with this exponential potential that appear in the origin sequence.

knot properties as asset classes

A valuation system is natural to this concept of knots. As the progression increases and the number of the designs increase the investment value of the originating knots creates the framework of an economic incentive to drive this value as art above the initial exchange value of a currency. This brings the properties of knots into an association with the token marketplace's protocols and methods of increasing the value base of the art.

A higher value is placed on tokens representing the discovery-generation knots in the class of multiple link linearities. This stabilizes the value of their parent knot designs because their single, uncombined state in the origin sequence is literally infinitely rarer than any of the pervasive combinations they become involved in.

The Core Element of a Ubiquitous Art

Multiple linking elements imply a mathematically calculable provenance for every combination. The high percentage of this property in the origin sequence and its potential occurrence as the sequence continues to grow supports the systemic hypothesis of the art. The origin sequence is giving a taste of what is to be created by a concept where every design bearing the properties of knots promises to continue to generate this same provenance order as far into the future as can be imagined.

Multiple Link Combination

Prior to the rise of blockchain a certificate such as the one shown here displayed the concept of knot acquisition. This could be printed for display and used to transfer ownership, to track provenance. With the application of the blockchain the order of these "constructs" displayed in the series below now represents the only outward example of the knot as a digital presence.

With knowledge of the properties of knots and with an initial sequence of over a hundred, the art's inclusion of blockchain technology in the system has brought a return to the start of the sequence to standardize the order of combinations the system will adopt for the continuing growth as additions to the sequence are made in the future.

In the startup the digital designs below and elsewhere on this web site are made into objects to use as rewards to those that participate in the art while it is preparing to become an autonomous, self generating system. These will be distributed until the launch is complete, and then there will be no more. Their physical presence as representations of this startup stage are intended to make them and their individually unique knots into the value baseline for the system.

The Great Knot, April 27, 2011

Michael Sullivan Smith, 2015
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