A new multipath semantic hierarchical network processor for dynamic processing across hierarchical structures can support unlimited new networking capabilities. This new hierarchical processing is accurate, flexible, useful, and simple to use. This is performed by the new hierarchical Left Link operation shown in this document which can replace the older Cartesian product model.
This paper describes how this hierarchical processing can be naturally used to support the multipath hierarchical data processor. This can further support a powerful user navigation dynamically searching across multiple hierarchical pathways using dynamic network processing. These advanced capabilities show examples of how these hierarchical and networking processing operates together seamlessly to produce powerful new dynamic capabilities.
— — — — —
The new semantic hierarchical network processing model presented within supports and produces many advanced new features and capabilities. This includes significant ways to perform the hierarchical data modeling and proven principled hierarchical processing using an advanced natural hierarchical Left Link operation. The older Left Join has been replaced with a Left Link operation introduced, which uses a virtual table linking to replace the older Cartesian product and its data replication problems. This creates a powerful hierarchical data model using tables separately linked for a flexible advantage using the Left Link. 
The new Left Link operation supports the older Left Join hierarchical processing, allowing the replacement of the standard Left Join with the new more flexible Left Link operation. This keeps separate structures physically separated while remaining dynamically combinable for maximum flexibility. Left Links never produce replicated data values, naturally producing accurate results. Replicated data can throw summaries off because of the unnecessary replications, while duplicate values are always meaningful.
Defining the Hierarchical Data Model
Dynamically defining the desired relational hierarchical data model using the new Left Link is shown in the bullets in Figure 1 below. It defines and controls the limits of processing within the desired hierarchical structure. This processing operates following natural hierarchical, relational, and semantic principles. These are further controlled by channeling all data modeling operations through the new Left Link operation.
The Left Link increased its hierarchical processing from the Left Join operation, making it more powerful. It naturally supports hierarchical data modeling and processing that is more flexible than standard relational processing. This is made possible by naturally using the new Left Link operations to increase hierarchical processing through a series of hierarchical Left Links that unify into a single virtually linked hierarchical structure. This is further utilized in the hierarchical structure by using its data to perform unlimited network processing across the hierarchical structure. The Left Link’s operation is shown in Table 1 below. It demonstrates how to build hierarchical structures.
Table 1 above defines a multipath hierarchical structure. The hierarchical data structure definition above in Table 1 shows how to data model the more powerful Left Link operation. A new dynamic WHERE clause makes this new Left Link operation more flexible and precise using multiple WHERE clauses instead of being limited to one WHERE clause.
The new Left Link operation operates hierarchically by naturally preserving data by combining rows and preserving data on the left side naturally. This supports the relational data model that uses the more powerful hierarchical Left Link operation to model the desired hierarchical structure. This naturally passes the semantic data along in the hierarchical data structure being processed. As the structure grows, the semantics increase. An example of the hierarchical data modeling used is shown below in Figure 2. 
Hierarchical or Flat Structure Differences
Standard processing for SQL produces a flat table processing. When multiple tables are used, the result also produces a flat Cartesian product. This generates unnecessary replicated data, which can cause accuracy and summary problems. The top SELECT statement in Figure 2 below is joining tables ‘A’, ‘B’, ‘C’ which produces a Cartesian product that shows node ‘A’ occurring two times instead of once in this example. This shows a standard join generating replicated data in place, which causes data accuracy problems. This is avoided by using the new Left Link.
In the bottom SELECT clause in Figure 2 below, a Left Link operation has replaced the older Left Join shown in Figure 1 below. This enables a hierarchical structure to be used instead of a standard flat table processing. In the SELECT statement in Figure 1 below, the Left Join is affected by the Cartesian product while the new Left Link is not. This allows it to separately link tables for flexibility. This hierarchical structure is defined by the Left Link operation which links structures into separate pieces rather than joining structures into a single contiguous, flat structure. These two methods are shown in Figure 1 and 2 below.
Relational Hierarchical Processing
Shown in figures 3 and 4 below is how data modeling can be naturally performed in extended ways. It demonstrates how hierarchical data processing uses new Left Links to perform data modeling that can be directly processed using hierarchical Left Links. This uses a subset of hierarchical processing that supports an advanced hierarchical processing that utilizes the hierarchical data modeling semantics creating more value than captured. Meaning can be directly derived.
This produces a powerful hierarchical processing with new capabilities derived by limiting processing to only Left Links. This naturally produces valid hierarchical data structures. Hierarchical processing is controlled by a set of standard hierarchical principles defined in the data model in figure 3 below. Breaking any of these hierarchical processing standards will automatically trigger an error condition, such as detecting pathways merging together, which is hierarchically invalid. 
In figure 3 above, deleting table C will also remove tables D and E. In Figure 4 below, the lower data model, D is now under the A table, and deleting table D will also delete table E. In Figure 4 below, the data definition demonstrates this more diverse multi-path structures and offers more choices. Notice in table A that the relational data definition can validly specify more than two paths coming from a single node. This is a natural extension allowing more sequential data modeling choices B, C, D, and E, which is shown in figure 4 directly below.
Standard SQL used flat structures with no semantics associated with it. The data modeling shown in figures 3 and 4 above produces powerful hierarchical processing models by using self-describing hierarchical processing semantics. It uses an accurate form of hierarchical Left links. This has two advantages. It naturally carries the hierarchical structure and semantic information, and can access it and make it available as the hierarchical structure grows. The Left Link naturally preserves correctness. They do not allow invalid or ambiguous structures. Hierarchical structures are persistent. Hierarchical structures preserve semantics.
Dynamic Network Hierarchical Processing
The new Dynamic WHERE clause can query the hierarchical data structures dynamically. This allows multiple WHERE clause queries to be sequentially processed one after the other until a desired result is found. The dynamic WHERE clauses can be used sequentially as many times as necessary. This means WHERE clauses can be repeated as necessary to find the desired result. WHERE clauses support dynamic data networking processing by directly referencing data across multiple pathways as shown below in Figure 5. Dynamic Networked WHERE clauses use any mix of ‘AND’ and ‘OR’ operations to derive complex results as in “WHERE A=B OR (B=C AND D>B)…” to any network complexity to search for a desired result. This dynamic networking can be used on top of hierarchical processing in Figure 6 below.
The new semantic Left Link operation and its natural hierarchical processing can advance processing in many new ways. By replacing SQL with only natural hierarchical Left Links, its data modeling capabilities and use are increased while using naturally correct relational processing. Hierarchical semantics growth increases as the syntax increases. This paper has shown how these new Left Links are being used to become a more powerful process than the older Cartesian product with its unnecessary data replication problems.
These new capabilities are found in relational hierarchical processing. They support advanced processing features in this natural hierarchical processing, such as using the new Left Link operation to support powerful hierarchical data modeling and processing. And finally there is a new powerful dynamic network processing across the underlying hierarchical data. It can continually search for desired results and findings in real time until a result is found. These capabilities were shown through working examples and descriptions that operate naturally.
 M. David. Semantic Hierarchical Processing Advancements. TDAN.com, October 18, 2017
 M. David. Advanced Standard SQL Dynamic Structured Data Modeling. Artech House, 2013.
 M. David. Naturally Increasing Data Value with Hierarchical Structures. XML Magazine, March 2011.
 M. David. Extending SQL’s Inherent Hierarchical Processing Operation. Database Journal, Nov, 2010.
 M. David. ANSI SQL Hierarchical Processing Can Fully Integrate Native XML. ACM SIGMOD Record, Vol. 32, Issue 1, March, 2003.
 M. David. Advanced ANSI Data Modeling and Structure Processing. Artech House Publishers, 1999.
 M. David. Advanced Capabilities of the Outer Join. ACM Sigmod Record, Vol. 21, No. 1, March 1992.