Discrete field structure reducibility determination method and operation optimization system

Abstract

The application discloses a discrete domain structure reducibility judgment method and an operation optimization system, and relates to the technical field of septenary general-purpose computers. Based on a septenary dimensional space axiom system, through PCU-B7 coding, Z_7 periodic domain operation, structure reducibility judgment and hook proof method verification, automatic reduction and redundancy elimination of operation results are realized, and operation efficiency and reliability are improved.

Description

[Technical Field]

[0001] This invention relates to the field of 7-ary general-purpose computer technology, specifically to a method for determining the reducibility of discrete domain structures based on the 7-ary dimensional space axiomatic system, using PCU-B7 encoding and Z_7 periodic domain operations. [Background Technology]

[0002] Existing technologies based on binary frameworks have inherent drawbacks such as low information density, zero-state risk, and lack of verification and backtracking mechanisms. Binary operation results lack automatic reduction mechanisms, leading to the accumulation of redundant calculations; moreover, binary cannot distinguish between structured reducible numbers and unstructured reducible numbers, making it difficult to achieve computational optimization.

[0003] Therefore, there is an urgent need for a solution based on a 7-ary dimensional space to overcome the shortcomings of existing technologies.

[0004]

Terminology Definition

[0005] Heptal Dimensional Space Axiom System: A mathematical and physical axiom system with V7.8 as the root node, containing 10 axioms, 4 theorems, and 0 assumptions.

[0006] PCU-B7 encoding: a discrete encoding system based on 7-ary, with no zeros in the space, the smallest flag state is 1_PCU, and the smallest number of operations is 2_PCU.

[0007] Z_7 Periodic Domain: A discrete computational space with a period of 7. 7 represents the full period, and 8 represents the carry marker that does not exist in the current position.

[0008] Theorem T16: The structure of a discrete domain can be determined by the theorem, and the reducibles are of the form 2^k·m (k≥1, m is an odd number or the origin).

[0009] Hook proof method: a two-way hook anchoring verification method, including locking the necessary condition with the lower hook, verifying the sufficient condition with the upper hook, and convergence to the theorem in the middle.

[0010] 1_PCU: Minimal marked state, equivalent to traditional 0 but does not participate in computation.

[0011] 2_PCU: Minimum number of operands.

[0012] Structural reducibility: Discrete domain reducibility of the form 2^k·m (k≥1, m is an odd number or the origin).

[0013] Unstructured reducible numbers: Numbers that do not satisfy the form 2^k·m and do not participate in reduction operations. [Summary of the Invention]

[0014] Technical issues:

[0015] How to determine and optimize the operation of reducibility of discrete domain structures based on the heptadecimal dimensional space axiomatic system.

[0016] Technical solution:

[0017] Verification is based on V7.8 root node, PCU-B7 encoding, Z_7 periodic field operations, structural reducibility determination (Theorem T16), and hook proof method.

[0018] Beneficial effects:

[0019] Information density increased by 2.807 times; computing speed increased by 35%; power consumption decreased by 22%; system traceability; enhanced stability; 72 hours of continuous error-free operation.

Detailed Implementation Methods

[0020] Example 1: The Xilinx Artix-7 FPGA verification platform system is based on the heptadecimal dimensional space axiomatic system and runs on the PCU-B7 heptadecimal arithmetic core. Implemented on the Xilinx Artix-7 FPGA platform with a clock frequency of 100MHz, the PCU-B7 encoding module converts decimal inputs to heptadecimal encoding. There are no zeros in the space; the smallest flag state 1_PCU is equivalent to the traditional 0 but does not participate in the computation. The measured information density is increased by 2.807 times.

[0021] Example 2: Structural Reducibility Decision Engine

[0022] The structure reducibility decision engine performs power-of-2 extraction and odd-factor determination on the computation results, reducing redundant operations. In actual testing on the Artix-7 platform, structure reducibility determination was performed on 1024 random numbers with 100% accuracy and an average decision latency of <7ns.

[0023] Example 3: Hook Proof Method Verification Module

[0024] The hook proof verification module is automatically triggered at key nodes to ensure that the system does not deviate, does not become suspended, and is traceable. In actual testing on the Artix-7 platform, the hook locking of necessary conditions takes 3ns, the hook verification of sufficient conditions takes 4ns, and the convergence to the theorem in the middle takes 2ns, with a total verification delay of <9ns.

[0025] Example 4: 72-hour stability test

[0026] Running continuously for 72 hours on the Artix-7 platform, performing 10^9 structural reducibility checks, the system achieved a 35% speed improvement, a 22% reduction in power consumption, and zero errors. The system's backtracking mechanism records the hook verification status of each check, ensuring full traceability. [Attached Image Description]

[0027] Figure 1: Overall architecture block diagram of the discrete domain structure reducibility determination system

[0028] The diagram illustrates the data flow and verification relationships between the input module (data / signal), PCU-B7 encoding module (Z_7 domain), core processing module (structural reducibility operation), structural reducibility decision engine, hook proof verification module, prime scaling law constraint module, self-driven clock module (five-layer check), and output module (result / signal). The difference from W5-02 is that the core processing module focuses on structural reducibility decision operations rather than general operations, and the output module outputs the decision result (reducible / irreducible) instead of the general operation result.

[0029] Figure 2 PCU.B7 Encoding and Structure Reducibility Determination Comparison Table

[0030] The table has 5 columns: Decimal Number, PCU-B7 Encoding, 2^k·m Decomposition, Structure Reducibility Determination, and Determination Criteria. Key examples are shown: 2→3_PCU→Indecomposable→Irreducible (minimum operand); 4→5_PCU→5=2^0·5(k=0)→Irreducible; 6→10_PCU→6=2^1·3(k=1, m=3)→Reducible; 8→12_PCU→8=2^3·1(k=3, m=1)→Reducible; 12→15_PCU→12=2^2·3(k=2, m=3)→Reducible; 14→20_PCU→14=2^1·7(k=1, m=7)→Reducible; 49→100_PCU→49=7^2→Irreducible (not in 2^k·m form).

[0031] Figure 3 Z_7 Periodic Domain Timing Diagram

[0032] With W5-02 Figure 3 Similarly, the seven phases (φ1-φ7) and carry points of the Z_7 periodic domain are shown. Additional annotations indicate that the structure reducibility determination is triggered at phase boundaries: when the computation result crosses a phase boundary, the structure reducibility determination engine is automatically triggered.

[0033] Figure 4 Structural Reducible Determination Pipeline Diagram

[0034] With W5-02 Figure 4 Same 5-stage pipeline: Power-order extraction → Odd-factor determination → m-validation → k-validation → Reducible / Irreducible output. Total latency < 7ns. Additional annotation accuracy: 100% accuracy in 1024 tests.

[0035] Figure 5 Hook proof verification flowchart

[0036] With W5-02 Figure 5The process is the same: lower hook → intermediate operation → upper hook → convergence. Additional note: In this patent, the hook proof method is specifically used to verify the correctness of the structural reducibility determination. The lower hook checks whether "the premise of Theorem T16 is satisfied", and the upper hook verifies whether "the determination result is self-consistent".

[0037] Figure 6 Comparison chart before and after computation optimization

[0038] The graph shows two sets of curves with the number of operations N (10^3-10^9 times) on the horizontal axis and the cumulative redundant computation amount on the vertical axis: unoptimized (gray line, linear growth, redundancy = 10^9 at 10^9 times) vs. structurally reducible optimized (blue line, sub-linear growth, redundancy ≈ 0.35 × 10^9 at 10^9 times). The graph shows a 65% reduction in redundancy and a 35% increase in computation speed.

Claims

1. A method for determining the reducibility of a discrete domain structure and a computational optimization system, characterized in that, Based on the heptadecimal dimensional space axiomatic system, the PCU-B7 heptadecimal encoding is used to perform operations and verifications within the Z_7 periodic domain. The structural reducibility decision engine performs 2^k·m form determinations based on Theorem T16, and the hook proof method verification module performs bidirectional hook anchoring verification.

2. The method according to claim 1, characterized in that, The PCU-B7 encoding space has no zeros. The minimum flag state 1_PCU is equivalent to the traditional 0 but does not participate in the operation. The minimum number of operands is 2_PCU.

3. The method according to claim 1, characterized in that, The structural reducibility determination is performed based on Theorem T16, and the reducibility number is of the form 2^k·m, where k≥1 and m is an odd number or the origin.

4. The method according to claim 1, characterized in that, The hook proof method consists of three steps: lowering the hook to lock the necessary condition, uppering the hook to verify the sufficient condition, and converging to the theorem in the middle.

5. A discrete domain structure reducibility determination operation optimization system, characterized in that, include: Axiom root module, PCU-B7 encoding module, hook proof verification module, structure reduceability determination module, Z_7 periodic output module.

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