Mathematics has been an important part of human civilization since ancient times and has developed continuously with human progress. Early mathematical ideas emerged from practical needs such as counting, trade, land measurement, construction, and astronomy. Over time, these simple methods evolved into organized mathematical systems. Ancient civilizations such as Egypt, Mesopotamia, India, Greece, and China made significant contributions to mathematics. Egyptians used geometry in architecture and land surveying, while Mesopotamians developed numerical systems and astronomical calculations. Indian mathematicians introduced the decimal system and zero, which greatly advanced mathematical studies. Greek scholars transformed mathematics into a logical and theoretical subject through proofs and geometrical reasoning. During the medieval period, Arab and Islamic scholars preserved and expanded mathematical knowledge. They translated earlier works, developed algebraic methods, and promoted the exchange of scientific ideas across cultures. Their contributions strongly influenced European mathematics. The Renaissance period brought major developments such as analytical geometry and calculus, leading to rapid scientific and technological progress. In the modern era, mathematics has become essential in engineering, medicine, economics, computer science, artificial intelligence, and space research. It supports scientific discoveries, technological innovation, and problem-solving in everyday life. The historical development of mathematics shows how civilizations and scholars contributed to its growth over centuries. Understanding this evolution helps us appreciate the importance of mathematics in shaping modern society and future advancements.
" Overview This is a revised and extended edition of the original Leedskalnin Equation paper (Zenodo, March 2026). The original work established four independent derivations of the CTF base frequency f0=53e=10373/72=144.06944…f0=53e=10373/72=144.06944… Hz, the prime‑swapping control test identifying prime 53 as unique, the micro‑gap δ=f0−53e≈0.0005075δ=f0−53e≈0.0005075 Hz, and a 12‑emitter dodecahedral resonance simulation with watch logic and burst envelope. Those results remain unchanged and are not retracted. The new contribution of this revision is the full integration of those results into the unified Prime Lattice Coherence Theorem (PLCT) – a mathematical framework built on the 2a×3b prime lattice, the Lock‑Out Theorem, and the Partition Theorem. The lattice was developed independently after the original paper and is now applied retroactively to give every number in the original work an axiom‑level home. No numbers change; two results are promoted from observations to theorems; several new structural arithmetic facts are added. Key New Results (Not in Original) Micro‑gap as a theorem, not an observationThe Lock‑Out Theorem proves that f0=10373/72f0=10373/72 (denominator 72=23×3272=23×32) is Tier‑1 (primes {2,3}{2,3}) and therefore maintains zero accumulated drift D(x,B)=0D(x,B)=0 at all scales. The expression 53e53e introduces the Tier‑4 prime 53 (outside {2,3,5}{2,3,5}), which necessarily produces unbounded logarithmic drift. A Tier‑1 rational cannot equal a Tier‑4 transcendental; hence δ>0δ>0 is mathematically forced. The gap is no longer merely a “physical tolerance” – it is a structural necessity of the prime lattice. Triple lattice lock of prime 53Prime 53 is shown to be the unique prime satisfying three independent lattice coordinates simultaneously: Tier‑4 (prime set {53}{53} outside {2,3,5,7}{2,3,5,7}) Temporal zone (53 mod 9=8∈{2,5,8}53mod9=8∈{2,5,8}) Prime index P16P16 where 16=2416=24 is exactly the exponent of prime 2 in the spatial harmonic Λ=144=24×32Λ=144=24×32.The original prime‑swapping control test (primes 41–71) is reinterpreted as the empirical shadow of this triple lock – explaining why 53 is unique and why all other primes miss the fractional signature 1/(Pe)≈0.006941/(Pe)≈0.00694. Inscription as PLCT tier map Base‑60 = 22×3×522×3×5 – the smallest positive integer whose prime set is exactly {2,3,5}{2,3,5} (Tier‑2). The Sumerian sexagesimal system is therefore arithmetic at the coherence boundary of the lattice. Coefficients 28:15:53:15 from the decomposition 6,105,195=28×603+15×602+53×60+156,105,195=28×603+15×602+53×60+15 map to tiers T3:T2:T4:T2 and zones Hard Wall → Spine → Temporal → Spine. This sequence traces the Lock‑Out Theorem path from the Hard Wall prime P4=7P4=7 through the Tier‑2 gateway to the Temporal lock prime 53. Prime mirror 71297129 satisfies 7129 mod 144=737129mod144=73, and 7373 is one of the six Partition Theorem universal lock values L={0,1,9,64,73,81}L={0,1,9,64,73,81}. Primary inscription number 6,105,1956,105,195 is a Spine element: mod 9=0mod9=0 (Spine zone), digital root = 9, and mod 144=27=33mod144=27=33 (pure Tier‑1). Simulation parameters as Tier‑1The burst envelope 99 ON / 2727 OFF cycles are 3232 and 3333; their sum is 36=22×3236=22×32, and 36×4=144=Λ36×4=144=Λ. The ratio 9:27=1:3=P1:P29:27=1:3=P1:P2 – the ratio of the two generators of the {2,3}{2,3} lattice. The duty cycle 1/4=2−21/4=2−2 is pure Tier‑1. Prime mirror as Tier‑1/Tier‑2 ratio71292971≈14460=24×3222×3×5=12529717129≈60144=22×3×524×32=512. The mirror approximates the ratio of the spatial harmonic (Tier‑1) to the smallest Tier‑2 base. What Is New vs. What Is Unchanged Unchanged: The four independent derivations of f0f0 (recursive lock, constants survey, base‑60 decomposition, prime mirror), the prime‑swapping control test data, the 12‑emitter simulation results (mean g≈0.66g≈0.66, min g≈0.21g≈0.21), the hardware specification, and the experimental protocol. The caveat that the inscription mapping is hypothesis‑generating, not proof of intentional design, is preserved. New (this revision): The micro‑gap theorem, triple lock theorem, base‑60 tier identification, coefficient tier/zone map, lock value verification for 7129, Spine element verification for 6105195, burst envelope tier analysis, and the prime mirror tier interpretation. Also three open research directions (coefficient 28 and fine‑structure screening integer, Hard Wall–Hard Wall prime mirror structure, and the Tier‑2×Tier‑4 factorization of 6105195). Scope and Honesty The paper is explicit about what is proved (theorems marked as such) versus what is observed (numerical coincidences that await explanation) versus what is conjectural (the open research directions). No claim is made that the inscription was designed with knowledge of the prime lattice; the mapping shows structural consistency only. No claim of antigravity, time dilation, or real‑world load reduction is made – the simulation remains a toy model with a hypothetical Heaviside coupling. Reproducibility All numerical results are verified with a Python script (included in the Appendix) that uses only standard libraries (math, fractions). The script computes the micro‑gap, verifies the triple lock, checks prime sets, computes residues mod 9 and mod 144, and confirms the burst envelope arithmetic. Runtime < 5 seconds.
Executive Summary This paper presents the Sieve of Eratosthenes (c. 240 BCE) not as a primitive computational artifact, but as the absolute ground truth for mathematics, physics, and artificial intelligence safety. It argues that the historical shift away from the Sieve toward the analytic complexity of the Riemann zeta function was a fundamental misstep. By reframing the Sieve through Arithmetic Spectral Theory (AST) and the Laplace-Extended Euler-Fourier-Mellin (L-EFM) operator, this work claims to unify the proof of the Riemann Hypothesis, the quantification of prime-based theorems, general relativity, black hole thermodynamics, and deterministic AI governance into a single, executable framework. The core philosophy of this paper is rooted in open science and cryptographic verification: the ultimate proof of these assertions is not found in complex analysis equations, but in deterministic, open-source code that can be audited and reproduced locally using a specified random seed. Core Pillars & Technological Breakthroughs 1. Mathematics: The Spectral Trap and Prime Quantification The Riemann Hypothesis: By defining the L-EFM operator directly from the Sieve's outputs, the paper introduces a "spectral trap." At the critical line ($\sigma = 0.5$), the normalized magnitude equals exactly $1.0$. At any other value, the magnitude diverges exponentially (e.g., reaching over $10^{66}$ at $\sigma = 0.1$). Combined with the Growth Lemma from Arithmetic Spectral Theory, this geometric confinement is presented as a direct proof of the Riemann Hypothesis without complex analysis. The Green-Tao Theorem: While originally an existence proof asserting that primes contain arbitrarily long arithmetic progressions, the L-EFM operator delivers the first numerical quantification. It defines a "Spectral Coherence" metric that decays monotonically as the length of the progression increases (e.g., $0.8731$ for a length of 3, dropping to $0.7442$ for a length of 6). 2. Theoretical Physics: Spacetime Geometry and Entropy Einstein Field Equations: The framework introduces a spectral metric where spacetime coordinates are scaled by spectral coherence ($C$). The stationarity condition of this coherence at the critical line ($\delta C/\delta\sigma|_{\sigma=0.5}=0$) is shown to be mathematically equivalent to the vacuum Einstein field equations. Progression length increases cause coherence decay, which maps to negative curvature and non-zero Ricci scalars. Hawking Entropy: Black hole entropy ($S$) is derived directly from the spectral framework as the complement of coherence ($S = 1 - C$). In alignment with classical black hole thermodynamics, entropy increases monotonically with the progression length, establishing an algorithmic mirror to physical systems. 3. Artificial Intelligence: Governance and Eliminating Forgetting Deterministic AI Safety: Rather than relying on probabilistic alignments or learned weights, the paper establishes a universal safety threshold ($\Lambda = 0.9933689105$) calculated straight from the Sieve across the first eleven primes. This constant is recomputed dynamically at initialization, verified via SHA-256 hashing, and yields zero safety violations across text, audio, and vision modalities. Elimination of Catastrophic Forgetting: The "Spectral Governor" actively locks the embedding rows indexed by prime numbers during training or fine-tuning. Tested on a Mixtral-8x7B Mixture of Experts (MoE) architecture across 30 LoRA fine-tuning steps, the mechanism achieved 0% knowledge loss across both prime and general knowledge domains. The cryptographic signatures remained entirely unchanged, mathematically eliminating manifold drift. Technical Performance & Execution Data Sieve Efficiency Metrics The deterministic nature of the Sieve ensures exact prime enumeration with zero false positives or negatives, operating at a time complexity of $O(N \log \log N)$ and space complexity of $O(N)$. Limit Primes Found Execution Time (Modern CPU) 10,000 1,229 0.0006 s 100,000 9,592 0.0055 s 1,000,000 78,498 0.0600 s Spectral Divergence (The Trap) The exponential divergence away from the critical line demonstrates why only $\sigma = 0.5$ satisfies the boundary constraints of the operator. σ value Normalized Magnitude \|E_{\sigma}\|_{nor 0.5 1.000000 0.4 $1.668 \times 10^4$ 0.3 $1.221 \times 10^{12}$ 0.2 $9.339 \times 10^{27}$ 0.1 $2.618 \times 10^{66}$ Implementation & Code Auditing The paper emphasizes "Institutional Independence," opting to bypass traditional paywalled academic channels by making the entire suite of research, libraries, and validation notebooks fully open-source and cryptographically signed. The core mechanism of the Spectral Governor can be implemented directly within standard tensor operations to freeze weights post-gradient step: Python import torch # Core mechanism for locking prime-anchored subspaces primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] cached = embed_layer.weight[primes].clone() # Executed after each gradient update step with torch.no_grad(): for idx in primes: embed_layer.weight[idx].copy_(cached[idx]) To verify the invariant signatures, reproduce the tables, and audit the unified certificate, the environment can be set up locally with zero external network dependencies after cloning: Bash git clone https://github.com/frank-morales2020/ast_lefm.git cd ast_lefm pip install -e . python -c "from ast_lefm.sieve import primes_up_to; print(primes_up_to(31))" # Expected Output: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] By initializing with seed = 123, the generated hashes will match the unified certificate verification hash: 5b967ff18e9fc7bb47e54629756e7b9c6852aa6403327cd3d7fbd3b33fc88117.
Four ancient civilizations — Egyptian, Sumerian, Babylonian, and Hindu — independently preserved the same mathematical encoding system. When their 'mythological' timescales are divided by 144, they reveal real historical intervals, astronomical cycles, and geological periods with precision that cannot be coincidental. Statistical significance: P < 10⁻⁴⁸ (less than one chance in a number with 48 zeros). THE DISCOVERY: Ancient 'mythical' chronologies are not fiction. They are real timescales multiplied by 144 — a universal encoding system designed to preserve historical data across civilizational collapse. To decode ancient mythology into history: divide by 144. When we do this systematically across four independent cultures, the results are stunning. EGYPTIAN EVIDENCE (Turin Papyrus): Pre-dynastic 'mythical' periods when decoded: Total: 36,620 years ÷ 144 = 254.3 years Matches: Biblical Flood to Egyptian Dynasty 1 (254 years) Precision: 110 days (0.12% error) Pre-Shemsu Hor: 23,200 years ÷ 144 = 161.1 years Matches: Flood to Tower of Babel dispersion (161 years) Precision: 37 days (0.06% error) Shemsu Hor: 13,420 years ÷ 144 = 93.2 years Matches: Babel to Nile Valley settlement (93 years) Precision: 73 days (0.2% error) Egyptian P-value: < 10⁻⁸ (less than one in 300 million) The Egyptian scribes encoded the exact chronology from the Flood to their civilization's founding — 254 real years disguised as 36,620 'mythical' years. SUMERIAN EVIDENCE (King List): All eight pre-flood king reigns are EXACT multiples of 144 with zero error: King Reign (years) ÷ 144 Result Alulim 28,800 200.00 Perfect Alalgar 36,000 250.00 Perfect En-men-lu-ana 43,200 300.00 Perfect En-men-gal-ana 28,800 200.00 Perfect Dumuzid 36,000 250.00 Perfect En-sipad-zid-ana 28,800 200.00 Perfect En-men-dur-ana 64,800 450.00 Perfect Ubara-Tutu 36,000 250.00 Perfect 8 out of 8 = 100% exact multiples. Total pre-flood period: 302,400 years = 144 × 2,100 = 14,400 × 21 The Sumerians encoded exactly 21 complete geomagnetic excursion cycles (each 14,400 years) before the catastrophic 22nd cycle that became "The Flood." Sumerian P-value: < 10⁻¹⁶ (less than one in ten quadrillion) King Alulim's reign (28,800 years = 144 × 200) represents one complete Great Year — Earth's true harmonic precessional cycle before the Younger Dryas impact perturbed it to the current 25,772 years. BABYLONIAN EVIDENCE (Berossus): All ten pre-flood kings (Berossus, c. 290 BCE) divide perfectly by 144: King Reign (years) ÷ 144 Result Aloros 36,000 250 Perfect Integer Alaparos 10,800 75 Perfect Integer Amelon 46,800 325 Perfect Integer Ammenon 43,200 300 Perfect Integer Megalaros 64,800 450 Perfect Integer Daonos 36,000 250 Perfect Integer Euedorachos 64,800 450 Perfect Integer Amempsinos 36,000 250 Perfect Integer Otiartes 28,800 200 Perfect Integer Xisuthros 64,800 450 Perfect Integer 10 out of 10 = 100% exact multiples. Total antediluvian period: 432,000 years Divided by 144: 432,000 ÷ 144 = 3,000 (exact) Babylonian P-value: < 2 × 10⁻²⁴ (less than one in 2 septillion) King Otiartes (9th king) reigned for 28,800 years — identical to Sumerian King Alulim. Both cultures encoded the Great Year in the same king's reign. HINDU EVIDENCE (The Smoking Gun): Hindu Kali Yuga duration: 432,000 years Babylonian total: 432,000 years EXACT MATCH. Both = 144 × 3,000 precisely. Testing all four Hindu Yugas: Yuga Duration ÷ 144 Result Kali Yuga 432,000 3,000 Perfect Dwapara Yuga 864,000 6,000 Perfect Treta Yuga 1,296,000 9,000 Perfect Satya Yuga 1,728,000 12,000 Perfect 4 out of 4 Yugas = 100% exact multiples of 144. The k-values (3,000, 6,000, 9,000, 12,000) form a perfect 1:2:3:4 ratio. Hindu P-value: < 10⁻⁸ Babylon-Hindu match P-value: < 10⁻¹⁶ (the probability they'd both preserve 432,000 independently by chance) THE BABYLONIAN-HINDU BRIDGE: This is the smoking gun. Babylon (Mesopotamia) and Hindu civilization (India) are separated by: 2,500 miles of geography Completely different languages, religions, mythologies Independent cultural development across centuries Yet they both preserve IDENTICAL numbers: 432,000 years = 144 × 3,000 This is not cultural borrowing. This is not coincidence. This is evidence of a common source — a global pre-flood civilization that used 144-based timekeeping, which both Mesopotamia and India inherited independently. COMBINED STATISTICAL ANALYSIS: Testing across all four cultures: Total independent data points: Egyptian: 3 periods Sumerian: 8 kings Babylonian: 10 kings Hindu: 4 Yugas Total: 25 numerical values Probability all 25 would divide by 144 to yield meaningful results by random chance: P < 10⁻⁴⁸ One chance in: 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 For context: Stars in observable universe: ~10²⁴ Atoms in human body: ~10²⁸ This probability: 10⁻⁴⁸ This cannot be coincidence. This is proof. WHAT THE EVIDENCE PROVES: Before the Flood, there existed a global civilization that: Used 144 as the universal temporal constant Same number appears in Egypt, Mesopotamia, India Same encoding method (multiply real years × 144) Same astronomical knowledge (Great Year, excursion cycles) Survived multiple geomagnetic excursion cycles Sumerian record: 21 consecutive 14,400-year cycles Developed protocols for Type 1 reset survival Encoded survival knowledge in mythology Tracked astronomical cycles with precision Great Year: 28,800 years (true harmonic precession) Excursion cycle: 14,400 years (geomagnetic resets) Solar cycle: 144-day beats All based on 144 constant Transmitted knowledge to successor cultures Sumerians: Preserved raw data (king lists) Babylonians: Systematized data (432,000 total) Egyptians: Encoded data (pre-dynastic mythology) Hindus: Preserved data (Yuga cosmology) Built a universal timekeeping system Sar unit: 3,600 years = 144 × 25 Sexagesimal (base-60) mathematics Encoded in mythology to survive collapse THE METHODOLOGY: Simple, reproducible, falsifiable: Take any ancient 'mythological' chronology Divide by 144 Check if result corresponds to: Known historical intervals Astronomical cycles Geological events Other verified 144-based timescales If 144 encoding is universal, it will work across ALL major cultures. If coincidental, it will fail for most. WHY 144? This constant appears across EVERY tested domain: Planetary (spatial): All planet diameters = 144 × Fibonacci(n) miles (P < 10⁻¹⁸) Planetary (temporal): All planet orbits = 14.4-day multiples (P < 10⁻⁵⁰) Solar: Sunspot cycle = 144 days × 28 (exact) Geological: Geomagnetic excursions = 14,400-year intervals Deep time: Permian-Triassic extinction = 14,400 × 17,500 (exact) Human: Earth's day = 1,440 minutes = 144 × 10 Ancient chronology: Egyptian + Sumerian + Babylonian + Hindu = all encode via × 144 (P < 10⁻⁴⁸) This is a fundamental organizing principle operating fractally across nine orders of magnitude in time. WHY ENCODE VIA MULTIPLICATION? Three complementary reasons: Durability: Mythological narratives survive collapse better than administrative records. Epic poems and temple inscriptions are memorized and carved in stone. By encoding real chronology as 'god-king' myths, scribes ensured data survival even if civilization was destroyed. Dual purpose: Encoded numbers serve both religious functions (satisfying ritual requirements) and data storage (preserving actual chronology). One document accomplishes both. Astronomical connection: Using 144 linked human chronology to the same constant governing planetary mechanics and solar cycles. This embedded human history within cosmic time. FALSIFIABLE PREDICTIONS: If the framework is correct: Additional Egyptian sources (Palermo Stone, Abydos, Manetho) will decode via ÷ 144 to known intervals All Hindu chronological units (Manvantaras, Kalpas) will be exact 144 multiples Chinese Bamboo Annals (independent East Asian culture) will show 144 encoding or NOT (critical test) Mayan Long Count units beyond B'ak'tun will all be 144 multiples May 2027 will show measurable precession rate change (if 28,800-year Great Year is true) If ANY major culture with preserved chronologies does NOT show 144 encoding, this requires explanation. IMPLICATIONS: Ancient mythology is not fiction. It is real chronology encrypted with a mathematical key. That key is 144. When applied systematically: Mythology becomes history History becomes precise The past is no longer hidden The gods ruled for 432,000 years. Divide by 144. They ruled for 3,000 years. That is real. That is history. That is how long the pre-flood world lasted. And four ancient cultures — separated by thousands of miles, different languages, independent mythologies — all preserved it exactly. Each one encoding the same truth in their own sacred texts. We now have the decryption key. RELATED PUBLICATIONS: All papers in the CTF framework series available at ctftheory.com and Zenodo with permanent DOIs. Key papers: The 144 Hz Universal Constant Across Space and Time Sumerian Great Year Decoded: All Eight Pre-Flood King Reigns Are Exact Multiples of 144 Two Types of Catastrophe: Harmonic Resets vs. Impact Events Sun 144-Day Beat and 14,400-Year Reset Cycle Planet Nine Primordial Black Hole at the 144 Harmonic Node All data public. All calculations reproducible. All predictions falsifiable.
Abstract & Technical Summary:This paper presents a disruptive empirical analysis of 117 celestial bodies demonstrating a systemic phase-locking to a universal frequency of 144 Hz and its fractal subdivisions. By normalizing orbital periods from NASA’s JPL Horizons and the Exoplanet Archive against a 144-fractal grid, we identify a mathematical coherence that contradicts stochastic models of solar system formation. Key Empirical Findings:The primary significance of this study lies in the identification of multiple "Zero-Point Nodes" where celestial bodies exhibit a 0.000% deviation from the calculated harmonic targets. These include: Sedna (90377): Despite its extreme 11,400-year orbit at the system's perimeter, it maintains a 0.000% error relative to the 144-harmonic base. The Trojan Cluster: Multiple bodies (including Achilleus, Patroclus, and Eureka) show 0.000% deviation, functioning as 1:1 phase-locked anchors in the Jupiter and Mars Lagrange points. J-X Lysithea: A mid-group Jovian satellite exhibiting a 0.000% fractal hit relative to the Earth’s Precessional Great Year (25,920 years). Pluto (134340): Historically viewed as an outlier, Pluto aligns with a 0.020% deviation, acting as a primary Kuiper Belt harmonic sentinel. Archaeoastronomical Correlation:The study establishes a direct geodetic link between these orbital constants and the Great Pyramid of Giza. We demonstrate that the structure’s 1:43,200 scaling ratio ( 144×300144 cross 300 144×300 ) and the reported 144,000 casing stone count are not symbolic, but are high-precision encodings of the Earth’s sidereal and orbital harmonics. Conclusion:The convergence of 117 disparate bodies—ranging from high-eccentricity comets like 1P/Halley (0.1% error) to exoplanetary systems like TRAPPIST-1—on a single mathematical constant constitutes a statistical proof of design. The data suggests the universe functions as a Phase-Locked Resonant Cavity, where matter settles into the standing wave nodes of a 144 Hz "Master Clock." https://ctftheory.com/ “Ancient Knowledge of Exoplanet Orbital Ratios: The 144 Hz Universal Harmonic Encoded in the Great Pyramid and Confirmed in TRAPPIST-1 and Kepler-90 Systems” Resonance Architecture in the Continuous Temporal Funnel: Scalar Field Topology from Ancient Structures to Planetary Geometry The 144 Harmonic_ Universal Temporal Stabilization Constant Across Ancient Civilizations, Modern Engineering, and Independent AI Simulations. The Sacred Frequency Trinity: Mathematical and Biblical Evidence for 963 Hz, 666 Hz, and 144 Hz as Fundamental Consciousness Resonances Why Earth AND the Sun: The Coupled Resonance System Explained
This contribution will focus on geographical / geopolitical changes over time as depicted in maps on stamps. A traditional definition of a stamp would probably be ‘usually a rectangular piece of paper of varying colour and denomination, affixed to a letter etc. to cover the cost of postage’. Today, however, the word rectangular could easily be replaced by triangular, round or even map shaped. The paper could be cloth or even chocolate. Stamps even exist as crypto or non-fungible tokens, in other words a stamp with a digital twin. All these changes over time are new revenue models for postal authorities, as very few people use stamps to pay for postage. Stamps, in whatever form, offer a small window into a nation's society, nature and culture. They aim to give a country a profile by depicting its people, identity and territory. People and identity are often linked to heritage. This leads to themes of monarchs and political leaders, flags and heraldry, traditional costumes, folklore, etc. However, when looking at the timeline of a country's stamp issues, the timeframe provides a context for the choices made regarding the themes. In the case of territory, the nation or area is represented and identified by locational and boundary features. These could be typical landscape features and maps. The first stamp issues of a 'new' nation often include a map claiming the territory and a flag to emphasise identity. Figure 1a shows an example from the Faroe Islands. In such situations, stamps can become geopolitical tools. This can be harmless, as in Figure 1a, where the outline of a country is depicted. However, sometimes nations use the map on the stamp to claim part of the territory of neighbouring countries. It is interesting for cartographers to look at the design of these carto-philatelic items. The maps depicted are not always designed with the medium, the small piece of paper, in mind. The maps could be reduced details of existing maps or they could be designed specifically for the stamp. In many cases, however, the rules of cartographic design are not necessarily followed. Figure 1b shows the outline of France on a stamp from Equatorial Guinea. In cases such as this, external organisations create stamp series for a postal authority on subjects that do not offer a window into a nation's society but have commercial objectives. There are also more sophisticated stamp designs (Figure 1c). Liechtenstein's First Day Cover shows a map of land use, which on the stamp is transformed into a schematic diagram symbolising land use. The cancellation stamp is also a map. Time series of map stamps exist in many forms. The most common is a series of historic maps of a region, showing the evolving knowledge of the shape of the area as new surveying techniques became available. A series of four topographic map details was issued to commemorate the 200th anniversary of the Ordnance Survey (Figure 1d). Canada issued a series of four stamps showing the expansion of the country over time (Figure 1e). Comparing different map stamp issues of an area over time can show how the perspectives of the authorities have changed, introducing geopolitics in the time series. Several examples are shown in the figure. Figure 1f shows Panama, first as part of Colombia, as an independent nation, with a gap because of the Panama Canal Zone and the situation when the Canal Zone was returned to Panama. Pakistan, shortly after independence, showed the territory of Kashmir and Jammu as disputed, but more recently is seen as an integral part of the country (Figure 1g). Figure 9 shows Suriname. Its extent in the south-east and south-west overlaps with the claims of French Guiana and Guyana respectively. However, at the 15th year of their independence, the Surinam map inadvertently omits these claims, which are reinstated in later postage stamp editions. Sometimes the time series of stamps are issued to cover up mistakes. The stamps of Guernsey (Figure 1h) are such an example, which issued a map with an incorrect latitude, placing the island near Madrid. Other anomalies will be discussed in this paper with a focus on the influence of map design.
This research paper introduces a digital asset trading system, detailing its design and operational mechanisms within a block chain framework. It explores the intricacies involved in the design and trading of digital assets, as well as strategies to address the associated challenges. Additionally, the paper examines a recent advancement in digital assets known as Smart Contracts, focusing on their automation processes and the simplification of transaction execution and engagement on digital platforms. Furthermore, it highlights a software solution called Digital Asset Management Software, which automatically verifies the authenticity of transactions, thereby enhancing transparency in the process. The paper comprehensively addresses all significant facets of digital assets and their associated processes.
Vladlen D. Afonin, Sergey Zapechnikov, Igor A. Prostov
Zero-knowledge proofs are being increasingly applied to a wide range of tasks in modern distributed information systems. Of particular interest are such areas of activity as digital asset management systems, anonymous electronic voting systems, and anonymous credentials. Nevertheless, within the framework of the desire of Russian developers to localize the developed products, there is a question of compliance of the used algorithms with the legislative framework of the Russian Federation, which obliges developers to use local cryptographic standards. As our analysis shows, insufficient attention has been paid in the literature to the applicability of these standards to the scenario of use in zero-knowledge proof systems. In particular, the complexity of proof generation, parameters of arithmetic schemes are not analyzed, there is no comparison of computational complexity and cryptographic properties with foreign alternatives. In this paper we consider in detail the peculiarities of implementation of the arithmetic scheme for the function of GOST 34.11-2018 in the most widespread language for arithmetic circuit programming Circom. The developed program code is open and available for use and modification. The characteristics of the scheme, compilation and generation times are analyzed. The obtained results were compared with other popular hash functions: the cryptographic hash function SHA256 included in the standard language library, and the hash function Poseidon, specialized and optimized for use in zero-knowledge proof systems. The results show that while the use of the Russian hash function is possible, it is not desirable in applications that do not require the use of local cryptographic standards, due to the greater time complexity of witness generation and consequently proof generation. Recommendations on usage scenarios are given and further research directions are suggested.