Blockchain Papers

Griff gurwell

" 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.

Kelly Vero

This chapter traces the evolution of video game tech stacks from early home computing to modern metaverse platforms. Blending personal narrative with technical insight, it explores programming languages, modular design and infrastructure across MMOs, and Web2 and Web3 ecosystems. Games like Mined-Out , RuneScape , Jetpac and Tomb Raider illustrate how early innovation laid the groundwork for today&s;s persistent digital experiences. The chapter argues that game developers, with their systems thinking and user-centred design, are natural architects of the metaverse.

Erika Nur Syarifah Daulay, Akhmad Budi Cahyono

The development of digital technology has introduced Non-Fungible Tokens (NFT) as a form of digital asset that has its own economic value and uniqueness. This opens up the potential for NFTs as objects of inheritance, however the traditional inheritance law system in Indonesia has not fully accommodated non-physical entities such as NFTs, especially due to unclear regulations regarding the transfer of rights to these assets after the death of the owner. This article discusses legal protection for heirs with NFT inheritance objects. This research uses normative or doctrinaire research methods using secondary data and a comparative legal approach, which involves analysis of relevant laws and regulations and NFT practices in several jurisdictions that have recognized the existence of NFTs. Based on the research results, NFTs can be inherited through a general will made by a notary, olographic, or private. However, the main challenge is access to digital wallets that store NFTs and are at risk of being lost if there is not sufficient technical information regarding access. To overcome this, inheritance planning with a dead's man switch mechanism in smart contracts can enable the automatic transfer of NFTs to heirs. However, legal recognition of this mechanism is still limited. This research highlights the need for clearer regulations and legal updates in Indonesia regarding digital asset inheritance, to provide legal certainty for owners and heirs as technology develops. It is hoped that the results of this research can contribute to the formulation of clearer regulations and provide adequate legal protection for heirs and heirs who own digital assets in Indonesia.

Mohd Fairuz Ali, Cheng Kin Meng, Ng Perng Jeu

Cultural heritage is a vital aspect of any society, and it is important to preserve it for future generations. However, traditional methods of cultural preservation have proven to be ineffective in the face of technological advancements and globalization. Blockchain technology, which includes NFTs, has emerged as a promising solution to cultural preservation. The main aim of this study is to investigate the potential of Non-Fungible Tokens (NFTs) in the preservation of the Malaysian Wau game cultural heritage. A mixed-methods approach is used in the study, which also includes surveys and interviews with Wau practitioners, NFTs major figures, and NFTs users. As a result of their ability to transfer ownership and control of digital assets in a secure and transparent manner, NFTs have been demonstrated to be a useful instrument for cultural preservation. Yet, there are obstacles to the adoption of NFTs as well, such as the high implementation costs and the requirement for advanced technical knowledge. The study concludes by offering recommendations for the implementation of NFTs in preserving cultural heritage of Malaysian, including the need for collaboration between NFTs stakeholders and the development of clear guidelines and standards assessing their practicality, and proposing strategies for their effective implementation in safeguarding the Malaysian Wau game heritage.

Johan Ling, Timothy Earle, Kristian Kristiansen

As exemplified by Viking and Bronze Age societies in northern Europe, we model the political dynamics of raiding, trading, and slaving as a maritime mode of production. It includes political strategies to control trade by owning boats and financing excursions, thus permitting chiefs to channel wealth flows and establish decentralized, expansive political networks. Such political institutions often form at the edges of world systems, where chieftains support mobile warriors who were instrumental in seizing and protecting wealth. Particular properties of the maritime mode of production as relevant to Scandinavia are the fusion of agropastoral and maritime modes of production. To exemplify these two sectors, we use the Thy and Tanum cases in which we have been involved in long-term archaeological research. The historic Viking society provides specificity to model the ancestral political society of Bronze Age Scandinavia. Our model helps understand an alternative path to institutional formation in decentralized chiefdoms with low population densities, mobile warriors, and long-distance trading and raiding in valuables, weapons, and slaves.

Miguel García García-Revillo, Miguel Jesús Agudo Zamora

The recent entry into force of the 2001 UNESCO Convention on the Protection of Underwater Cultural Heritage means certainly good news for the protection of this part of the legacy of past generations. A great deal still remains to be done, however. 2001 Convention has a limited personal and material scope of application. In its absence, the international regime applicable to this kind of heritage spreads out among a number of heterogeneous instruments focused on diverse topics. One of the problems that the said diversity and heterogeneity causes is the variety of terms and definitions used by it. On the other hand, the implementation of a series of instruments so different becomes particularly complex when referring to States that have partially transferred their competences “up” to a regional integration organization, like the European Union, and “down” to decentralized territorial units, like the so-called Autonomous Communities. To this respect, the case of Spain provides with a good example of such difficulties.