On the Feasibility, Limitations, and Logistics of a Kardashev-Scale Bitcoin Network April 2025 u/8a8 Contents Contents .............................................................................. ... 1 Abstract ................................................................................. 2 Introduction ........................................................................... 2 Type I: A Planetary Bitcoin ......................................................... ... 3 Energy and Infrastructure Bitcoin Mining Ramifications I. Bitcoin Mining Context II. Raw Hashrate vs. Effective Contributed Hashrate III. Hashrate Efficiency Over Time Bitcoin Usage Adaptations I. Second Layer Maturation II. Base Layer Confirmations Type II: A Stellar Bitcoin ............................................................ ... 18 Energy and Infrastructure Bitcoin Mining Ramifications I. Center of Hash II. Oscillating Difficulty Adjustments III. Relative Hashrate Efficiency Ratio IV. The Consecutive Block Monopoly & Tier 2 Hash Centers V. Adjusted Mining Feasibility Index Bitcoin Usage Adaptations I. Minability vs. Usability II. Interplanetary Base-Layer Settlements Type III: A Galactic Bitcoin ......................................................... ... 33 Energy and Infrastructure Bitcoin Ramifications I. The Bitcoin Mining Hard Limitation II. Federated Proof of Work Sidechains III. Bitcoin at Relativistic Velocities Conclusion ........................................................................... ... 40 Citations .............................................................................. .. 4 1 Abstract This paper explores the feasibility of Bitcoin mining and usage as humanity advances through the Kardashev Scale, from a planetary (Type I) to a stellar (Type II) and ultimately a galactic (Type III) civilization. We analyze how Bitcoin and its Proof-of-Work (PoW) consensus mechanism can adapt to vastly different energy capacities, and interstellar-spanning distances. This paper proposes ideas such as new necessary mathematical models for hashrate efficiency, relative hashrate, and a Mining Feasibility Index to provide a framework for assessing mining viability across interplanetary and interstellar distances. Additionally, we propose the use of Federated Proof-of-Work sidechains and localized second-layer networks to enable scalable and secure usage of Bitcoin across stellar and galactic distances, even in the presence of relativistic travel and causality constraints. This work outlines a long-term vision for how Bitcoin could remain viable in a high-energy, space-faring future. Introduction The Kardashev Scale [1], introduced by astrophysicist Nikolai Kardashev in 1964, classifies civilizations based on their ability to harness energy. A Type I civilization utilizes all available resources on its home planet, a Type II civilization harnesses the energy output of its home star, and a Type III civilization operates on a galactic scale. As humanity progresses through these types of civilizations, decentralized Proof-of-Work networks like Bitcoin must evolve to overcome new obstacles. Just as gold has been a store of value for thousands of years, Bitcoin maximalists aim for Bitcoin to remain viable for future generations. As an energy-consuming Proof-of-Work currency, Bitcoin presents a unique case study in how such a system might function in a Kardashev-scale civilization. In a future where humanity spans the solar system and beyond, precious metals and other materials may be easily harvested via asteroid mining [2], and the abundance of usable energy will dwarf what we see as feasible today. In this space-faring age of post-scarcity across interstellar distances , we explore how Bitcoin can overcome the innate limitations of spacetime and still succeed as a viable form of currency. 2 Type I: A Planetary Bitcoin Energy and Infrastructure Scale A Type I civilization is one that fully harnesses the energy of their home planet and has started colonizing other planets within the local solar system. A civilization of this scale would have a dramatically higher energy production compared to our world today, spurred by scaling more efficient renewable energy solutions, as well as new forms of energy production infeasible to us today, such as fusion power. At this stage, humanity may have already begun to propagate colonies to distant planets, like Mars. We will visit some of these theoretical colonies in this section to envision what a potential Bitcoiner in such a location may experience when interacting with the network, from both a Bitcoin miner and a Bitcoin user perspective. Bitcoin Mining Ramifications I. Bitcoin Mining Context Bitcoin’s Blockchain is constructed of blocks that are built upon each other[3]. These blocks take miners an average of ten minutes to find, and this interval is regularly & automatically maintained every 2016 blocks to ensure that the average continues to be ten minutes[4]. This is done by increasing or decreasing the difficulty for miners to find a correct block. If the amount of mining power in the network doubles, the next adjustment will increase the difficulty a like amount, ensuring that the block time remains an average of 10 minutes between blocks. 3 As a result of the Proof-of-Work consensus mechanism that Bitcoin uses, the block time is not exactly 10 minutes , but instead can be represented by a Gamma probabilistic distribution. Each second, there is roughly a 1/600 probability that the next block will be found. This means that the next block is always approximately 10 minutes away. 5 minutes worth of Bitcoin mining does not make the network any closer to mining that block, as it is not a progress bar of completion. This is akin to rolling a die once per minute hoping for a six. On average, you will get a six every six minutes. But there is still a 1/6 chance of rolling the number you want each minute, regardless of other outcomes. Fig 1. Gamma probabilistic distribution of block times 𝑃 𝐵𝑇 = 𝑡*𝑒 −𝑡/600 600 2 Above is a visualization of the gamma distribution function that represents the probability of a block being found after a specific amount of time ( P BT ). As displayed, the most likely time for a block to be found is around the 10 minute mark, however, it is not impossible for a block to take upwards of an hour or more to be found as well. 4 This works perfectly if everyone is always synchronized, but sometimes this isn’t the case. Orphaned blocks are those that the Bitcoin network rejects for a number of reasons, namely submitting a block when the network has already found another solution and moved on. No one cares about a miner’s solution to block #123 if everyone already found a different valid solution to it, propagated that block around the globe, appended it to the blockchain, and are now deep into working on block #124. II. Raw Hashrate vs. Effective Contributed Hashrate At interplanetary distances, the speed of light increasingly becomes a factor that must be taken into account, as information can only travel as fast as light. This creates an environment of information asynchronicity for a space-faring civilization. If you are several light-minutes away (e.g. Mars), any new Bitcoin block will take several minutes to reach you. If you are attempting to mine Bitcoin at this distance, there is a significantly higher risk that any block you find will be orphaned. This is because it is much more likely that an Earth-based miner would have announced their own correct solution before your solution has a chance to arrive at Earth (Even if you found a solution first in your own timeframe), thus the network has already moved on, and you receive no block reward. This reduces your Effective Contributed Hashrate because only some of your valid block solutions will be accepted by the network. At any distance within Earth’s bounds, your Effective Contributed Hashrate is essentially equal to your Real Hashrate due to the near instantaneous perceptible speed of light relative to the size of Earth and the timeframes that the blockchain requires. In this section, however, we will travel much farther and calculate Hashrate Efficiency as a function of distance from Earth. Let us consider a hypothetical future Bitcoin miner that exists 100 million kilometers ( 5.5 light-minutes ) away from Earth. Imagine a scenario in which block X was found at T=0 minutes, and block X+1 was found at T=10 minutes. The hypothetical distant miner will not be aware of block X until T=5.5 minutes, due to the latency of the speed of light. Unbeknownst to them, 5 even if they find their own block X+1 shortly thereafter and send the solution back to Earth, it will arrive too late. They will not become aware of this until T=15.5 minutes, when they find out that block X+1 was mined at T=10 on Earth. Their effective hashrate for this entire time will have been zero - they were always mining with no chance of contributing to block X+1 in retrospect. Fig 2. Chronological Time Order of Events with a Space-Miner 5.5 Light-Minutes from Earth 1. T=0.0 min: Earth miners find Bitcoin Block X , they broadcast their solution to the network, and begin trying to solve the next block. 2. T=5.5 min: The space-miner 5.5 light-minutes away learns about Earth’s solution to Block X , they begin work on the next block on-top of Earth’s solution. 3. T=7.5 min: The solo space miner gets lucky and finds a solution to Block X+1 A , they broadcast their solution to the network, and begin their own progress on Block X+2 A 4. T=10 min: Earth miners find their own solution to Block X+1 B , they broadcast this solution to the network, and begin work on Block X+2 B 5. T=13 min: The space-miner’s Block X+1 A solution arrives at Earth. The network orphans this block as a solution ( Block X+1 B ) was already found earlier from their perspective. 6. T=15.5 min: The space-miner learns of Earth’s solution to Block X+1 B . They now know that their solution arrived at Earth too late, and that their block was orphaned. 7. T=15.5 min+: The lone space-miner stops work on Block X+2 A , and begins to also work on-top of Block X+2 B , the Earth block, instead of their own orphaned block. 6 However, let us now imagine a scenario where the space-miner’s solution arrives at Earth before any Earth-based miner has the opportunity to find a different solution. This time, Earth accepts the space-miner’s solution and begins work on-top of that block. Therefore, we can see that the longer a specific block takes to be found by the network, the more hash contribution a distant miner can provide. We can describe this relationship as a function of distance by figuring out the projected Hashrate Contribution Time for the Next Marginal Block ( H CTNMB ). We will take the two-way distance to the destination ( 2d ) as the Consensus Distance ( d CD ), as the miner must be aware of the current blockchain state, and then send back the resultant block. We can then divide this by the speed of light to get the time it takes light to travel the consensus distance, and divide this again by the variable block time. To avoid impossible negative values (as it is impossible to contribute a negative percent of the time), we will also set the minimum result to be 0. 𝐻 𝐶𝑇𝑁𝑀𝐵 = 𝑚𝑎𝑥(0, 1 − 𝑑 𝐶𝐷 /𝑐 𝑇 𝐵 ) Let us plot some common distances within our own solar system to help illustrate what the H CTNMB will be at each specific location. Fig 3. Hashrate Contribution Time for the Next Marginal Block 7 This chart allows us to see that each planet remains at a zero hashrate contribution time proportion until the potential next-block-time increases to the point in which it is possible for a miner to have contributed towards the network hashrate, and ultimately enough time to send back a successful block back to Earth. Each planet’s hashrate efficiency approaches 100% as Block Time approaches infinity, as it is impossible to have an efficiency that surpasses that of an Earth-based miner in this scenario. These values, however, are the expected hashrate efficiency for the miner over just the next block, this is a scenario in which the block time distribution is not considered. To see a clearer picture for an miner existing beyond Earth, we must find the average effective contributed hashrate across the entire gamma probabilistic distribution of block times (fig 1). To find this, we must understand that the variable that affects this effectiveness is the probability of whether or not a valid block solution found by an off-Earth miner will be eventually orphaned or accepted by the Bitcoin network. The probability of a miner’s valid block being accepted by the network is the Hashrate Efficiency ( H E ) of the miner, this is because a miner that only gets half of their valid blocks accepted, will essentially have a resulting hashrate efficiency of 50%. The complement of this percentage is the probability of that same block solution being orphaned by the network ( P O ). This results in the following equation: 𝐻 𝐸𝑓𝑓 = 1 − 𝑃 𝑂 The probability of a block solution being orphaned by the network as a result of light-time latency is an exponential cumulative distribution function that approaches 100% as distance from Earth increases towards infinity. Specifically, it would reflect the following equation, where d CD is the consensus distance ( 2d ), and c is the speed of light in km/s (300,000). We then divide the two-way light distance by 600, the mean block time in seconds. 𝑃 𝑂 = 1 − 𝑒 −( 𝑑 𝐶𝐷 /𝑐 600 ) 8 We can use these equations to solve for H E , and by inserting the information from our hypothetical off-Earth miner from the beginning of this section, a distance of 100,000,000 kilometers from Earth would result in an hashrate efficiency of 32.92% 𝐻 𝐸𝑓𝑓 = 𝑒 −( 𝑑 𝐶𝐷 /𝑐 600 ) 𝐻 𝐸𝑓𝑓 = 𝑒 −( 200000000/300000 600 ) 𝐻 𝐸𝑓𝑓 = 0. 3292 Using this, we can now find the Effective Contributed Hashrate ( H EC ) of a Bitcoin miner by multiplying their Raw Hashrate ( H R ) by the specific miner’s Hashrate Efficiency ( H E ). 𝐻 𝐸𝐶 = 𝐻 𝑅𝐶 * 𝐻 𝐸𝑓𝑓 𝐻 𝐸𝐶 = 100𝑇𝐻/𝑠 * 0. 3292 𝐻 𝐸𝐶 = 32. 92𝑇𝐻/𝑠 For our 100 million kilometer-away miner, this results in a raw hashrate of 100 TH/s becoming an effective contributed hashrate of 32.92 TH/s. This can also be used to determine how much hashrate this hypothetical miner will need in order to have the equivalent hashrate contribution of a raw 100 TH/s on Earth. In this case, ( ) = 303.77 TH/s will be necessary 100 𝑇𝐻/𝑠 0.3292 to match the Earth miner’s hashrate. This 100,000,000 kilometer figure we’ve been using is very arbitrary though. So let us instead re-use our previous common distances within our own solar system to help illustrate what the hashrate efficiency may be at each specific location. 9 Location Distance (Km) Light-Distance (Seconds) Hash Efficiency Earth 0 0 100% Moon 384,400 1.28 99.57% Mars (min) 56,000,000 186 53.67% Mars (max) 400,000,000 1,320 1.17% Jupiter (min) 588,000,000 1,960 0.15% Fig 4. Hashrate Efficiency Within our Solar System Each of these distances represents a point on the continuous polynomial of the Hashrate Efficiency function . Viewed as a continuous range, the exponential decay of efficiency can be seen in the following graph. Fig 5. Hashrate Efficiency as a Function of Distance 10 While it may initially seem natural for these extra-terrestrial miners to only mine towards blocks that have lengthy block times, the limitations of the speed of light, and the inability to know exactly how long a given block will be while it is being mined, make it impossible for miners to know in advance whether or not they should stop mining a given block. Therefore, it is always in their best interest for the miner to continue mining, with the understanding that their effective hashrate efficiency is all they can base their decisions off of. III. Hashrate Efficiency Over Time Thus far, we have been considering the Effective Hashrate of points in space that are a fixed distance relative to Earth. This, however, is not the case for many stellar objects, as they are always moving in relation to one another. This can be seen as the difference between the Mars (closest) and Mars (farthest) in the previous charts. If we were a Martian miner experiencing this changing distance throughout the Earth-Mars orbit cycles, we would see this figure oscillate between those minimums and maximums. Fig 6. Hashrate Efficiency on Mars Over Time 11 This chart illustrates not only the smaller Mars-Earth orbit cycles, but also the larger super-cycles that result from each planet’s own elliptical solar orbit. This paints a clearer picture for how dynamic these relationships can become. In a hypothetical scenario where it is possible to store vast amounts of energy for later use, it may be fiscally beneficial for a future Martian miner to store their energy during lower Hashrate Efficiency periods, and use this stored energy to mine Bitcoin only during higher Hashrate Efficiency periods. Bitcoin Usage Adaptations I. Second Layer Maturation As both the global population and Bitcoin adoption rate increases, it will become increasingly obvious that Bitcoin’s blockchain can not accommodate everyone’s raw transactions. With its fixed size, the blockchain can handle approximately 7-10 transactions per second [5]. Solutions to these scalability concerns have seen various stages of success and have been developed for many years by this point, most notably with the Bitcoin Lightning Network [6]. You can think of second-layer solutions as a figurative upper-storey on a building. The ground floor of which, as the base-chain, can only fit a finite number of people. To give these people more space, they have the ability to ascend the stairs to the upper floor, where they can move around easier. However, in order to get to this floor, all individuals still need to venture through the ground floor to access the staircase. These second-layer solutions, akin to ascending the hypothetical staircase, can serve capacities that are orders of magnitude larger than the base chain, for a fraction of the fee, and be periodically settled back onto the Bitcoin blockchain as needed. Within a Type I civilization, it would be mandatory for a robust, matured framework for these second layers to exist in order for Bitcoin to still be a viable form of accepted money. To allow these second-layer payments to remain relatively instantaneous, it may be easier to relegate each user group to their own localized second-layer network. In this solution, Earth and 12 Mars may have separate second-layer networks, enabling any transactions on Earth to propagate the entire localized second-layer network in sub-second speeds. This essentially would create different planetary flavours of Bitcoin, depending on whether or not you ascended the base chain via the metaphorical Mars staircase, or Earth staircase. These separate networks would be necessary due to Bitcoin users’ prerequisite to have an instantaneous method of payment using Bitcoin. Without separate networks, the latency caused by the distance between the Earth and Mars may enable the double-spending of coins on the two different planets, before the recipient of either has the opportunity of discovering the other usage of their received coins. It’s important to note that these different second-layer planetary Bitcoin networks do not create new Bitcoin, as the Bitcoin used on them still originates from the main chain, and must pass back through the main chain as well. II. Base Layer Confirmations It is standard practice for a recipient of an on-chain Bitcoin payment to require a transaction to be confirmed by the network before they acknowledge the payment. This binary approach to a transaction being confirmed or unconfirmed can also be further subdivided. Some recipients may require a transaction to not just be confirmed , but for a transaction to have 2, 3, 4, or any number of confirmations. When someone requires a transaction to have at least n confirmation(s), it means that the transaction should, at minimum, be n block(s) deep into the block chain, with the subsequent blocks built on-top of it. The deeper your transaction’s block is in the blockchain, the more immutable/ permanent that transaction can be considered. Altering this transaction would require re-doing its respective block, as well as all of the blocks above it. This does not affect us today, as the risk of consecutive orphaned blocks or attacks on the network are low enough ( as a result of the 13 incredibly robust and secure compute network that Bitcoin has ) that most individuals, businesses, and institutions consider a single confirmation enough to suffice. For a Type I civilization, this immutability of the blockchain will remain relatively unchanged compared to today for those that reside on Earth. As discovered in the previous section regarding Bitcoin Mining Ramifications for a Type I civilization , Earth-mined blocks have an inherent advantage in immutability. Therefore, if your transaction is included in a block mined by Earth, you can have the same amount of confidence in the transaction’s permanence as someone does today with the respective amount of confirmations. The recommended number of confirmations, however, may differ depending on where you are using Bitcoin. While a user on Earth may be satisfied with their transactions having a single confirmation, a Bitcoin user that exists beyond Earth may require more. This is because not all transaction confirmations can be considered equal. Consider an on-chain Bitcoin transaction between two users on Mars. The sender broadcasts the transaction to the network with a high-priority fee, and the recipient awaits for this transaction to be confirmed in the next block. Thirty minutes later, the transaction gets its first confirmation by being included in a block. Depending on where this block was mined (Earth or Mars), may determine whether or not the recipient is satisfied with the transaction’s immutability. The recipient bases this on the block’s P O (the probability of the block in question being orphaned by the network as a result of light-time latency). Using our equations from the previous section, If the block was mined on Earth, the probability to be orphaned is 0%, thus the transaction can be considered safe by the recipient. If the transaction was included in a block that was just mined on Mars, this probability ranges from 46.33% to 98.83%, depending on where Earth and Mars are in their respective orbits. Not wanting to leave the result of this payment to such a chance, The Martian Bitcoin recipient may require additional confirmations for transactions included in blocks mined on Mars in comparison to blocks mined on Earth. 14 This does not, however, inherently make a Martian block-confirmation a metaphorical identical roll-of-the-die for all Bitcoin users. While irrelevant to us in the previous section as we only considered the miner’s frame of reference, the reality is that the probability of a block being accepted or orphaned is a relative to the triple relationship of distances between Earth, the Miner, and the user/observer . This is because the user may have a more up-to-date or out-of-date perspective of Earth’s consensus due to their light-time distance in comparison to that of the miner on Mars. Fig 7. Observer-Earth-Mars Example Distance Relationship Let us consider the probability of a martian-mined block being orphaned from three different perspectives, at the moment they become aware of the Mars-mined block. We will then be able to build a generalized framework around this i) Martian Perspective Mars mines and broadcasts a block at local T=0 and broadcasts it. Mars most up-to-date view of Earth ( d EM ) is at T= -5 minutes due to light-latency Mars must wait until its view of Earth is T= +5 minutes to ensure the block is accepted. Therefore Mars must wait 10 minutes (round-light-trip) to know the fate of their block. ii) Earth Perspective Earth becomes aware of a valid Mars-mined block at local T=0 Earth understands they lost the race to solving the latest block Earth immediately accepts the block without waiting. 15 iii) Observer Perspective The observer becomes aware of a valid Mars-mined block at local T=0 They know that they are 1 light-minute from Earth ( d EO ), 6 light-minutes from Mars ( d OM ), and that Earth is 5 light-minutes from Mars ( d EM ). They know that Mars mined the block at T= -6 minutes. They know that Earth received this block at T= -1 minute. They know their most up-to-date view of Earth is at T= -1 minute. Therefore, the observer can accept the block as Earth would have otherwise objected. We can generalize this relevant distance, which we can call the Consensus Distance ( d CD ), as a function of the three distance relationships as follows: 𝑑 𝐶𝐷 = 𝑑 𝐸→𝑀 − (𝑑 𝑂→𝑀 − 𝑑 𝐸→𝑂 ) Using this new definition for d CD , we can redefine our P O distribution to more accurately represent a miner-agnostic view of the fate of a block. 𝑃 𝑂 = 𝑚𝑎𝑥(0, 1 − 𝑒 −( (𝑑 𝐶𝐷 − 𝑐𝑡 )/𝑐 600 ) ) We can now use this formula to plot out the probability of a block being orphaned from the perspective of a user located anywhere in space. We will represent the plane that is defined by the three points (Earth, Miner, Observer) as the XY plane, and colour each point according to the orphan probability that the observer can assign to a martian-mined-block that has arrived at t=0 . In this scenario, we will set the miner, Mars, at 400,000,000 kilometers (22.2 light-minutes) away from Earth. This formula also allows us to determine the orphan probability of a given block at any time after receiving it as well, by altering the amount of time that information has had to propagate space. 16 Fig 8. Martian block orphan risk across different tolerances over time As shown in figure 8, the consensus juggernaut of Earth creates a wave of blockchain-truth that propagates space at the speed of light. Being not just in proximity to Earth, but in the wake of Earth’s shadow relative to Mars, allows an observer to be much more confident in a block that Mars provides. 17 With a majority of all Bitcoin transactions happening on the aforementioned second layers, and only the most important transactions happening on-chain, it can be reasonable to assume that users creating on-chain transactions will require the safest confirmations, taking the origin of the mined block into account. Transactions in which there is a 1/10000 orphan probability may be a risk that the entities involved may not be willing to take. Type II: A Stellar Bitcoin Energy and Infrastructure Scale A Type II civilization can be characterized by the ability to completely harness the energy output of their home star. This incredible amount of electricity production via large-scale megastructures like dyson-spheres gives rise to a new era of energy-hungry Proof-of-Work consensus mechanisms like Bitcoin [7] Humanity as a Type II civilization may have colonies around the solar system that rival in scale to that of Earth. Fledgling expeditions may also have set out into interstellar space to attempt to reach other star systems as well. We will revisit these now developed extraterrestrial colonies in this section to understand how mining and using Bitcoin has changed as humanity progressed from a Type I to Type II civilization. 18 Bitcoin Mining Ramifications I. Center of Hash Up until this section, we have been essentially calculating the hashrate efficiency of a solo-miner in a location based on the proximity of that miner to Earth. While this may have been apt for a Type I civilization that still has a vast majority of Bitcoin network compute power on Earth, a Type II civilization with developed extra-terrestrial colonies may not fit this model. Instead, the majority of compute may be located elsewhere and calculations must be based on the distance to this point. To understand what this spatial point is, and what affects it, we must understand how to derive it. Let us first consider the relationship between the Planets and the Sun. While it may be convenient to say these planets revolve around the Sun, the pedantic truth is that all planets revolve around the Solar System’s Center of Mass. Just as the Sun has a gravitational effect on Jupiter, Jupiter also has a ( albeit much smaller ) gravitation effect on the Sun. This dynamic point in space is a function of where all of the mass exists in relation to each other. Bitcoin mining for a Type II civilization works much like this system at a stellar scale. [8] Fig 9. Center of Mass vs Center of Hash 19