Mathematical analysis of Cloudian HyperStore’s durability claims, from the defensible 14 nines to the physically impossible 26 nines - and why vendors publish numbers that dwarf the universe’s existence.

Cloudian HyperStore markets data durability ranging from “14 nines to 18 nines, or even 26 nines or higher” [1]. This appears in whitepapers, datasheets, and partner materials as a key competitive differentiator. The lower end of this range - 14 nines - represents legitimate engineering with standard erasure coding. The upper end - 26 nines - represents something else entirely: a number so astronomically large it loses all connection to physical reality.

Let’s examine what these numbers actually mean, why some are defensible while others are absurd, and what happens when storage vendors publish durability claims that exceed the age of the universe.

What Durability Numbers Mean

Data durability measures the probability that stored data remains intact over a given period, typically one year. The notation “N nines” means 99.999…% (with N nines after the decimal point). Each additional nine represents a 10× improvement in durability, or equivalently, a 10× reduction in expected data loss probability.

The calculation typically follows this pattern:

Annual Data Loss Probability = 1 - Durability
Mean Time To Data Loss (MTTDL) ≈ 1 / Annual Data Loss Probability

For 11 nines (99.999999999%), the annual data loss probability is 10^-11, giving an MTTDL of approximately 100 billion years. For comparison, the universe is 13.8 billion years old.

Storage vendors calculate durability using Markov models that incorporate: component failure rates (typically from manufacturer specifications), erasure coding parameters (N data shards, M parity shards, tolerance for M failures), rebuild time windows (how long it takes to reconstruct lost data), and correlated failure probabilities (likelihood of multiple simultaneous failures).

The mathematics is well-established. Azure publishes their methodology [2]. Google explains their 11 nines calculation [3]. Backblaze discusses the practical meaning and limitations of these numbers [4]. The formulas work. The question is whether the resulting numbers retain meaning at extreme scales.

Cloudian’s Erasure Coding Architecture

Cloudian HyperStore uses standard Reed-Solomon erasure coding, configurable from 4+2 (tolerates 2 failures, 50% overhead) to higher configurations like 7+5 (tolerates 5 failures, 71% overhead) [1][5]. This is solid, well-understood technology. Reed-Solomon codes have been in production use for decades, from CDs to distributed storage systems. The mathematics is published and verifiable.

At 7+5 configuration, Cloudian claims 14 nines durability. This number is defensible. With 7 data fragments and 5 parity fragments across 12 nodes, the system tolerates any 5 simultaneous node failures. Using standard component failure rates (say, 1% annual disk failure rate), reasonable rebuild times (hours to days depending on data volume), and accounting for correlated failures during rebuild windows, 14 nines emerges from the calculations.

This matches industry norms. AWS S3 claims 11 nines with their internal erasure coding scheme [6]. Azure achieves 12-16 nines depending on replication configuration [2]. Google Cloud Storage specifies 11 nines [3]. These vendors use similar erasure coding approaches with similar mathematics. The resulting durability numbers cluster in the 11-16 nines range for a reason: that’s what the math produces with realistic component failure rates and rebuild times.

Cloudian’s 14 nines claim for high-redundancy configurations fits this pattern. It represents legitimate engineering trade-offs - more parity overhead buys better durability. Organizations can verify the calculation independently using published failure rates and standard MTTDL formulas.

Where “26 Nines” Comes From

Cloudian’s marketing materials state managers can “set durability at whatever level of protection is needed — 14 nines, 18 nines or even 26 nines or higher” [1]. This suggests that by increasing erasure coding redundancy, customers can achieve arbitrarily high durability numbers.

Mathematically, this is trivial. Each additional parity shard increases failure tolerance, which reduces annual data loss probability, which increases the durability percentage. Keep adding parity and the number of nines grows. The formula doesn’t care whether the result makes physical sense.

Let’s calculate what 26 nines actually means:

Durability: 99.99999999999999999999999999%
Annual Data Loss Probability: 10^-26
MTTDL: 1 / (10^-26) = 10^26 years

Ten septillion years. Written out: 100,000,000,000,000,000,000,000,000 years.

The universe is 13.8 billion years old, or 1.38 × 10^10 years. Cloudian’s 26 nines claim represents an MTTDL that is one quadrillion times the current age of the universe. Current cosmological models predict the universe will experience heat death in approximately 10^100 years [7]. Cloudian’s 26 nines doesn’t even approach that timescale - it’s still in the rounding error.

To put this in perspective: if you stored data on Cloudian’s 26 nines system at the moment of the Big Bang, the expected time until data loss would be 7.25 × 10^15 universe lifetimes. The atoms in your storage drives would have decayed via proton decay (estimated at 10^36 years) long before the mathematics predicts data loss.

Why This Number Exists in Marketing Materials

Storage vendors compete on specifications. When competitors claim 11 nines, you claim 14 nines. When customers ask “how high can it go?”, marketing teams want an answer. The mathematics allows any number of nines by adding more parity. The marketing materials reflect this mathematical flexibility without acknowledging where it diverges from physical reality.

Cloudian isn’t unique in publishing absurd durability numbers. Azure markets 16 nines for geo-zone-redundant storage [2]. Dell ECS claims 11 nines [8]. Pure Storage, NetApp, and others publish similarly extreme figures. The industry convention treats durability numbers as a competitive benchmark rather than an operational metric.

The problem is that these extreme numbers carry implied precision that cannot exist. The MTTDL calculations assume: constant component failure rates over billions of years, no technological obsolescence (the same drives running from the Big Bang to heat death), no human operational errors, no software bugs, no firmware issues, no natural disasters, no wars or societal collapse, no cosmic events (supernovae, gamma ray bursts, etc.), and perfect execution of rebuild procedures across geological timescales.

None of these assumptions hold even for decades, let alone 10^26 years. As one storage professional noted in The Register’s forum discussion: “Around the 8th nine we start moving from practical to purely academic” [9]. At 26 nines, we’ve left “academic” and entered “physically meaningless.”

What Durability Numbers Should Measure

Backblaze’s analysis provides useful perspective [4]. Durability calculations model data loss from routine hardware failures during normal operation. They assume perfect software, correct operational procedures, no natural disasters, and no human errors. In practice, data loss occurs from: operator mistakes (accidental deletion, wrong commands), software bugs (corruption, incorrect erasure coding implementations), correlated failures (entire rack losing power, cooling failures), network partitions and split-brain scenarios, bit rot and silent corruption, and natural disasters affecting multiple data centers.

The “Mean Time to Meaningless” paper by Greenan and Plank examines how Markov models for MTTDL break down at extreme durability values [10]. They note that the models assume exponential failure distributions and independence between failures - assumptions that don’t hold in practice, especially during rebuild windows when system load is high and failure probabilities become correlated.

Google’s transparency about their 11 nines calculation is instructive [3]. They explain the erasure coding scheme, show the math, and acknowledge limitations. They don’t claim 26 nines because even Google, with virtually unlimited engineering resources, recognizes where the mathematics diverges from operational reality.

Useful durability numbers should: reflect achievable redundancy with realistic overhead (not theoretical maximums requiring 50× or 100× parity), account for operational failure modes (not just component failures), acknowledge where precision exceeds verification capability, and provide context for what the number actually protects against.

Cloudian’s 14 nines claim meets these criteria. It reflects a specific 7+5 erasure coding configuration with verifiable mathematics and realistic operational assumptions. The 26 nines claim fails all four tests.

The Industry Pattern

Storage vendors face a dilemma. Customers compare specifications in RFPs. When every vendor claims 11 nines, differentiation requires higher numbers. Marketing teams know that “up to 26 nines or higher” sounds more impressive than “14 nines with realistic configurations.” The mathematics allows these claims even when physics renders them meaningless.

This creates a race to absurdity. If Cloudian markets 26 nines, competitors face pressure to match or exceed it. Pure Storage could claim 30 nines with enough theoretical parity. Dell could extrapolate to 40 nines. Eventually the entire industry is publishing MTTDLs measured in units of “observable universe lifetimes” while the actual durability people experience comes from operational practices, not erasure coding redundancy.

AWS limits their public claims to 11 nines [6]. Google specifies 11 nines [3]. These companies have more engineering resources than most storage vendors. They could calculate higher numbers with more parity. They choose not to because credibility matters more than specification sheet wins.

The issue isn’t Cloudian-specific. It’s an industry problem. But Cloudian’s “26 nines or higher” represents an extreme example of what happens when marketing teams get access to durability calculators without understanding where the mathematics breaks down.

What Customers Actually Need

Organizations evaluating storage systems need different information: what erasure coding configurations are available and what overhead do they impose, what operational failure modes exist beyond component failures, how does the system behave during degraded operation and rebuilds, what verification mechanisms detect silent corruption, how quickly can data be recovered after failures, what happens during correlated failure scenarios (rack-level, site-level), and what operational procedures prevent human error.

A system claiming 26 nines durability with 50× parity overhead doesn’t help if operators can accidentally delete entire buckets. A system with 14 nines durability and solid operational safeguards, clear failure modes, and transparent recovery procedures provides better protection in practice.

Cloudian’s HyperStore architecture includes legitimate features worth evaluating: flexible erasure coding configurations, standard Reed-Solomon implementation, bucket-level protection policies, and S3-compatible API. These features matter more than whether the theoretical maximum durability calculation produces 14, 18, or 26 nines.

The question for evaluating any storage vendor shouldn’t be “what’s your maximum durability number?” It should be: “What erasure coding configuration do you recommend for my use case, what overhead does that impose, and what operational failure modes do I need to plan for?”

The Math We Should Show

Here’s what useful durability analysis looks like:

Configuration: 7+5 erasure coding across 12 nodes

Component Failure Rate: 1% annual per disk (manufacturer specification)

Rebuild Time: 24 hours for 10TB of data at 1 GB/s

Calculation: Using standard MTTDL formulas with these inputs yields approximately 10^14 years (14 nines). This assumes perfect rebuild execution, no correlated failures, and no operational errors.

Limitations: Real-world durability depends on operational practices. The calculation models hardware failures during normal operation, not the full failure space.

Comparison: Similar to AWS S3 (11 nines), Google Cloud Storage (11 nines), and Azure GRS (12 nines) using comparable erasure coding approaches.

This provides actionable information. Customers can verify the math, understand the assumptions, and make informed trade-offs between redundancy overhead and durability improvements. They can also recognize where the calculation stops being useful - well before 26 nines.

Where Cloudian Gets It Right

Cloudian’s configurable erasure coding genuinely provides flexibility. Different workloads warrant different redundancy levels. Archival data might justify 7+5 for 14 nines durability. Active data might use 4+2 for 11 nines with lower overhead. Having bucket-level configuration granularity is operationally useful.

The 14 nines claim for high-redundancy configurations is defensible. It matches what the mathematics produces with realistic assumptions. Organizations can independently verify the calculation and make informed decisions about whether the additional parity overhead justifies the durability improvement for their use case.

Cloudian’s S3 compatibility and standard Reed-Solomon implementation provide transparency that proprietary approaches like VAST’s LDEC don’t offer. Operators can reason about failure modes using established erasure coding knowledge rather than vendor-specific algorithms.

These legitimate technical strengths get overshadowed when marketing materials include durability claims that exceed the universe’s lifespan. It raises questions: if they’ll publish 26 nines without acknowledging its meaninglessness, what other marketing claims should we scrutinize?

What Needs to Change

The storage industry should adopt norms around durability claims:

Specify realistic configurations: State the actual erasure coding scheme and overhead, not theoretical maximums requiring impractical redundancy.

Show the math: Publish the calculation methodology, component failure rates, and assumptions. Let customers verify independently.

Acknowledge limitations: Explain what the durability calculation models (hardware failures) and what it doesn’t (operational errors, software bugs, disasters).

Cap meaningless precision: Numbers beyond 15-16 nines exceed practical verification. Acknowledge where mathematics diverges from physics.

Focus on operations: Emphasize operational safeguards, failure mode transparency, and recovery procedures - the factors that actually prevent data loss.

Some vendors already follow these practices. AWS publishes durability information with clear assumptions [6]. Google explains their 11 nines calculation and what it means [3]. These vendors recognize that credibility matters more than having the highest number on a specification sheet.

The Core Issue

Cloudian HyperStore is legitimate storage technology using standard erasure coding. The configurable redundancy provides genuine flexibility. The 14 nines durability claim for 7+5 configurations reflects defensible engineering mathematics.

But “26 nines or higher” has no connection to operational reality. It’s a number that emerges from a formula when you add enough parity terms, displayed in marketing materials without acknowledging that the result exceeds the universe’s lifespan by one quadrillion times.

Storage technology is complex enough without vendors publishing MTTDLs measured in cosmic timescales. Customers making purchasing decisions need honest information about achievable redundancy, realistic failure modes, and operational practices - not durability claims that assume perfect operation across periods exceeding proton decay.

When marketing teams gain access to durability calculators, someone needs to ask: does this number help customers make informed decisions, or does it just look impressive on a datasheet? At 26 nines, the answer is obvious.

Because when your MTTDL calculation requires assuming your storage system will outlast the heat death of the universe, you’ve crossed from engineering into absurdity.

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References

[1] Cloudian, “Modern Enterprise Data Protection with Cloudian,” https://cloudian.com/resource/whitepapers/modern-enterprise-data-protection-cloudian/

[2] Huang, C., et al. (2012). “Erasure Coding in Windows Azure Storage,” USENIX ATC. https://www.usenix.org/system/files/conference/atc12/atc12-final181_0.pdf

[3] Google Cloud, “Understanding Cloud Storage 11 9s durability target,” https://cloud.google.com/blog/products/storage-data-transfer/understanding-cloud-storage-11-9s-durability-target

[4] Backblaze, “Cloud Storage Durability: What Do All Those 9s Mean?” https://www.backblaze.com/blog/cloud-storage-durability/

[5] Cloudian, “How Cloudian HyperStore Delivers Scalability and Data Security,” https://www.cloudstackcollab.org/how-cloudian-hyperstore-delivers-scalability-and-data-security/

[6] AWS, “Amazon S3 Durability,” https://aws.amazon.com/s3/faqs/

[7] Krauss, L. M., & Starkman, G. D. (2000). “Life, the universe, and nothing: Life and death in an ever-expanding universe.” The Astrophysical Journal, 531(1), 22.

[8] Dell Technologies, “Dell ECS Technical FAQ,” https://infohub.delltechnologies.com/en-us/l/dell-ecs-technical-faq/general-faq-3/

[9] The Register Forums, “Mmm, yes. 11-nines data durability? Mmmm, that sounds good. Except it’s virtually meaningless,” https://forums.theregister.com/forum/all/2018/07/19/data_durability_statements/

[10] Greenan, K., & Plank, J. S. (2010). “Mean time to meaningless: MTTDL, Markov models, and storage system reliability.” HotStorage. https://www.usenix.org/legacy/event/hotstorage10/tech/full_papers/Greenan.pdf

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StorageMath applies the same mathematical scrutiny to every vendor. Cloudian’s legitimate engineering deserves recognition. Their “26 nines or higher” marketing deserves correction. Customers need honest durability analysis, not cosmic MTTDLs.