What is ASKA and how does it improve security?

ASKA (Adaptive Security Kernel Architecture) is a hardware-enforced security system that replaces traditional OS trust models. Instead of trusting a single kernel, ASKA creates a distributed mesh where every component monitors others, making it impossible for attackers to compromise the system by exploiting a single vulnerability. It's suitable for everything from IoT devices to enterprise servers.

How does ChronoLedger solve blockchain's timestamp problem?

ChronoLedger integrates hardware-secured timekeeping directly into blockchain consensus. Using specialized Temporal Mining Nodes with atomic clocks and secure processors, it creates tamper-proof timestamps that cannot be manipulated. This enables applications requiring precise, verifiable time like high-frequency trading, legal documents, and regulatory compliance.

Are ASKA and ChronoLedger open source?

Yes, both projects have open-source components available on GitHub. While core innovations are patent-pending, we believe in community collaboration and provide reference implementations, documentation, and development tools. Visit github.com/nshkrdotcom for repositories.

What hardware is required for ASKA?

ASKA can run on various hardware platforms. For development, an FPGA development board is sufficient. Production deployments will use custom ASICs or secure processors. The architecture is designed to be lightweight enough for IoT devices while scalable for enterprise systems.

Can ChronoLedger work with existing blockchains?

Yes, ChronoLedger includes a temporal bridge protocol that allows existing blockchains to benefit from hardware-secured timestamps. This enables cross-chain time synchronization and allows legacy systems to gain temporal security without complete migration.

Temporal Blockchain: Mathematical Model

This document compiles all key mathematical equations and formulas used throughout the Temporal Blockchain System, providing a single, consistent reference for all mathematical aspects. Formal definitions of variables and parameters are included.

1. Temporal Distributed Trust Architecture

Equation:

$$T(C, t) = \sum_{i=1}^{n} w_i(t) \cdot v_i(C, t) \cdot r_i(t)$$

Definitions:

$T(C, t)$: Trust value of claim $C$ at time $t$.
$n$: Total number of Temporal Mining Nodes (TMNs).
$w_i(t)$: Weight of TMN $i$ at time $t$.
$v_i(C, t)$: Validation score from TMN $i$ for claim $C$ at time $t$ (normalized to a 0-1 range).
$r_i(t)$: Temporal reputation coefficient of TMN $i$ at time $t$ (normalized to a 0-1 range).

Diversity Constraint: $$D = -\sum_{i=1}^{n} p_i \log p_i > D_{min}$$

Definitions

$D$: Diversity value.
$p_i$: Proportional influence/weight of node “type” (groups of common methods/hardware).
$D_{min}$: A configured minimum threshold.

2. Temporal Asymmetric Resistance

Equation:

$$R(a, t) = k \cdot \left(\frac{P(a, t)}{P_{baseline}(t)}\right)^\alpha \cdot TF(a, t)$$

Definitions:

$R(a, t)$: Systemic resistance encountered by actor $a$ at time $t$.
$k$: Scaling constant.
$P(a, t)$: Power level of actor $a$ at time $t$.
$P_{baseline}(t)$: Baseline power level at time $t$.
$\alpha$: Resistance exponent ($\alpha > 1$).
$TF(a, t)$: Temporal factor based on $a$’s historical temporal accuracy.

3. Temporal Attribution Chains

Attribution Chain Structure:

$$A(I) = {(s_1, r_1, t_1, h_1), (s_2, r_2, t_2, h_2), …, (s_n, r_n, t_n, h_n)}$$

Definitions:

$A(I)$: Attribution chain for information $I$.
$s_i$: Source entity at step $i$.
$r_i$: Relationship/transformation at step $i$.
$t_i$: Hardware-verified timestamp from TMNs at step $i$.
$h_i$: Hardware attestation cryptographic proof at step $i$.

Integrity Verification:

$$V(A(I)) = \prod_{i=1}^{n} v(s_i, r_i, t_i, h_i, s_{i+1})$$

Definitions:

$V(A(I))$: Result (boolean) of the validation across the entire chain.
$v(s_i, r_i, t_i, h_i, s_{i+1})$: Verification function for each link in the chain.

4. Proof of Temporal Authority (PoTA) Consensus

4.1 Vote Weighting

Equation:

$$W(a) = \alpha \cdot R(a, t) + (1 - \alpha) \cdot S(a, t)$$

Definitions:

$W(a)$: Voting weight of agent $a$.
$R(a, t)$: Temporal reputation of agent $a$ at time $t$ (normalized to a 0-1 range).
$S(a, t)$: Stake of agent $a$ at time $t$ (normalized to a 0-1 range).
$\alpha$: Parameter controlling the relative importance of reputation vs. stake (0 ≤ α ≤ 1).

4.2 Reputation Update Rule

Equation:

$$R(a, t+1) = R(a, t) + \beta \cdot (Accuracy(a, t) - R(a, t)) - \gamma \cdot Penalty(a, t)$$

Definitions:

$R(a, t+1)$: Updated reputation of agent $a$ at time $t+1$.
$R(a, t)$: Reputation of agent $a$ at time $t$.
$\beta$: Learning rate for reputation updates (0 < β < 1).
$Accuracy(a, t)$: Accuracy of agent $a$’s timestamps in the block at time $t$ (normalized to a 0-1 range).
$\gamma$: Penalty coefficient (γ ≥ 0).
$Penalty(a, t)$: Penalty applied to agent $a$ at time $t$ (normalized to a 0-1 range).

4.3 Accuracy Calculation

Equation:

$$Accuracy(a, t) = 1 - \frac{|T_{node}(a, t) - T_{consensus}(t)|}{ToleranceWindow(t)}$$

Definitions:

$T_{node}(a, t)$: Timestamp provided by node $a$ in the block at time $t$.
$T_{consensus}(t)$: Final consensus timestamp for the block at time $t$.
$ToleranceWindow(t)$: Acceptable tolerance window at time $t$.
Result is normalized (0-1) scale.

4.4 Byzantine Fault Tolerance Condition

Equation:

$$W_{faulty} < \frac{1}{3} W_{total}$$

Definitions:

$W_{faulty}$: Total voting power of faulty validators.
$W_{total}$: Total voting power of all validators.

Or, if using a reputation based model for voting/governance, a rule can exist: where the total influence from actors proven, later as bad/malicious: cannot ever exceed 1/3 of total.

4.5 System-Wide Temporal Accuracy

Equation:

$$Accuracy_{system}(t) = 1 - \frac{|T_{consensus}(t) - T_{true}(t)|}{MaximumDeviation}$$

Definitions:

$T_{consensus}(t)$: Consensus timestamp for block at time $t$.
$T_{true}(t)$: “True” time at time $t$ (as determined by the TMNs’ atomic clocks).
$MaximumDeviation$: System-wide parameter defining the maximum acceptable deviation.

5. Drift Compensation (Kalman Filter - Simplified)

While the full Kalman filter involves multiple equations, a simplified representation for the drift correction is:

Equation:

$$T_{corrected}(t) = T_{measured}(t) - DriftEstimate(t)$$

Definitions:

$T_{corrected}(t)$: Corrected time at time $t$.
$T_{measured}(t)$: Measured time from the atomic clock at time $t$.
$DriftEstimate(t)$: Estimated clock drift at time $t$, calculated by the Kalman filter.

6. Offline Timestamp Verification

Verification involves checking against pre-shared initialization vectors. No single equation fully captures this; it is a multi-step process.

7. Time-Manipulation Resistance

Equation: $$R_{time}(a) = C \cdot (1 - e^{-k \cdot N_{diverse}}) \cdot \log(S_{temporal})$$

Definitions:

$R_{time}(a)$: System’s resistance against an actor a attempting to change time values.
$C$: System constant.
$N_{diverse}$: Number of diverse TMNs in the network.
$S_{temporal}$: Temporal stake required to participate in consensus.

8. Long-Term Time Security

Equation: $$S_{long}(t) = S_0 \cdot e^{-\lambda t} \cdot \sqrt{N_{TMN}(t)}$$

Definitions:

$S_{long}(t)$: Long term security levels at a time t.
$S_0$: Initial security parameter.
$\lambda$: Decay constant related to cryptographic security.
$N_{TMN}(t)$: Projected number of active TMNs at time $t$.

9. Offline Security Guarantee

Equation: $$S_{offline}(t, \Delta t) = S_{base} \cdot (1 - \frac{\Delta t}{t_{max}})^2 \cdot e^{-\alpha \cdot \Delta t}$$

Definitions:

$S_{offline}(t, \Delta t)$: Security guarantees during an offline period, that begins at t, lasting \Delta t units of time.
$\Delta t$: Duration of offline operation.
$t_{max}$: Maximum secure offline period.
$\alpha$: Drift coefficient of the atomic clocks.
$S_{base}$: Security when the system is online.

This document serves as a comprehensive reference for the core mathematical underpinnings of the Temporal Blockchain system.