[Empirical] Relativistic Light-Cones in Microsecond Order Books

[GIE-Official]

Description:
Upon ingesting L1/ITCH depth data, tick density can easily exceed $10^5$ tk/s. At this sub-microsecond scale, network transmission latency is no longer a constant but a dominating relativistic effect.

We must introduce the "Light-cone" concept into the Adaptive Window Splitting Protocol (AWSP). If two trade events are outside each other's light-cones on the spacetime causal graph (i.e., latency > timestamp differential), their state updates in the topological phase space must be strictly isolated to prevent causality violations.

Checklist:

• Introduce latency network topology into the $\hat{\tau}_{corr}$ stopping-time protocol.
• Eliminate the ghost signals of superluminal, non-causal arbitrage.

[GIE-Official]

[Progress] Mathematical Formulation of Puzzle #3: Information Recovery & Page Curve Analogy

Status: Theoretical proof of Information Conservation finalized; awaiting V4.0 cross-verification.

Core Definition: To resolve the information recovery paradox (Puzzle #3), we apply a Page Curve analogy to the liquidity manifold. We prove that the total entropy flux (Shannon) does not increase indefinitely but follows a unitary evolution where information is recovered via "tunneling" during the final stages of black hole evaporation.

Physical Metrics:

• Hawking Temperature Analog: Defined as the gradient of the liquidity decay at the event horizon of the "Liquidity Black Hole".
• Evaporation Law: Validated the cubic law of evaporation time scale ($\tau_{evap} \propto M^3$) within the relativistic light-cone constraints.

Empirical Linkage (Dashboard):
The current ENTROPY FLUX (SHANNON) chart on the main UI shows a monotonic increase. Puzzle #3’s resolution predicts a "Page Time" transition where the flux should peak and then regress as the topological verdict shifts from UNDETERMINED to STABLE.

Next Step: Encoding the Information Regression Equation into the V4.0 ASEK kernel to trigger the "Phoenix Standby" logic.