The Abrams Event Address: Mathematical Formalization of 4D Spacetime Indexing

1. The Problem of Disjointed Coordinate Systems

Human coordinate frameworks have historically been fractured along functional lines. Postal systems rely on geopolitical boundaries that mutate across decades. Geodetic systems such as GPS (WGS 84) provide spatial positioning along latitude and longitude, yet frequently discard the vertical axis or treat elevation as an uncalibrated secondary measurement.

Crucially, time is universally relegated to an external metadata tag. In mission-critical contexts—such as autonomous vehicle telemetry, chain-of-custody evidence logging, or atmospheric sensor data—treating time as detached metadata invites collision, desynchronization, and tampering.

2. Theoretical Architecture of the AEA Quadkey

The Abrams Event Address establishes a four-dimensional manifold $(X, Y, Z, T)$ governed by the invariant spacetime line element $ds^2 = g_{\mu\nu} dx^\mu dx^\nu = -c^2 d\tau^2$. Spatial dimensions $(X, Y)$ are mapped using a modified space-filling Hilbert curve, guaranteeing that points geographically proximate in physical space share contiguous prefix strings in the address token.

Altitude ($Z$) is quantized relative to mean sea level (EGM2008 geoid) in logarithmic metric brackets, preventing address explosion while preserving centimeter-level resolution near the planetary boundary layer.

To resolve events across high-velocity orbital platforms and varying gravitational potentials without centralized clock synchronization, proper time $\Delta \tau$ is integrated along the worldline: $\Delta \tau = \int \sqrt{-(1/c^2) g_{00} - (2/c^2) g_{0i} v^i - (1/c^2) g_{ij} v^i v^j} \, dt$.

Time ($T$) is normalized to a 48-bit microsecond counter since the Unix epoch, paired with a 16-bit CRC checksum that ensures invalid or corrupted coordinate strings can be immediately detected without accessing a remote network ledger.

3. Applications in Decentralized Evidence & Robotics

By treating every real-world occurrence as an immutable point in spacetime, decentralized protocols can verify physical co-presence without exposing private identity markers. An AEA token proves an interaction occurred at a specific point in spacetime with mathematical finality.

4. Embedded C-ABI Architecture & Interface Boundaries

To satisfy the deterministic requirements of autonomous flight software and robotic avionics, the AEA reference core is implemented in pure bare-metal Rust compiled with #![no_std]. The engine operates strictly within statically bounded stack memory with zero dynamic heap allocations, eliminating the hazard of runtime allocator failures during critical operations.

The library compiles into a self-contained static archive (libaea.a) exposing standardized C calling conventions via include/aea.h. The byte-aligned struct definitions are designed to support integration with flight-software environments including the NASA Core Flight System (cFS) software bus and ROS 2 odometry topics, providing a deterministic state sealer when communications are severed.

5. Reference Implementation, Serialization Invariants & Falsifiability

The published wire format, designated AEA-STATE/1, occupies exactly 136 bytes: a 104-byte canonical telemetry prefix followed by a 32-byte SHA-256 integrity seal. The prefix explicitly tags the reference chart (ITRF2020 for Earth-fixed crust, GCRS for geocentric inertial space, BCRS for solar system barycentric coordinates) and the time scale (continuous TAI atomic seconds, eliminating leap-second discontinuities).

To ensure bit-for-bit reproducibility across disparate architectures, serialization enforces strict canonicalization rules: all integers and double-precision IEEE-754 floats are encoded in Little-Endian byte order, and negative zero (-0.0) is normalized to positive zero (+0.0) prior to digest computation.

Falsifiability is guaranteed through published Known-Answer Test (KAT) vectors. The canonical calibration benchmark—encoding Stephen Hawking’s 2009 Cambridge reception at 52.205878° N, 0.117867° E on 2009-06-28 12:00 UTC—produces the deterministic SHA-256 seal 9f6cc1096562729a902167fd622e66a264a239f3e9a9d804414659e3ab97800e. Perturbing any spatial coordinate by one millimeter or altering a single bit in the 104-byte prefix causes immediate verification failure.

The scope of the public standard is intentionally bounded: it functions as an immutable state sealer and coordinate tagger, not an active relativistic numerical integrator or gravity solver. Downstream trajectory filters ingest AEA records to execute relativistic transformations without lost or ambiguous frame conventions.