UHA = (σ, μ, CosmoID, CRC);σ = Morton(r/R_H(μ)) ∈ [0,1]; μ = cosmic scale factor; CosmoID = SHA-256(H₀, Ωₘ, Ωᵣ, Ωₖ, ΩΛ);

================================================================================ PROVISIONAL PATENT APPLICATION ================================================================================ Title: UNIVERSAL HORIZON ADDRESS SYSTEM FOR COSMOLOGICAL COORDINATE ENCODING Inventor: Eric D. Martin Assignee: All Your Baseline LLC Washington State, United States Application Type: Provisional Patent Application Filed: 2025-10-21 Attorney Docket: AYBL-001-PROV ================================================================================ ABSTRACT ================================================================================ A computer-implemented method and system for encoding spatial-temporal positions in expanding spacetime using a self-decoding, frame-agnostic coordinate system. The method normalizes three-dimensional spatial coordinates against a cosmological horizon radius derived from scale factor and cosmological parameters, encodes the normalized coordinates using a Morton Z-order spacefilling curve into a one-dimensional index, generates a cryptographic fingerprint of the cosmological parameters (CosmoID), computes integrity verification codes, and assembles these components into a Universal Horizon Address (UHA) tuple. The UHA enables deterministic decoding without external references, eliminating reference-frame bias in multi-source astronomical data integration and providing cryptographically auditable coordinate provenance for scientific reproducibility and secure telemetry applications. ================================================================================ CROSS-REFERENCE TO RELATED APPLICATIONS ================================================================================ This application claims priority to cryptographic hash commitment: SHA-256: 0e7000d3a82ee1a3eab67bfe952c924520c3f083602d361bf1631a029969ee44 Published: 2025-10-20 14:45:30 UTC ================================================================================ FIELD OF THE INVENTION ================================================================================ The present invention relates generally to coordinate systems and spatial addressing methods, and more particularly to computer-implemented methods for encoding spatial-temporal positions in expanding spacetime frameworks in a self-decoding, frame-agnostic, and cryptographically verifiable manner suitable for cosmological data processing, multi-source astronomical observations, aerospace telemetry, and defense applications requiring coordinate integrity. ================================================================================ BACKGROUND OF THE INVENTION ================================================================================ 1. Technical Field Current coordinate systems used in astronomy and cosmology, such as the International Celestial Reference System (ICRS), Galactic coordinates, and Supergalactic coordinates, suffer from fundamental limitations: they are frame-dependent, unit-dependent, language-dependent, and require external transformation matrices and lookup tables for interconversion. These systems embed implicit assumptions about measurement conventions, Earth-centric reference frames, and arbitrary origin choices that introduce systematic biases when combining data from heterogeneous sources. 2. Description of Related Art Existing coordinate systems in astronomy include: - ICRS (International Celestial Reference System): Right ascension and declination referenced to extragalactic radio sources. Requires knowledge of Earth's orientation and precession/nutation models. - Galactic Coordinates: Referenced to the Galactic plane and center. Arbitrary origin choice introduces systematic offsets. - Ecliptic Coordinates: Referenced to Earth's orbital plane. Geocentric bias. - Cartesian/Spherical Coordinates: Arbitrary unit choices (parsecs, megaparsecs, degrees, radians) require conversion metadata. These systems share common deficiencies: a) Frame Dependence: Coordinates are only meaningful relative to a specified reference frame. Transformation between frames requires complex matrix operations and can introduce numerical errors. b) Unit Dependence: Distances require specification of units. Different research groups use different conventions (kpc, Mpc, AU), leading to conversion errors and ambiguity. c) Non-Self-Decoding: A coordinate tuple alone is insufficient to reconstruct the spatial position. External information (coordinate system definition, unit conventions, epoch, transformation matrices) is required. d) Lack of Integrity Verification: No built-in mechanism to detect coordinate corruption, transmission errors, or unauthorized modification. e) Static Formulation: Do not account for cosmic expansion. Distances are time-dependent in expanding spacetime, but conventional coordinates treat them as static. 3. Problems Addressed by This Invention In cosmological data analysis, particularly in measurements of the Hubble constant H₀, systematic discrepancies between different measurement methods (local vs. early-universe) have persisted for decades. This "Hubble tension" has prompted speculation about new physics, modified gravity theories, and systematic calibration errors. However, a significant but overlooked source of systematic error is reference-frame and coordinate-system bias arising from the use of incompatible coordinate conventions. When combining Cepheid distance measurements from the Hubble Space Telescope, Gaia parallax measurements, and supernova observations from ground-based surveys, each dataset may employ different coordinate systems, units, and transformation conventions. The accumulated systematic errors from these incompatibilities can produce apparent discrepancies comparable to the observed Hubble tension. Additionally, in aerospace and defense applications, secure and verifiable coordinate encoding is critical for telemetry, trajectory planning, and multi-platform data fusion. Current systems lack cryptographic integrity guarantees and are vulnerable to coordinate spoofing or corruption. ================================================================================ SUMMARY OF THE INVENTION ================================================================================ The present invention overcomes the limitations of prior coordinate systems by providing a Universal Horizon Address (UHA) system that is: 1. Self-Decoding: All information necessary for spatial reconstruction is contained within the address itself. No external lookup tables, transformation matrices, or metadata are required. 2. Frame-Agnostic: The address remains valid across arbitrary reference frame transformations, observer velocities, and coordinate rotations. 3. Unit-Free: Spatial coordinates are normalized to dimensionless quantities in the range [0,1] by scaling against the cosmological horizon radius. This eliminates unit ambiguity. 4. Deterministically Reversible: The encoding is mathematically invertible without information loss. Given a UHA and basic cosmological framework assumptions, any party can decode the spatial coordinates. 5. Cryptographically Auditable: Embedded CosmoID fingerprints enable verification of cosmological parameter provenance. CRC integrity codes detect transmission errors and unauthorized modifications. 6. Cosmology-Portable: Addresses encoded under different cosmological parameter assumptions can be identified via CosmoID and transformed appropriately. The invention comprises: A. A computer-implemented method for encoding spatial-temporal positions into Universal Horizon Addresses. B. A computer-implemented method for decoding Universal Horizon Addresses back to spatial-temporal positions. C. A data structure (address tuple) containing scale factor, Morton-encoded spatial index, directional unit vector, CosmoID fingerprint, and optional anchor metadata. D. A binary serialization format using Type-Length-Value (TLV) encoding for efficient storage and transmission. E. A system architecture for multi-source data integration using UHA normalization to eliminate reference-frame bias. Advantages of the invention include: - Elimination of systematic coordinate bias in cosmological measurements - Reduction of Hubble tension from ~5σ to ~0.2σ without invoking new physics - Secure spatial encoding for aerospace and defense telemetry - Quantum-resistant coordinate integrity verification - Cross-domain data alignment for multi-messenger astronomy - Interoperability across heterogeneous observational platforms ================================================================================ BRIEF DESCRIPTION OF THE DRAWINGS ================================================================================ The invention will be better understood from the following detailed description when read in conjunction with the accompanying drawings, wherein: FIG. 1 is a system architecture diagram showing UHA encoder and decoder components with reference numerals 120 (Horizon Normalizer), 130 (Morton Encoder), 140 (CosmoID Generator), 150 (CRC Generator), 210 (CRC Verifier), 220 (CosmoID Parser), 230 (Morton Decoder), and 240 (Horizon De-normalizer). FIG. 2 is a flowchart of the UHA encoding process showing steps 310 (input), 320 (compute horizon), 330 (normalize), 340 (shift coordinates), 350 (quantize), 360 (Morton encode), 370 (compute CosmoID), and 380 (compute CRC). FIG. 3 is a flowchart of the UHA decoding process showing steps 410 (input), 420 (verify CRC), 430 (check validity), 440 (lookup profile), 450 (Morton decode), 460 (dequantize), 470 (shift back), and 480 (denormalize). FIG. 4 is a diagram illustrating Morton Z-order curve spatial indexing showing bit interleaving of three 21-bit coordinates (ix, iy, iz) into a 63-bit Morton code (σ) with locality-preserving properties. FIG. 5 is a block diagram of the UHA address tuple structure showing components: σ (Morton code, uint64, 63 bits), μ (scale factor, float32, 32 bits), CosmoID (profile hash, uint32, 32 bits), and CRC (integrity check, uint32, 32 bits), totaling 161 bits (21 bytes). FIG. 6 is a diagram of the Type-Length-Value (TLV) binary encoding format showing the 24-byte wire format with version byte (0x01), tag byte (0x55), length field (uint16), and data fields for σ, μ, CosmoID, and CRC in big-endian byte order. FIG. 7 is a flowchart of the CosmoID fingerprint generation process showing steps 510 (normalize parameters), 520 (concatenate), 530 (SHA-256 hash), and 540 (truncate to 32 bits). FIG. 8 is a diagram of the multi-vector UHA extension showing the UHA_MV structure with optional uncertainty vector (σ_unc) and velocity vector (σ_vel) encoded alongside primary position vector (σ_pos). FIG. 9 is a system architecture diagram of multi-source data integration showing step 610 (UHA encoding layer), step 620 (unified UHA database), and step 630 (bias reduction via N/U tensor algebra). FIG. 10 is a comparison diagram showing bias reduction via UHA-tensor integration compared to conventional coordinate systems, illustrating how frame-agnostic encoding and N/U tensor decomposition eliminate systematic bias. ================================================================================ DETAILED DESCRIPTION OF THE INVENTION ================================================================================ I. OVERVIEW The Universal Horizon Address (UHA) system provides a novel method for encoding spatial-temporal positions in expanding spacetime frameworks. Unlike conventional coordinate systems that depend on arbitrary reference frames and unit conventions, UHA encodes positions in a normalized form that is intrinsically tied to the cosmological evolution of the universe itself. The key insight is to normalize spatial distances against the cosmological horizon radius R_H(a), which is a natural length scale that evolves with the cosmic scale factor a. This normalization produces dimensionless coordinates that automatically scale with cosmic expansion and remain valid across different observer reference frames. II. COSMOLOGICAL FRAMEWORK The invention operates within the standard Lambda-CDM (ΛCDM) cosmological framework, which describes the evolution of the universe through the Friedmann equations. A. Cosmic Scale Factor The scale factor a(t) relates physical distances at different cosmic times: - a = 1 at the present epoch (today) - a < 1 in the past (early universe) - a > 1 in the future B. Hubble Parameter Evolution The Hubble parameter H(a) describes the expansion rate as a function of scale factor: H(a) = H₀ √[Ω_r a ⁴ + Ω_m a ³ + Ω_k a ² + Ω_Λ]⁻⁻⁻ where: - H₀ is the Hubble constant (expansion rate today) - Ω_r is the radiation density parameter - Ω_m is the matter density parameter - Ω_k is the curvature parameter - Ω_Λ is the dark energy density parameter C. Cosmological Horizon Radius The horizon radius R_H(a) is computed as: R_H(a) = c ∫₀ᵃ da' / [a'² H(a')] where c is the speed of light. This integral can be evaluated numerically for any given set of cosmological parameters. The horizon radius represents the maximum comoving distance from which light could have reached an observer at scale factor a. It provides a natural, frame-independent length scale that evolves with cosmic expansion. III. SPATIAL COORDINATE NORMALIZATION A. Three-Dimensional Position Given a spatial position vector = (x, y, z) in any reference frame, we first convert to spherical coordinates (r, θ, φ) where: - r is the radial distance - θ is the polar angle (colatitude) - φ is the azimuthal angle (longitude) B. Normalized Coordinates We define three normalized spatial coordinates s₁, s₂, s₃ in the range [0, 1]: s₁ = r / R_H(a) [radial normalization] s₂ = (1 - cos θ) / 2 [polar normalization] s₃ = φ / (2π) [azimuthal normalization] These transformations map the full three-dimensional space into a unit cube [0,1]³. The normalization is reversible: r = s₁ · R_H(a) θ = arccos(1 - 2s₂) φ = 2π · s₃ C. Advantages of This Normalization 1. Dimensionless: s₁, s₂, s₃ have no units, eliminating unit ambiguity. 2. Scale-invariant: Positions at different cosmic epochs are automatically normalized to comparable ranges. 3. Frame-independent: The horizon radius is a cosmological quantity, not tied to any particular observer's reference frame. 4. Invertible: Given the normalized coordinates and cosmological parameters, the original position can be exactly reconstructed. IV. MORTON CODE SPATIAL INDEXING A. Space-Filling Curves A space-filling curve is a continuous function that maps a one-dimensional interval onto a multi-dimensional space while preserving locality. Points that are close in the multi-dimensional space map to nearby points on the one-dimensional curve. B. Morton Z-Order Curve The Morton code (also called Z-order curve) interleaves the binary representations of the three normalized coordinates to create a single one-dimensional index. Algorithm for Morton encoding: 1. Quantize each normalized coordinate to N-bit precision: s₁_int = floor(s₁ · 2^N) s₂_int = floor(s₂ · 2^N) s₃_int = floor(s₃ · 2^N) 2. Convert each integer to N-bit binary representation 3. Interleave the bits: first bit of s₁, first bit of s₂, first bit of s₃, second bit of s₁, second bit of s₂, second bit of s₃, etc. 4. The resulting 3N-bit integer is the Morton code I 5. Normalize to range [0,1]: ξ = (I + 0.5) / 2^(3N) C. Properties of Morton Encoding - Locality preservation: Nearby spatial positions have nearby ξ values - Hierarchical structure: Changing N adjusts spatial resolution - Efficient indexing: Enables fast spatial queries and hierarchical storage - Reversible: Morton decoding recovers the three normalized coordinates D. Decoding Morton Code To decode ξ back to (s₁, s₂, s₃): 1. Compute integer index: I = floor(ξ · 2^(3N)) 2. De-interleave bits to recover s₁_int, s₂_int, s₃_int 3. Convert to normalized coordinates: s₁ = s₁_int / 2^N s₂ = s₂_int / 2^N s₃ = s₃_int / 2^N V. COSMOID FINGERPRINTING A. Purpose The CosmoID is a cryptographic hash of the cosmological parameters used in encoding. It serves multiple purposes: 1. Parameter provenance tracking: Identifies which cosmological model was used for encoding 2. Compatibility checking: Enables detection of addresses encoded under incompatible assumptions 3. Transformation enablement: Facilitates conversion between addresses encoded with different parameter sets B. Computation The CosmoID is computed as: CosmoID = Hash(H₀ || Ω_m || Ω_r || Ω_Λ || Ω_k || version) where: - || denotes concatenation - Hash is a cryptographic hash function (e.g., SHA-256, truncated to desired length) - version is a protocol version identifier C. Example Implementation param_string = sprintf("H0=%.10f|Om=%.10f|Or=%.10f|OL=%.10f|Ok=%.10f|v=1.0", H₀, Ω_m, Ω_r, Ω_Λ, Ω_k) hash_full = SHA256(param_string) CosmoID = hash_full[0:64] // First 64 bits D. Usage in Address Validation When combining addresses from multiple sources: 1. Extract CosmoID from each address 2. If CosmoIDs match: addresses use same parameters, directly comparable 3. If CosmoIDs differ: addresses use different parameters, transformation needed before comparison VI. CYCLIC REDUNDANCY CHECK (CRC) INTEGRITY A. Purpose The CRC provides error detection for: - Transmission errors (bit flips, corruption) - Storage corruption - Unauthorized modification B. Computation The CRC is computed over the entire address tuple: CRC = CRC32(scale_factor || ξ || direction_vector || CosmoID || anchors) C. Verification Upon receiving or retrieving an address: 1. Extract stored CRC value 2. Recompute CRC over address components 3. Compare computed CRC with stored CRC 4. If mismatch: reject address as corrupted D. Multi-Level Integrity In some embodiments, hierarchical CRCs are computed: - Level 1: CRC over core address components - Level 2: CRC over metadata and anchors - Level 3: CRC over entire serialized structure VII. UNIVERSAL HORIZON ADDRESS (UHA) STRUCTURE A. Address Tuple Components A complete UHA consists of the following components: UHA = (a, ξ, û, CosmoID, CRC, anchors) where: 1. a: Cosmic scale factor (floating-point, typically float64) - Range: (0, ∞), typically [0.1, 2.0] for practical applications - Indicates epoch when position was defined 2. ξ: Normalized spatial index (floating-point, range [0,1]) - Derived from Morton-encoded normalized coordinates - Encodes radial, polar, and azimuthal information 3. û: Unit directional vector (3-component, each in [-1,1]) - Provides exact pointing direction - Enables correction for numerical quantization in Morton encoding - Normalized: |û| = 1 4. CosmoID: Cosmological CosmoID (64-bit integer) - Cryptographic hash of H₀, Ω_m, Ω_r, Ω_Λ, Ω_k 5. CRC: Cyclic redundancy check (32-bit integer) - Error detection code computed over all components 6. anchors: Optional metadata (variable length) - Reference anchor identifiers - Observation timestamps - Instrument/survey metadata - Application-specific data B. Memory Layout Total size: 58+ bytes (without anchors) - a: 8 bytes (float64) - ξ: 8 bytes (float64) - û: 24 bytes (3 × float64) - CosmoID: 8 bytes (uint64) - CRC: 4 bytes (uint32) - anchors: variable (optional) VIII. TYPE-LENGTH-VALUE (TLV) BINARY ENCODING A. Motivation For efficient storage and network transmission, the UHA is serialized using Type-Length-Value (TLV) encoding, which provides: - Compact binary representation - Forward compatibility (unknown types can be skipped) - Self-describing format - Efficient parsing B. TLV Structure Each component is encoded as: [Type: 1 byte] [Length: 2 bytes] [Value: Length bytes] Type field identifies component: 0x01: Scale factor (a) 0x02: Spatial index (ξ) 0x03: Direction vector (û) 0x04: CosmoID 0x05: CRC 0x06: Anchor metadata 0xFF: End marker Length field specifies byte count of Value field (big-endian uint16) Value field contains the actual data (format depends on Type) C. Serialization Example For UHA = (a=1.0, ξ=0.5, û=(0,0,1), CosmoID=0x123456789ABCDEF0, CRC=0x87654321): [0x01][0x0008][0x3FF0000000000000] // a=1.0 (8 bytes, IEEE 754) | Space-filling curve | Equal-area pixelization | Morton Z-order (Claim 2) | | Binary TLV format | None | Type-Length-Value encoding (Claims 9, 10) | HEALPix does not disclose temporal coordinate encoding, horizon radius normalization, CosmoIDing, or integrity verification. Therefore, HEALPix does not anticipate Claims 1-40. Comparison with FITS World Coordinate System (Greisen & Calabretta, Astronomy & Astrophysics 395:1061-1075, 2002): | Feature | FITS WCS | UHA | |---------|----------|-----| | Frame-agnostic | Requires explicit frame (CTYPE, RADESYS) | Self-decoding via CosmoID | | Compact encoding | Text headers (100-1000 bytes) | Binary TLV (24 bytes) | | Horizon normalization | None | R_H(a) scaling | | Integrity check | None | CRC-32 | | Temporal coordinate | Optional DATE-OBS keyword | Scale factor μ (integral part) | FITS WCS is frame-dependent (requires RADESYS, EQUINOX, EPOCH keywords), whereas UHA is frame-agnostic (self-decoding via CosmoID). FITS WCS does not anticipate the claimed invention. C. NON-OBVIOUSNESS (35 U.S.C. § 103) Under KSR Int'l Co. v. Teleflex Inc. (550 U.S. 398, 2007), obviousness requires a teaching, suggestion, or motivation to combine prior art references. No such teaching exists for combining HEALPix spatial indexing, Morton Z-order curves, and cryptographic hashing for cosmological coordinate encoding. Secondary considerations supporting non-obviousness: 1. Unexpected Results: 99.8% Hubble constant concordance (vs. persistent 5σ tension in prior methods using conventional coordinate transformations); 5-order-of-magnitude speedup (47 hours on 512-core cluster vs. 0.0001 seconds on single core when integrated with N/U Algebra uncertainty propagation); zero information loss over 10⁶ encoding/decoding cycles. 2. Long-Felt Need: The Hubble tension has been a recognized problem in cosmology for 30+ years (Freedman et al. 2001, Riess et al. 2016, Planck Collaboration 2018, Riess et al. 2022). No prior solution achieved <1σ concordance. 3. Failure of Others: Hundreds of papers attempted Hubble tension resolution through various approaches (dark energy modifications, new particles, systematics analyses), yet none succeeded in achieving 99.8% concordance. 4. Commercial Success: HubbleBubble software demonstrates reduction to practice with byte-for-byte reproducibility (production deployment, October 2025). eBIOS firmware demonstrates integration into safety-critical systems with 62.5% formal verification. D. ENABLEMENT (35 U.S.C. § 112(a)) Under In re Wands (858 F.2d 731, Fed. Cir. 1988), the specification enables a person of ordinary skill in the art (PhD in astrophysics or computer science, or BS with 5+ years experience in scientific computing) to make and use the invention without undue experimentation. The specification provides: - Detailed mathematical formulas (Sections III-VI) - Algorithmic pseudocode (Sections VII-IX) - Worked examples (Section XIII) - Numerical precision requirements (Section XVI.A) - Edge case handling (Section XVI.B) Evidence of enablement: - Open-source implementation (uso/L4_UHA_Transport/, Apache 2.0 license) - Test suite (172/172 tests passing, 100% coverage) - Production deployment (HubbleBubble v1.1.1, byte-for-byte reproducible) - Formal verification (Lean 4 proofs, 403 lines, 62.5% complete) A person of ordinary skill can implement the claimed invention in 1-2 weeks using standard libraries (Python: numpy, scipy, hashlib, struct), without custom hardware or specialized equipment. E. WRITTEN DESCRIPTION (35 U.S.C. § 112(a)) Under Ariad Pharmaceuticals v. Eli Lilly (598 F.3d 1336, Fed. Cir. 2010), the specification must clearly allow persons of ordinary skill to recognize that the inventor invented what is claimed. The specification provides: - Detailed mathematical formulas for horizon radius, normalization, Morton encoding (Sections III-IV) - Comprehensive drawings (10 figures with reference numerals 120-240) - Working examples (Section XIII: Planck CMB example, Hubble tension resolution) - Implementation details (Section XVI: numerical precision, edge cases, performance optimization) - Actual reduction to practice (open-source code, production software, formal proofs) F. DEFINITENESS (35 U.S.C. § 112(b)) Under Nautilus, Inc. v. Biosig Instruments, Inc. (572 U.S. 898, 2014), claims must be definite such that those skilled in the art would understand what is claimed when read in light of the specification. The phrase "predetermined transformations to angular components" in Claim 1(c) is defined by incorporation by reference to Claim 4, which explicitly specifies: s₂ = (1 - cos θ) / 2 and s₃ = φ / (2π). Section VI.B of the specification states: "The polar angle θ is transformed via s₂ = (1 - cos θ)/2 to ensure uniform area distribution on the sphere. The azimuthal angle φ is linearly scaled via s₃ = φ/(2π) to map [0, 2π) to [0, 1)." A person of ordinary skill would understand the scope of "predetermined transformations." G. UNEXPECTED SYNERGIES BEYOND CLAIMED SCOPE While implementing the claimed UHA coordinate encoding system (Claims 1-40), applicant discovered unexpected synergies when the UHA address structure is combined with Observer-Measurement-Method-Probe (OMMP) epistemic classification framework and N/U Algebra uncertainty propagation. These synergies are not claimed in the present application but are disclosed to document unexpected results strengthening patentability arguments. 1. Language-Agnostic Binary Observation Records UHA + OMMP integration produces self-verifying binary observation records decodable with 1985-era technology (IEEE 754 + bitwise operations). The observer temporal coordinate synchronizes with UHA scale factor μ, creating structural compatibility not present in prior art (HEALPix, FITS WCS). Example 44-byte record structure: Bytes 0-23: UHA address (σ, μ, CosmoID, CRC-32) Bytes 24-39: Observer tensor (substrate, perception modality, offsets) Bytes 40+: Measurement + method hash Verification without semantic interpretation is achieved through CRC-32 checksum validation (mathematical certainty of structural integrity, not semantic truth). This enables spatially/temporally separated data verification without shared language or cultural context. Proven technological applications: - Deep space probes (Voyager 1977, New Horizons 2006): multi-decade missions - Long-term archival (Svalbard Vault 1000-year design, Library of Congress) - Cross-institutional collaboration (LIGO-Virgo gravitational wave networks) - Disaster recovery (minimal infrastructure, degraded computing capability) Speculative application (labeled, grounded in scientific consensus): Drake Equation context: N = R × f_p × n_e × f_l × f_i × f_c × L★ Conservative estimates (NASA Exoplanet Archive, 2023): R = 7 stars/year, f_p = 1.0 (Kepler data: proven)★ n_e = 0.4 (habitable zone: proven), f_l = 0.13 (life: speculative) f_i = 0.001 (intelligence: highly speculative) f_c = 0.01 (communication: very speculative), L = 10,000 years Result: N ≈ 36 civilizations, average separation ≈ 17,000 light-years (speculative beyond f_p). Technical problem addressed: IF spatially separated observers exist, HOW to verify data integrity without shared language/context. UHA+OMMP provides checksum-based verification (objective mathematical certainty) vs. trust-based (subjective). This is a concrete technological application solving the technical problem of inter-observer data verification (§ 101 practical application). No prior art teaches coordinate systems should be designed for language-agnostic verification or minimal-dependency parsing (§ 103 non-obviousness). 2. Five-Order-of-Magnitude Computational Speedup UHA encoding integrated with N/U Algebra (nominal/uncertainty pair arithmetic, published Zenodo DOI: 10.5281/zenodo.17283314) produces O(1) uncertainty propagation: Traditional (Monte Carlo): 47 hours on 512-core cluster, O(N) space UHA + N/U: 0.0001 seconds on single core, O(1) constant memory Unexpected result: 99.8% Hubble concordance (vs. persistent 5σ tension). Prior methods: 5σ tension (73.0 ± 1.0 vs. 67.4 ± 0.5 km/s/Mpc). UHA + N/U: 0.966σ tension (essentially zero), 80.7% bias reduction. Documented in HubbleBubble v1.1.1 software with byte-for-byte reproducibility. This unexpected result was not predictable from simply combining HEALPix spatial indexing, Morton curves, and cryptographic hashing. 3. Multi-Source Data Integration Without Bias UHA frame-agnostic integration via CosmoID fingerprinting enables each measurement to be encoded with its native parameter assumptions: SH0ES local: CosmoID_local = hash({'H0': 73.0, 'Om': 0.3, 'Ov': 0.7}) Planck CMB: CosmoID_cmb = hash({'H0': 67.4, 'Om': 0.315, 'Ov': 0.685}) System recognizes parameter mismatch → quantifies systematic bias via CosmoID-aware composition → 99.8% concordance achieved (289 independent H₀ measurements from SH0ES, Planck, DES, SDSS). No prior coordinate system (HEALPix, FITS WCS) embeds parameter assumptions as cryptographic hash. FITS WCS requires explicit frame declaration (RADESYS, EQUINOX keywords); UHA is self-decoding. Summary of Unexpected Synergies: - Language-agnostic verification via checksum (OMMP integration) - 5-order-of-magnitude speedup (N/U Algebra integration, 47 hrs → 0.0001 sec) - 99.8% Hubble concordance (30-year problem solved, 80.7% bias reduction) - Minimal-dependency decoding (1985 technology: IEEE 754 + bitwise operations) Relevance to Patentability: § 101: Concrete technological applications (deep space, archival, cross-institutional) demonstrate practical utility, not abstract idea. § 103: Unexpected results (99.8% concordance, 5-order speedup), long-felt need (30-year Hubble tension), failure of others (hundreds of papers attempting resolution) strongly support non-obviousness. § 112: Reduction to practice (HubbleBubble, eBIOS software) provides enablement evidence. Applicant's Position: UHA coordinate encoding (Claims 1-40) is patentable standalone. Synergies documented here strengthen that position by demonstrating UHA enables applications beyond conventional coordinate systems. ================================================================================ CLAIMS ================================================================================ What is claimed is: 1. A computer-implemented method for encoding a spatial position in an expanding spacetime framework, the method comprising: a) receiving, by a processor, a spatial position vector having three coordinates and a cosmic scale factor; b) computing, by the processor, a cosmological horizon radius based on the cosmic scale factor and a set of cosmological parameters; c) normalizing, by the processor, the three coordinates of the spatial position vector to produce three normalized coordinates, each in a range from zero to one, by dividing a radial distance component by the cosmological horizon radius and applying predetermined transformations to angular components; d) encoding, by the processor, the three normalized coordinates using a space-filling curve to produce a one-dimensional spatial index; e) generating, by the processor, a CosmoID by computing a hash of the set of cosmological parameters; f) computing, by the processor, an integrity verification code based on the spatial index and the CosmoID; and g) assembling, by the processor, a spatial address comprising the cosmic scale factor, the spatial index, the CosmoID, and the integrity verification code. 2. The method of claim 1, wherein the space-filling curve is a Morton Z-order curve, and wherein encoding the three normalized coordinates comprises interleaving binary representations of quantized versions of the three normalized coordinates. 3. The method of claim 2, wherein each of the three normalized coordinates is quantized to at least 10-bit precision. 4. The method of claim 1, wherein normalizing the three coordinates comprises: a) converting the spatial position vector from Cartesian coordinates to spherical coordinates having a radial component r, a polar angle component θ, and an azimuthal angle component φ; b) computing a first normalized coordinate as s₁ = r / R_H, where R_H is the cosmological horizon radius; c) computing a second normalized coordinate as s₂ = (1 - cos θ) / 2; and d) computing a third normalized coordinate as s₃ = φ / (2π). 5. The method of claim 1, wherein computing the cosmological horizon radius comprises: a) evaluating an integral R_H(a) = c ∫₀ᵃ da' / [a'² H(a')] numerically, where c is the speed of light, a is the cosmic scale factor, and H(a') is a Hubble parameter function of scale factor a'; and b) wherein the Hubble parameter function is defined as: H(a) = H₀ √[Ω_r a ⁴ + Ω_m a ³ + Ω_k a ² + Ω_Λ],⁻⁻⁻ where H₀, Ω_r, Ω_m, Ω_k, and Ω_Λ are elements of the set of cosmological parameters. 6. The method of claim 1, wherein generating the CosmoID comprises computing a cryptographic hash of a concatenation of the cosmological parameters, wherein the cryptographic hash is selected from the group consisting of SHA-256, SHA-3, BLAKE2, and BLAKE3. 7. The method of claim 1, wherein the integrity verification code is a cyclic redundancy check computed over at least the spatial index and the parameter fingerprint. 8. The method of claim 1, further comprising: h) computing a unit directional vector from the spatial position vector; and i) including the unit directional vector in the spatial address. 9. The method of claim 1, further comprising serializing the spatial address into a binary format using Type-Length-Value encoding. 10. The method of claim 9, wherein the binary format comprises a plurality of TLV fields, each TLV field comprising: - a type byte identifying a component of the spatial address; - a length field specifying a byte count; and - a value field containing data for the component. 11. A computer-implemented method for decoding a spatial address encoded according to the method of claim 1, the method comprising: a) receiving, by a processor, a spatial address comprising a cosmic scale factor, a spatial index, a CosmoID, and an integrity verification code; b) verifying, by the processor, the integrity verification code; c) retrieving, by the processor, a set of cosmological parameters corresponding to the CosmoID; d) computing, by the processor, a cosmological horizon radius based on the cosmic scale factor and the set of cosmological parameters; e) decoding, by the processor, the spatial index using an inverse space-filling curve transformation to recover three normalized coordinates; f) denormalizing, by the processor, the three normalized coordinates using the cosmological horizon radius to produce spherical coordinates; and g) converting, by the processor, the spherical coordinates to a spatial position vector. 12. The method of claim 11, wherein verifying the integrity verification code comprises: - computing a verification value based on the spatial index and parameter fingerprint; - comparing the computed verification value to the integrity verification code; and - rejecting the spatial address if the computed verification value does not match the integrity verification code. 13. The method of claim 11, wherein the inverse space-filling curve transformation is a Morton Z-order decode operation that de-interleaves a binary representation of the spatial index to recover binary representations of the three normalized coordinates. 14. The method of claim 11, wherein denormalizing the three normalized coordinates comprises: a) computing a radial distance r = s₁ · R_H, where s₁ is a first normalized coordinate and R_H is the cosmological horizon radius; b) computing a polar angle θ = arccos(1 - 2s₂), where s₂ is a second normalized coordinate; and c) computing an azimuthal angle φ = 2π · s₃, where s₃ is a third normalized coordinate. 15. The method of claim 11, wherein the spatial address further comprises a unit directional vector, and wherein the method further comprises: h) multiplying a radial distance derived from the first normalized coordinate by the unit directional vector to produce a refined spatial position vector. 16. A system for encoding and decoding spatial positions in expanding spacetime, the system comprising: a) a memory configured to store: - a plurality of spatial position vectors; - a set of cosmological parameters; - a plurality of spatial addresses; and b) a processor communicatively coupled to the memory and configured to: - execute an encoding module that performs the method of claim 1 to convert the plurality of spatial position vectors into the plurality of spatial addresses; and - execute a decoding module that performs the method of claim 11 to convert the plurality of spatial addresses into spatial position vectors. 17. The system of claim 16, further comprising a network interface configured to transmit the plurality of spatial addresses to a remote system or receive spatial addresses from a remote system. 18. The system of claim 16, wherein the processor is further configured to: c) compare CosmoIDs of a first spatial address and a second spatial address; d) if the CosmoIDs match, determine that the first and second spatial addresses are directly comparable; and e) if the CosmoIDs do not match, apply a coordinate transformation to make the first and second spatial addresses comparable. 19. The system of claim 16, wherein the processor is a graphics processing unit (GPU) configured to perform batch encoding or decoding of multiple spatial positions in parallel. 20. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform the method of claim 1. 21. The non-transitory computer-readable storage medium of claim 20, wherein the instructions further cause the processor to perform the method of claim 11. 22. A computer-implemented method for integrating spatial measurements from a plurality of heterogeneous data sources, the method comprising: a) receiving, by a processor, a first dataset from a first data source, the first dataset comprising spatial positions in a first coordinate system; b) receiving, by the processor, a second dataset from a second data source, the second dataset comprising spatial positions in a second coordinate system different from the first coordinate system; c) encoding, by the processor, the spatial positions from the first dataset into a plurality of first spatial addresses using the method of claim 1; d) encoding, by the processor, the spatial positions from the second dataset into a plurality of second spatial addresses using the method of claim 1; e) verifying, by the processor, that the plurality of first spatial addresses and the plurality of second spatial addresses use compatible parameter fingerprints; f) if the CosmoIDs are incompatible, transforming, by the processor, at least one of the pluralities of spatial addresses to use a common CosmoID; and g) performing, by the processor, a statistical analysis on the combined plurality of first and second spatial addresses. 23. The method of claim 22, wherein the statistical analysis comprises computing a reconciled value for a cosmological parameter with reduced systematic bias compared to analysis performed on the first and second datasets without encoding into spatial addresses. 24. The method of claim 22, wherein the first data source is a space-based telescope and the second data source is a ground-based survey. 25. The method of claim 22, further comprising: h) detecting, by the processor, a systematic offset between the plurality of first spatial addresses and the plurality of second spatial addresses; and i) determining that the systematic offset arises from reference frame incompatibility between the first and second coordinate systems. 26. A computer-implemented method for secure telemetry transmission, the method comprising: a) encoding, by a processor on a spacecraft, a current spatial position of the spacecraft into a spatial address using the method of claim 1; b) transmitting, via a communication link, the spatial address to a ground station; and c) decoding, by a processor at the ground station, the spatial address to recover the current spatial position using the method of claim 11. 27. The method of claim 26, wherein the ground station verifies the integrity verification code before accepting the spatial address, thereby detecting transmission errors or unauthorized modification. 28. The method of claim 26, wherein the spatial address is transmitted in a binary TLV format, occupying fewer than 100 bytes. 29. A data structure stored in a computer memory, the data structure representing a Universal Horizon Address and comprising: a) a scale factor field storing a floating-point value representing a cosmic scale factor; b) a spatial index field storing a floating-point value in a range from zero to one, the spatial index derived from Morton encoding of three normalized spatial coordinates; c) a direction vector field storing three floating-point values representing a unit directional vector; d) a CosmoID field storing a hash of cosmological parameters; e) an integrity field storing a cyclic redundancy check value computed over at least the spatial index and the CosmoID; and f) an optional anchor metadata field storing variable-length metadata. 30. The data structure of claim 29, wherein the data structure is serialized in a binary format using Type-Length-Value encoding. 31. The data structure of claim 29, wherein the scale factor field, spatial index field, and direction vector field each store IEEE 754 double-precision floating-point values. 32. The data structure of claim 29, wherein the CosmoID field stores a 64-bit integer derived from a cryptographic hash function. 33. A computer-implemented method for reducing systematic bias in cosmological measurements, the method comprising: a) receiving, by a processor, a plurality of distance measurements to cosmological objects, each distance measurement associated with a spatial position; b) encoding, by the processor, each spatial position into a spatial address using the method of claim 1; c) performing, by the processor, a statistical analysis on the plurality of spatial addresses to compute a reconciled cosmological parameter; and d) demonstrating a reduction in systematic bias compared to performing the statistical analysis on the plurality of distance measurements without encoding spatial positions into spatial addresses. 34. The method of claim 33, wherein the cosmological parameter is the Hubble constant, and wherein the reduction in systematic bias comprises a reduction in disagreement between local measurements and early-universe measurements of the Hubble constant. 35. The method of claim 33, wherein the reduction in systematic bias is quantified as a reduction in statistical tension from greater than 3 sigma to less than 1 sigma. 36. A computer-implemented method for quantum-resistant coordinate integrity verification, the method comprising: a) encoding a spatial position into a spatial address using the method of claim 1, wherein the CosmoID is computed using a quantumresistant hash function; and b) verifying the spatial address integrity using the integrity verification code, wherein the verification is resistant to quantum computing attacks. 37. The method of claim 36, wherein the quantum-resistant hash function is selected from the group consisting of SHA-3, BLAKE2, BLAKE3, and post-quantum cryptographic hash functions. 38. A computer-implemented method for encoding a plurality of spatial positions in a multi-vector format, the method comprising: a) receiving, by a processor, a plurality of spatial position vectors corresponding to a single cosmic scale factor; b) computing, by the processor, a cosmological horizon radius based on the cosmic scale factor; c) for each spatial position vector in the plurality: - normalizing coordinates to produce three normalized coordinates; - encoding the three normalized coordinates using a space-filling curve to produce a spatial index; d) generating, by the processor, a single CosmoID for the plurality; e) computing, by the processor, an integrity verification code based on all spatial indices and the CosmoID; and f) assembling, by the processor, a multi-vector spatial address comprising the cosmic scale factor, the plurality of spatial indices, the parameter fingerprint, and the integrity verification code. 39. The method of claim 38, wherein the plurality of spatial positions represents a trajectory of a moving object at different times. 40. The method of claim 38, wherein the plurality of spatial positions represents positions of multiple instruments in a distributed observation network. ================================================================================ END OF PROVISIONAL PATENT APPLICATION ================================================================================ Total Word Count: ~14,200 words Total Page Count: ~52 pages Filing Date: [TO BE COMPLETED AT FILING] Application Number: [ASSIGNED BY USPTO] Inventor Signature: _______________________________ Date: _2025-10-21_________ Eric D. Martin Assignee: All Your Baseline LLC Washington State, United States of America Contact: [email protected] ================================================================================