Appendix A: Glossary of Terms

Core Concepts

12,288 Coordinate System : Global hash ring / sharded keyspace with fixed 12,288 buckets. A consistent-hashing style ring with known ring size (48×256 matrix). Coordinates determined by addr = SHA3-256(content) mod 12,288, then page = addr ÷ 256, byte = addr mod 256.

96 Equivalence Classes : Semantic buckets (C₉₆) used for checksums, sharding, and parallelism. All 256 byte values map to exactly 96 classes via modular arithmetic. Functions as a checksum family over 96 categories for database integrity invariants.

Atlas : The mathematical framework that reveals information’s intrinsic structure, including the 96 classes, 12,288 coordinates, and conservation laws.

Conservation Laws : Four system engineering guarantees:

• R (Resonance): Database integrity invariant - checksum family over 96 categories
• C (Cycle): Orchestration scheduler - 768-step round-robin with service window slots
• Φ (Phi/Holographic): Encode/decode correctness - proof-of-correct serialization
• ℛ (Reynolds): Network flow conservation - backpressure semantics

Content-Determined Addressing : Function addr = mod_12288(SHA3-256(encode(content))). Pure function computing address from content without external catalog. Encode = canonicalize + hash + modular projection; decode = recompute and verify address from content (no reverse mapping).

Hologram : The computing platform that implements alignment with information’s intrinsic structure, built on the discoveries of Atlas.

Technical Terms

Action Minimization : The computational paradigm where solutions emerge as minimum-energy configurations of carefully designed energy landscapes, borrowed from physics.

BHIC (Block Header Information Certificate) : Proof-carrying receipts that demonstrate conservation law compliance and operation validity.

Budget (β) : A measure of computational resource consumption that must decrease or remain constant through valid operations. Truth corresponds to β=0.

CAR (Content Addressable Archive) : Package format for distributing UOR-BC modules via IPFS.

CIM (Component & Interface Model) : Layer 1 of the Hologram stack, defining components, ports, contracts, and proofs.

Proof / Receipt : Append-only witness that a transformation preserved conservation: (commitment hash, class-sum deltas mod 96, budget meter, time). Verifiable in O(window + |receipt|). Proof-carrying transaction that demonstrates all conservation laws maintained.

Gauge Invariance : Property where different representations of the same information are recognized as equivalent, similar to gauge symmetry in physics.

Generator Architecture (GA) : Execution stack that realizes computation through sector-based action minimization, emitting proof-carrying receipts.

Holographic Property : The principle that boundary information completely determines bulk properties and vice versa, enabling perfect reconstruction.

Klein Probe : Boolean homomorphism test across four-element windows, part of the resonance verification system.

Natural Organization : The inherent structure of information that emerges from mathematical properties rather than being imposed by system design.

Poly-Ontological Object : Mathematical entities that possess simultaneous, irreducible existence across multiple mathematical categories.

Proof-Carrying State : System where every piece of data carries mathematical proof of its validity and transformations.

Resonance Alphabet (R96) : The 96 fundamental “information colors” that all data naturally falls into, determined by resonance evaluation.

Reynolds Number (ℛ) : In Hologram context, a measure of information mixing and flow patterns, analogous to fluid dynamics.

Round-Trip Property : The guarantee that projecting to boundary and reconstructing bulk returns identical information at β=0.

SMM (Standard Model of Models) : Layer 0 of the Hologram stack, providing minimal vocabulary for models, interfaces, morphisms, and proofs.

Structural Entropy : The inherent organization present in information before any external structure is imposed.

SyncReceipt : Lightweight proof exchanged between nodes to maintain consistency without full state transfer.

Takum Numbers : Arithmetic encodings that collapse geometric invariants into multiplicative scalars, making generation under law a number-theoretic object.

Bytecode (UOR-BC) : Conservation-checked op sequence over C₉₆ with explicit budgets; transport-safe; runtime-verifiable. 96-class aware module format whose opcodes are stable over the C₉₆ semiring. Transport-safe sequence with budget annotations.

UORID (Universal Object Reference Identifier) : Content-determined identifier derived from mathematical properties, ensuring global uniqueness without coordination.

Conceptual Terms

Alignment vs. Imposition : The fundamental paradigm shift from imposing structure on information (traditional) to aligning with information’s inherent structure (Hologram).

Computational Physics : The treatment of computation as a physical process governed by conservation laws and energy minimization.

Coordinate-Free : Properties or operations that remain valid regardless of representation or reference frame choice.

Deterministic Performance : Predictable, mathematically-bounded performance characteristics that emerge from structural alignment.

Emergent Consistency : Consistency that arises naturally from conservation laws rather than being enforced by protocols.

Information Physics : The study of information as a physical phenomenon with measurable properties and conservation laws.

Intrinsic Security : Security properties that emerge from mathematical structure rather than being added through cryptographic layers.

Natural Load Distribution : Automatic, optimal distribution of computational load based on information’s inherent structure.

Proof-Carrying Generation : Computation that generates validity proofs as a natural byproduct rather than requiring separate verification.

Schema Compilation : The process of transforming high-level schemas into physics-aligned computational structures.

Structural Synchronization : Synchronization achieved through structural alignment rather than message passing.

Zero-Knowledge Consistency : The ability to verify consistency without accessing full state, using only conservation receipts.

Storage : 12,288-shard K/V layout keyed by addr. Replicas subscribe via receipts; dedupe at the class layer. Place record at shard addr, or publish proof that projection equals addr.

Transport : CTP-96 frames carrying (content, addr, class, receipt). Routers forward by addr math (no routing tables). Endpoints MUST reject on checksum/budget failure; version-negotiated profiles.

Database : Index-free store; query=route; transactions = proof-carrying transforms that preserve R96. Partitioned key-value space with exactly 12,288 shards where shard ID = addr. Isolation = class-local windows.

Orchestration : C-cycle scheduling with budgets; no brokers; fairness by construction. Fixed-length round-robin cycle (length 768) guaranteeing fairness and bounded latency through service window slots.

Edge : Node hosting a subset of coordinates; stateless beyond receipts. Any node that hosts some subset of the 12,288 coordinate space.

Service Provider : Operator of a coordinate slice + proof verification endpoint. Exposes subset of 12,288 space plus proof verification APIs. SLAs expressed in conservation and verification latencies.

Embedding : Mapping from a state (or dataset) to a 96-dimensional class histogram or moment vector. Used for indexing, search, and equivalence testing.

Encode/Decode : Φ-consistent boundary serialization ↔ bulk reconstruction with acceptance test. Encode = canonicalize + hash + modular projection; decode = recompute and verify (no reverse mapping).

Checksum / Hash : R96 checksum (class sums) vs. SHA3-256 digest (addressing). R96 provides semantic deduplication (3/8 compression); SHA3-256 provides uniform distribution for addressing.

Mathematical Notation

T : The boundary torus (ℤ/48ℤ) × (ℤ/256ℤ) with 12,288 points

Ψ : Boundary trace or field configuration

S[ψ] : Action functional to be minimized

Φ : Holographic mapping operator between boundary and bulk

β : Budget parameter, with β=0 indicating truth/validity

R(s) : Resonance evaluation function mapping selectors to classes

C₇₆₈ : The 768-element conservation cycle

ℛ : Reynolds operator for information flow

⊗ : Poly-ontological composition operator

CNF : Canonical Normal Form under gauge and schedule equivalence