Index

A

Action functional 122-125, 208-212, 315-320, 412-418

• density 125, 210
• landscape 418-420
• minimization 123, 209, 316-319
• sectors 124, 210-211

Active window 89-92, 156-159, 289-292

• management 291-292
• size optimization 290, 421
• verification 289-290

Address map (H) 62-65, 94-97

• collision-free property 64, 96-97
• computation 63, 95
• perfect hashing 62-65, 94-97

Algorithmic reification 105-110

• program as proof 106-107
• witness chains 107-109

B

Budget 45-48, 78-81

• arithmetic 47, 80
• conservation 81, 294-295
• crush function 48, 81
• ledger 47-48, 80-81
• semiring (C₉₆) 46, 79

Byzantine fault tolerance 326-328

• detection 327
• receipt-based 326-327
• threshold 328, 422

C

C768 (Cycle structure) 42-44, 76-78

• fairness invariants 43-44, 77-78
• schedule rotation 42-43, 76
• verification 296

CAM (Content-Addressable Memory) 58-65, 94-99

• deduplication 338-339
• perfect hash 62-65, 94-97
• storage implementation 408-409

Category theory 198-202, 421

• functors 200-201
• lawful configurations 199
• morphisms 199-200
• monoidal structure 201

Compilation 122-127, 208-215, 348-362

• as action minimization 123, 209, 349
• as stationarity 125-126, 212-213
• gauge alignment 356-357
• universal optimizer 348-350

Configuration 25-28, 55-58

• gauge equivalence 57-58
• lawful 58, 88
• space Σ^𝕋 26, 56

Consensus 325-328

• Byzantine fault tolerance 326-328
• pipelined 328
• receipt-based 325-326

Content addressing 58-65, 94-99, 322-324

• deduplication 324, 338-339
• routing 323-324
• universal address space 322-323

Convergence 373-376

• certificates 373-374
• Lyapunov functions 374-375
• PAC bounds 375-376

Crush function (⟨·⟩) 48, 81

D

Database systems 336-347

• index-free architecture 336-337
• MVCC 343-344
• perfect hash tables 338
• query optimization 344-345

Denotational semantics 100-104

• budget calculus 102-103
• equational theory 103-104
• process objects 101-102

Distributed systems 322-335

• consensus 325-328
• content-addressed storage 322-324
• network protocols 329-331
• state machine replication 333
• transactions 332

E

Equational theory 103-104, 136-137

Expressivity 196-197, 420

• characterizing functions 196
• embedding λ-calculus 197

F

Fairness 43-44, 77-78, 296

G

Gauge 36-38, 69-71

• alignment (linking) 356-357
• classification problem 420
• fixing 60-61, 95-96
• invariance 37, 70
• transformations 37, 70

Gradient-free optimization 370-372

• evolutionary strategies 372
• quantum-inspired 371
• receipt-guided 370-371

H

Hardware acceleration 423

I

Implementation 402-417

• core structures 402-407
• example usage 416-417
• minimal kernel 311-314

Incremental verification 300

Information objects 24-25, 54-55

• intrinsic semantics 25, 55
• poly-ontological 85-87, 134-136

J

JIT compilation 361-362

• action-guided 361
• adaptive recompilation 362

L

Lattice (𝕋) 30-34, 66-69

• 12,288 structure 31, 67
• coordinates 32, 68
• memory layout 291
• neighborhoods 33, 68
• toroidal topology 31, 67

Lawfulness 28-29, 58-59, 82-89

• as type system 82-87
• domain 58-59
• verification 88-89

Learning see Machine learning

Linear-time verification 288-290

• active window 289-290
• streaming 289

Lift operator (lift_Φ) 44-45, 78-79

M

Machine learning 366-382

• action flow 380-381
• convergence 373-376
• gradient-free 370-372
• neural networks 377-379
• single loss function 366-369
• task encoding 367-368

Memory management 290-292

• lattice layout 291
• window management 291-292

Morphisms 100-102, 272-273

• class-local 101, 272
• composition 102, 273
• identity 101, 272
• primitive types 272

MVCC (Multi-Version Concurrency) 343-344

N

Neural networks 377-379

• attention mechanisms 379
• lattice networks 377-378

Normal form (NF) 60-61, 95-96

• canonicalization 61, 96
• uniqueness 61, 96

Normalization 198, 421

O

Observational equivalence 104, 137

Optimization 122-127, 208-215, 358-360

• dead code elimination 359
• loop optimization 360
• passes 358-359
• universal framework 358

P

PAC learning 375-376, 422

Parallel execution 283, 298-299

• lock-free operations 283
• verification 298-299
• work distribution 298

Perfect hash see Address map

Phase transitions 381-382, 423

Φ operator 44-45, 78-79

• coherence verification 297
• lift 44, 78
• projection 45, 79
• round-trip 45, 79

Poly-ontological 85-87, 134-136

• coherence 421
• objects 85-86, 134-135
• type system 86-87, 135-136

Process objects 100-102, 409-411

• composition 102
• denotation 101
• grammar 100

Projection operator (proj_Φ) 45, 79

Proof generation 299-300

• succinct proofs 299
• zero-knowledge 300, 422

Q

Quantum 371, 423

• implementation 423
• optimization 371

Query 337, 344-345

• as proof 337
• optimization 344-345

R

R96 (Resonance classes) 40-42, 74-76

• checksum 41-42, 75-76
• digest computation 295
• verification 295-296

Receipt 45-48, 78-81, 275-277, 406-408

• authentication 330-331
• building 275-277
• chain validation 293-294
• components 46, 79, 275
• compression 277, 294
• consensus 325-326
• verification 295-297

Research problems 420-424

• categorization 420-423
• collaboration opportunities 424
• timeline 424

Resonance see R96

Runtime architecture 272-287

• concurrency control 283
• error handling 284
• morphism engine 272-274
• performance 283-284
• type checking 274-275

S

Schedule rotation (σ) 42-43, 76

• C768 structure 42, 76
• fairness 43, 77

Security 142-145, 240-243

• collision resistance 144, 242
• integrity 143, 241
• memory safety 143, 241
• type safety 142, 240

State machine replication 333

Storage engines 346-347

• column-oriented 347
• LSM trees 346

T

Transactions 332, 342-343

• ACID properties 342-343
• distributed 332
• receipt-coordinated 332

Type checking 274-275, 411-412

• budgeted 83-84, 132-133
• pipeline 274-275
• three-phase 274

Type system 82-89, 130-139

• budgeted judgments 83, 132
• constructors 84-85, 133-134
• poly-ontological 85-87, 134-136
• subtyping 85, 134

U

Universal optimizer 348-350

V

Verification 288-303

• budget conservation 294-295
• caching 301
• incremental 300
• linear-time 288-290
• parallel 298-299
• receipt 295-297
• witness chains 293-294

W

Window see Active window

Windowed resource classes 108-109

• CC (Conservation-Checkable) 108
• HC (High-commutative) 109
• RC (Resonance-commutative) 108
• WC (Window-constrained) 109

Witness 107-109, 293-294, 413-414

• chain validation 293-294
• compression 294
• structure 293

Z

Zero-knowledge 300, 422

• proofs 300
• receipts 422

ℤ/96 see Budget semiring

12,288 30-34, 66-69

• lattice structure 31, 67
• optimality 423
• = 48 × 256 factorization 31, 67

Page numbers refer to chapter sections. Bold entries indicate primary definitions or main discussions of topics.