Part I: Foundations
1 Operational Transformation
2 Assignment
3 Mapped values
4 Amount of information in a value
5 Selective undo
Part II: The lattice of database states
6 Mathematical foundations
6.1 Partially ordered sets
6.2 Infimum and supremum
6.3 Hasse diagrams of finite posets
6.4 Lattices
7 The lattice of database states
Part III: OT control algorithms
8 Operational Transform Control Algorithms
9 Apache Wave
Part IV: OT on text
10 Operational Transformation On Text
Part V: The cxOT library
11 cxOT
Part VI: cxOT control algorithms
12 Base vector time
Part VII: Historical research archive
13 Third-party operational transformation ideas
14 Control-algorithm foundations
14.1 Operational Transform Convergence
14.2 Control Algorithm
14.3 Quadratic complexity
14.4 Merging operations
14.5 Vector Time
14.6 Context relations and transformation variants
15 Research from 2005
15.1 Log Compression Algorithm
15.2 Single character insertion and deletion operations
15.3 Single character move operations
15.4 Multi-character insertion and deletion operations
15.5 Assignment operations
15.6 Set operations
15.7 Bag Operations
15.8 Map Operations
16 Research from 2006
16.1 Single-character move operations, revised
16.2 Multi-character move operations
17 Research from 2007
17.1 Log compression of move operations
17.2 Single-character move, insert and delete operations
18 Research from 2008
18.1 Multi-character CDM operations
18.2 Explicit-Join Repository Graph
18.3 Check-in-Only Repository Graph
18.4 Repository — Assignable fields
18.5 Lossy assignment operations
19 Multi-character CDM operations
19.1 Effects Document
19.2 Operations
19.3 Coordinate systems
19.4 Character identity, moves and aliased extractions
19.5 Applying operations
19.6 Structural list operations
19.7 Elementary interval transformations
19.8 Dual inclusion transformation
19.9 Move tracking and transpose helpers
19.10 Transpose
19.11 Merge
19.12 Complexity
19.13 Relationship to a repository representation
19.14 Tests
19.15 Implementation correspondence
20 Composite-operation primitives
20.1 Notation
20.2 Operation factorisation
20.3 List representation of composite operations
20.4 Precedes relation on composite operations
20.5 Generalised symmetric merge
20.6 Notes on causality with regard to the primitive operators
20.7 Full database states
20.8 Vector times paired with database values
20.9 Piecewise merge of paired states
20.10 Scratch pad
20.11 State machine based on interval operations
20.12 Control algorithm using interval operations
21 Efficient HB Suffix
21.1 Operations for deltas on a numerical field
21.2 Composite operations on bags based on deltas
21.3 Composite operations for insertions into a string
21.4 Siteid inheritance
21.5 The largest LFactor we can take
21.6 3-partitions of q-contiguous operations
21.7 Effective siteids
21.8 Control algorithm using merge and factorisation
21.9 Control algorithm with transient HB-suffix
21.10 Assignment operations
21.11 Vector<T> operations
21.12 Bogus solution for assignment
21.13 References
22 Research from 2009
22.1 Composite set operations
22.2 Composite set operations 4
23 Research from 2010
24 Research from 2019
25 Research from 2021–2022
25.1 String operations
25.2 SUN triples
25.3 Merging coincident string insertions
25.4 Update effective siteids when apply local operations
25.5 Right to left merge of coincident insertions?
25.6 Siteid comparison fails on composite insertions
25.7 Temporal Index values on insertion intervals
25.8 Composite operations on a text field
25.9 Factorisation of composite insertions and deletions on a text field
25.10 Merge composite string operations
25.11 Take RFactor of insertions/deletions on text field
25.12 Monotone increasing extents on interval set
25.13 Abstractions over reflected vectors in a database
25.14 Idea to avoid the need to split intervals
25.15 Sending a delta on a vector field
25.16 Initial state
25.17 Sets
26 Research from 2023
26.1 Assignment operations
27 Links to pdfs
28 History of the ceda-core implementation

Part VII: Historical research archive

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