Edition README
Universal Generative Deformation Calculus
README.md
1 # Universal Generative Deformation Calculus
2
3 **Author:** Komorebi P.
4 **Version:** 1.1.0
5
6 This release implements the following construction:
7
8 ```text
9 object
10 -> every admissible direction at that object
11 -> every admissible direction at every child
12 -> infinite raw path forest
13 -> quotient by exact path and object relations
14 -> completion of convergent infinite routes
15 -> certified mathematical families
16 ```
17
18 The central point is state dependence. A child is not assigned a copy of the root's direction list. The system calls `directions(child, depth)` again, so each generated object exposes its own abstract direction fiber.
19
20 ## Mathematical layers
21
22 The package keeps three layers separate.
23
24 1. **Raw paths** store every finite construction route, including different routes with the same endpoint.
25 2. **Quotient nodes** use an exact canonical key to identify equivalent endpoints while preserving edge and path multiplicity.
26 3. **Completed branches** add limits only under a declared metric, topology, inverse limit, direct limit, or other completion rule.
27
28 Unary directions produce a rooted path forest. Multi-input operations such as multiplication, tensoring, gluing, or nonlinear interaction produce an operadic hyperforest.
29
30 ## Main deliverables
31
32 - `paper/Universal_Generative_Deformation_Calculus.pdf`
33 - `paper/Universal_Generative_Deformation_Calculus.tex`
34 - `generative_deformation/` reference Python package
35 - `tests/` independent test suite
36 - `results/results.json`
37 - `results/checks.csv`
38 - `examples/generated/` machine-readable explored forests
39 - `paper/figures/` Python-generated PDF and PNG figures
40 - `paper/tables/` reproducible tables
41 - `dist/komorebi_generative_deformation-1.1.0-py3-none-any.whl`
42
43
44 ## Visual atlas edition
45
46 Version 1.1.0 replaces the original sparse figure set with a coherent visual atlas. It includes:
47
48 - the seed-to-forest-to-quotient-to-completion architecture
49 - state-dependent direction fibers in four domains
50 - raw-tree versus quotient-graph comparison
51 - certified continuous direction covers
52 - infinite-branch completion and stability regimes
53 - multi-input operadic hyperforests
54 - growth and path-partition phase diagrams
55 - family-certificate and exploration-frontier workflows
56 - polynomial, analytic, sequence, Gaussian, qubit, matrix, shape, graph, and congruence-lift atlases
57 - a cross-domain comparison of raw-route and quotient-object growth
58
59 All figures are generated by Python in vector PDF and matching PNG formats.
60
61 ## Installation
62
63 From PowerShell in the extracted release directory:
64
65 ```powershell
66 python -m pip install -e .
67 ```
68
69 Or install the included wheel:
70
71 ```powershell
72 python -m pip install .\dist\komorebi_generative_deformation-1.1.0-py3-none-any.whl
73 ```
74
75 ## Complete verification
76
77 ```powershell
78 .\Run_All.ps1
79 ```
80
81 This installs the package in editable mode, runs all experiments, executes the test suite, and recompiles the paper.
82
83 The recorded release has:
84
85 - 50 of 50 independent tests passed
86 - 18 of 18 experiment checks passed
87 - 59-page compiled paper
88 - 20 Python-generated figure pairs in PDF and PNG
89 - 11 worked finite realizations spanning algebra, analysis, probability, geometry, graphs, quantum states, sequences, and congruence lifting
90 - no LaTeX overfull or underfull boxes
91 - no undefined references
92 - clean PDF preflight
93
94 ## Explore a built-in deformation system
95
96 Integer walk:
97
98 ```powershell
99 python -m generative_deformation explore --example walk --depth 12 --max-paths 9000 --out .\walk_output
100 ```
101
102 Analytic grammar from `cosh(x)`:
103
104 ```powershell
105 python -m generative_deformation explore --example analytic --depth 3 --max-paths 1800 --out .\analytic_output
106 ```
107
108 Polynomial grammar from `x**2 + 1`:
109
110 ```powershell
111 python -m generative_deformation explore --example polynomial --depth 4 --max-paths 4000 --out .\polynomial_output
112 ```
113
114 Additional exact reference systems:
115
116 ```powershell
117 python -m generative_deformation explore --example sequence --depth 3 --max-paths 800 --out .\sequence_output
118 python -m generative_deformation explore --example gaussian --depth 4 --max-paths 5000 --out .\gaussian_output
119 python -m generative_deformation explore --example qubit --depth 5 --max-paths 1800 --out .\qubit_output
120 python -m generative_deformation explore --example matrix --depth 3 --max-paths 800 --out .\matrix_output
121 python -m generative_deformation explore --example shape --depth 3 --max-paths 600 --out .\shape_output
122 python -m generative_deformation explore --example graph --depth 3 --max-paths 700 --out .\graph_output
123 python -m generative_deformation explore --example adic-simple --depth 4 --max-paths 100 --out .\adic_simple_output
124 python -m generative_deformation explore --example adic-singular --depth 5 --max-paths 300 --out .\adic_singular_output
125 ```
126
127 Each output directory contains `forest.json`, `nodes.csv`, and `edges.csv`.
128
129 ## Define a new domain
130
131 Subclass `DeformationSystem` and implement:
132
133 ```python
134 from generative_deformation import DeformationSystem, Direction
135
136 class MySystem(DeformationSystem):
137 name = "my-system"
138
139 def directions(self, state, depth):
140 return [Direction("first_move"), Direction("second_move")]
141
142 def apply(self, state, direction):
143 ...
144
145 def canonical_key(self, state):
146 ...
147 ```
148
149 Optional methods provide validation, invariants, serialization, and a metric.
150
151 ```python
152 from generative_deformation import ExplorationConfig, PerturbationForest
153
154 forest = PerturbationForest(MySystem(), [seed]).explore(
155 ExplorationConfig(max_depth=6, max_paths=100000)
156 )
157 forest.export("my_output")
158 ```
159
160 ## Continuous directions
161
162 An uncountable direction fiber is not enumerated point by point. It is represented as a parameter family and explored through certified finite covers. `IntervalDirectionFamily` supplies exact dyadic nets. `propagated_cover_error` computes the pathwise endpoint bound
163
164 ```text
165 e[k+1] <= L[k] e[k] + M[k] epsilon[k].
166 ```
167
168 The paper proves the closed product-sum bound.
169
170 ## Multi-input interactions
171
172 `InteractionRule` and `generate_interactions` implement finite prefixes of the operadic extension. The built-in scalar realization includes addition, multiplication, and averaging.
173
174 ## Family certificates
175
176 `FamilyCertificate` records:
177
178 - member nodes
179 - parameters
180 - closure directions
181 - invariant fields
182 - exact relations
183 - verification failures
184
185 The certificate proves internal closure relative to the declared grammar. It does not prove historical novelty.
186
187 ## Scope boundary
188
189 “Every direction” means every direction in the declared admissible fiber. The framework does not pretend to enumerate every conceivable target-dependent map. A grammar that hides the target inside a custom operation is rejected by the anti-encoding condition.
190
191 Finite exploration is a prefix of an infinite object. Completeness requires a theorem about finite branching, fair enumeration, continuous coverage, convergence, or compactness. A large finite run is not a substitute for such a theorem.