MANUSCRIPT_STATUS.md
Hypergraph Lumpability and Bayesian Refinement
MANUSCRIPT_STATUS.md
1 # Manuscript status
2
3 ## Identity
4
5 | Field | Value |
6 |---|---|
7 | Title | **Hypergraph Lumpability and Bayesian Refinement for Dynamical Systems with Projector Resolutions** |
8 | Subtitle | **Exact Interaction Quotients, Filtering Cocycles, and Certified Coarse Models** |
9 | Author | **Komorebi P.** |
10 | Release | **0.1.4** |
11 | Manuscript length | **52 pages** |
12
13 ## Freeze state
14
15 ```text
16 internal_complete: true
17 submission_ready: false
18 external_proof_review: pending
19 literature_priority_review: pending
20 major_new_section_required: false
21 ready_to_begin_paper_2: true
22 ```
23
24 The manuscript is complete at the internal project level. It contains the declared definitions, theorem chain, proofs, examples, algorithms, numerical certificates, limitations, open problems, appendices, dependency ledger, references, and reproducibility materials. Work on the next paper can begin without adding another major section here.
25
26 Before journal submission, the manuscript still needs an independent proof review and a systematic comparison with work on nonlinear lumping, polynomial differential equivalence, probabilistic bisimulation, Bayesian sufficiency, and related quotient theories.
27
28 ## Final editorial pass
29
30 Version 0.1.4 preserves the completed theorem and proofreading state and adds the final publication figure system.
31
32 The certificate generator now produces nine publication visual assets as vector PDF and 600 dpi PNG files. The manuscript places them in seven figure environments. Two paired layouts present the quotient criterion and the hyperedge compression results without expanding the page count unnecessarily.
33
34 1. The prose was read from beginning to end and revised for clarity, rhythm, and precision.
35 2. Ordinary prose now contains no semicolon punctuation.
36 3. Ordinary prose avoids dash punctuation and word hyphens.
37 4. Necessary mathematical signs, internal identifiers, commands, proper names, and bibliographic ranges remain intact.
38 5. The analytic descent proof now handles the constant coefficient explicitly.
39 6. The proof of existence of a best coarse interaction no longer suggests uniqueness under an arbitrary norm.
40 7. The polynomial descent proof now identifies the coefficient comparison as a polynomial with values in the coarse space.
41 8. The rooted tree notation now defines its leaf count.
42 9. Every theorem, proposition, lemma, and corollary has an explicit proof.
43 10. The normalization bound, positive likelihood regime, implementation, tests, and generated certificate ledgers agree with one another.
44 11. The exact evidence theorem now states the required initial aggregation and defines sequence evidence before it is used.
45 12. The hidden Markov specialization now writes every composition symbol explicitly.
46 13. The numerical algorithm now distinguishes exact algebraic acceptance from tolerance based approximation.
47 14. The combined quotient and pruning defect is defined before its bounds are applied.
48 15. The likelihood oscillation criterion is stated only in the nontrivial coarse setting where necessity holds.
49 16. The evidence error proof now states the probability vector assumption that supplies the unit norm bound.
50 17. The quotient diagram and its coefficient labels now match the theorem exactly.
51
52 ## Mathematical state
53
54 The central finite chain is
55
56 \[
57 CA_m^f=A_m^cC^{\times m}
58 \Rightarrow
59 CF_f=F_cC
60 \Rightarrow
61 C\Phi_t^f=\Phi_t^cC.
62 \]
63
64 It combines with
65
66 \[
67 CL_y^f=s_yL_y^cC
68 \Rightarrow
69 C\mathsf B_y^f=\mathsf B_y^cC
70 \Rightarrow
71 C\Psi_{1:N}^f=\Psi_{1:N}^cC.
72 \]
73
74 The paper also proves finite bounds for interaction defects, errors in quotient flows, likelihood variation within fibers, posterior error, evidence error, and hyperedge pruning.
75
76 ## Implemented verification
77
78 The deterministic certificate generator records **35 passing checks and 0 failures**. The checks cover the following areas.
79
80 1. Exact tensor quotients of orders one, two, and three
81 2. Annihilation of hidden inputs
82 3. Recovery in packet coordinates
83 4. A deliberate negative control that is not lumpable
84 5. Symmetry inheritance
85 6. Hidden output annihilation
86 7. Exact quotient transitivity
87 8. The interaction defect identity across two levels
88 9. Intertwining of fine and coarse vector fields
89 10. Exact nonlinear prediction and Bayesian filtering
90 11. Evidence preservation
91 12. Mass and positivity preservation in the finite example
92 13. Invariance under a global likelihood scale
93 14. The symmetric normalization perturbation inequality
94 15. Controlled dynamical and observational perturbation bounds
95 16. First order perturbation scaling
96 17. Recursive posterior and evidence certificates
97 18. Hyperedge energy and residual identities for optimal retention
98
99 The independent pytest module contains **8 passing test functions**.
100
101 ## Build verification
102
103 | Check | Result |
104 |---|---:|
105 | LaTeX errors | 0 |
106 | Undefined references | 0 |
107 | Undefined citations | 0 |
108 | Overfull boxes | 0 |
109 | Theorem statements without an explicit proof | 0 |
110 | Referenced figures missing | 0 |
111 | Semicolons in ordinary prose | 0 |
112 | Banned stylistic dash compounds in ordinary prose | 0 |
113 | Deterministic manuscript audit | 22 passed, 0 failed |
114
115 The PDF was rendered page by page and reviewed through a complete contact sheet. The title page, theorem pages, normalization section, numerical ledger, figures, appendices, and bibliography were also checked at full page resolution.
116
117 ## Claim boundary
118
119 This release does not establish any of the following claims.
120
121 1. Historical priority for every equivalent quotient formulation
122 2. Universal optimality or efficient discovery of a packet partition
123 3. Global existence of nonlinear flows
124 4. Automatic sparsity or guaranteed compression gains
125 5. Infinite dimensional Bayesian consistency
126 6. A general theory of stochastic or memory bearing quotients
127 7. Empirical superiority of coarse filtering in arbitrary applications
128
129 The main externally auditable contribution is the assembled theorem chain connecting interaction descent at every arity, naturality of rooted trees and flows, Bayesian refinement, and certified approximate filtering.