Stratified Universality

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1 \begin{longtable}{@{}L{0.09\textwidth}L{0.29\textwidth}L{0.22\textwidth}L{0.30\textwidth}@{}}
2 \caption{Compact index to the theorem concordance. The detailed hypotheses and obligations appear in Appendix~\ref{app:full-concordance}.}\label{tab:compact-concordance}\\
3 \toprule
4 ID & Component & Status & Strongest source\\
5 \midrule
6 \endfirsthead
7 \toprule
8 ID & Component & Status & Strongest source\\
9 \midrule
10 \endhead
11 \midrule
12 \multicolumn{4}{r}{\small Continued on next page}\\
13 \endfoot
14 \bottomrule
15 \endlastfoot
16 FND-01 & Typed linear syntax and module semantics & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
17 FND-02 & Finite free seed presentations & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
18 FND-03 & Seed rank and functorial inequalities & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
19 FND-04 & Closed seed-rank formulas & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
20 FND-05 & Exact packet coordinates and reconstruction & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
21 FND-06 & Block algebra and support calculus & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
22 FND-07 & Coordinate transport and transfer naturality & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
23 FND-08 & Subobject, quotient, and packet exactness & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
24 FND-09 & Preservation profiles and theorem transport & \StatusInternal & \nolinkurl{PSC_I_Symbolic_Core.tex}\\
25 FND-10 & Finite resolved transfer and refinement calculus & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex}\\
26 FND-11 & Universal corner extension and faithful realization & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex}\\
27 FND-12 & Recognition and finite faithful dimension & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex}\\
28 FND-13 & Karoubi, countable, W*, and affiliated completion & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex}\\
29 FND-14 & Nonlinear packet operad and refinement coherence & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex; Nonlinear_Transfer_Operad.tex as specialized source}\\
30 FND-15 & Local analytic nonlinear inversion & \StatusInternal & \nolinkurl{Resolution_Theory_Final_Journal_Manuscript.tex}\\
31 FND-16 & Universal Lane Transport Theorem, finite profiled form & \StatusInternal & \nolinkurl{block15_section.tex, Universal Lane Transport Theorem and corollaries}\\
32 FND-17 & Holonomy-Twisted Universal Lane Transport and Orbit Descent & \StatusInternal & \nolinkurl{block16_section_final.tex, holonomy-twisted transport, orbit descent, orbital composition, and cyclotomic realization}\\
33 CAT-01 & Representation groupoids separated from directional transformations & \StatusFramework & \nolinkurl{Abstraction_as_a_Resolved_Practice(1).tex; PSC Paper I category of seeded packet systems}\\
34 GLU-01 & Finite graph holonomy and global-frame criterion & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
35 GLU-02 & Gauge classification of finite transports & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
36 GLU-03 & Maximal path-flat core & \StatusInternal & \nolinkurl{Affine_Mahler_Packets_and_Periodic_Test_Sets.tex (Core-Transfer Addendum 04)}\\
37 GLU-04 & Split analysis as a genuine two-chart atlas & \StatusInternal & \nolinkurl{Affine_Mahler_Packets_and_Periodic_Test_Sets.tex (Addendum 04)}\\
38 GLU-05 & Exact affine Mahler chart composition and trivial CRT holonomy & \StatusInternal & \nolinkurl{Affine_Mahler_Packets_and_Periodic_Test_Sets.tex (Addendum 04)}\\
39 DSC-01 & Descent commutes with complete resolution & \StatusConditional & \nolinkurl{Projector_Calculus_Final_Current.tex}\\
40 OBS-01 & Canonical obstruction relative to declared correction data & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
41 OBS-02 & Obstruction naturality and packet decomposition & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
42 OBS-03 & Relative/cohomological obstruction & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
43 OBS-04 & Nonlinear correction and complete filtered lifting & \StatusInternal & \nolinkurl{PSC_Paper_III_Strengthened_Annals_Edition.tex}\\
44 GAL-01 & Finite Galois projector realization & \StatusClassical & \nolinkurl{Resolution_Theory_Galois_Expanded_Journal_Manuscript.tex}\\
45 GAL-02 & Effective linear semilinear descent & \StatusClassical & \nolinkurl{Resolution_Theory_Galois_Expanded_Journal_Manuscript.tex}\\
46 GAL-03 & Brauer obstruction to projective descent & \StatusClassical & \nolinkurl{Resolution_Theory_Galois_Expanded_Journal_Manuscript.tex}\\
47 GAL-04 & Tannakian reconstructed symmetry & \StatusClassical & \nolinkurl{Resolution_Theory_Galois_Expanded_Journal_Manuscript.tex}\\
48 LIN-01 & C-finite recurrence \(\leftrightarrow\) rational OGF \(\leftrightarrow\) finite state & \StatusClassical & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
49 LIN-02 & Minimal linear dimension and similarity normalization & \StatusClassical & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
50 LIN-03 & Complete persistent C-finite packet invariant & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
51 HOL-01 & P-recursive \(\leftrightarrow\) D-finite coefficient translation & \StatusClassical & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
52 DIG-01 & Finite digit realization \(\leftrightarrow\) finite k-kernel & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
53 DIG-02 & Fixed-radix automaton normal form & \StatusClassical & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
54 ALG-01 & Selected algebraic branch \(\to\) packet polynomial system & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
55 TRN-01 & Invertible transform \(\leftrightarrow\) transported packet resolution & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
56 PRD-01 & Euler-product exponents \(\leftrightarrow\) logarithmic-derivative recurrence & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
57 MUL-01 & Prime-power seeds reconstruct multiplicative functions & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
58 LOC-01 & Finite Newton--Mahler reconstruction and local transfer & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex}\\
59 LOC-02 & Exact Mahler \(\leftrightarrow\) affine polyphase coordinate transport & \StatusInternal & \nolinkurl{Projector_Seed_Calculus_for_Integer_Sequences_Local_Polyphase_Extension.tex; Addendum 04 strengthens it}\\
60 LOC-03 & Sharp minimal integral packet and universal decoder & \StatusInternal & \nolinkurl{Affine_Mahler_Packets_and_Periodic_Test_Sets.tex (Addendum 04)}\\
61 FMH-01 & Rational functional-Mahler mask \(\to\) Cartier representation & \StatusInternal & \nolinkurl{Komorebi_Custom_GF_Cartier_Padic_Research_Report_0.3.pdf}\\
62 FMH-02 & Functional-Mahler finite state \(\to\) automaton & \StatusInternal & \nolinkurl{Komorebi_Custom_GF_Cartier_Padic_Research_Report_0.3.pdf}\\
63 FMH-03 & Finite-mask Cartier transitions \(\leftrightarrow\) carry matrices & \StatusInternal & \nolinkurl{Komorebi_Custom_GF_Cartier_Padic_Research_Report_0.3.pdf}\\
64 ASM-01 & One explicit profile-indexed resolved envelope & \StatusConjectural & \nolinkurl{Controlling handoff §4 Gap A; local ingredients in Paper I, Resolution Theory, and nonlinear operad sources}\\
65 ASM-02 & Authoritative declared stratum atlas & \StatusFramework & \nolinkurl{Controlling handoff §4 Gap B}\\
66 ASM-03 & Bridge semantic, packet, refinement, and residual naturality & \StatusConjectural & \nolinkurl{Controlling handoff §4 Gap C; local naturality inputs FND-07/FND-09/OBS-02}\\
67 ASM-04 & Triple-overlap and quadruple coherence & \StatusConjectural & \nolinkurl{Controlling handoff §2.6 and §4 Gap C}\\
68 ASM-05 & Effective descent for the heterogeneous atlas & \StatusConjectural & \nolinkurl{Controlling handoff §4 Gap D}\\
69 ASM-06 & Native normalization and complete invariants beyond existing slices & \StatusConjectural & \nolinkurl{Controlling handoff §4 Gap E}\\
70 ASM-07 & Coherent invariant descent and conditional global completeness & \StatusConjectural & \nolinkurl{Controlling handoff §4 Gap F}\\
71 ASM-08 & Theorem concordance and edition control & \StatusInternal & \nolinkurl{This Work Package 0; Master_Theorem_Migration_Ledger.csv; later migration maps}\\
72 ASM-09 & Finite Profiled Resolved Atlas Assembly Theorem & \StatusConditional & \nolinkurl{This Work Package 0, §6 and companion LaTeX theorem file}\\
73 SEM-01 & Universal behavioral coimage and task-relative minimum & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
74 SEM-02 & Maximal stable invisible core & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
75 SEM-03 & Greatest-fixed-point construction and finite certification & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
76 SEM-04 & Task--congruence Galois connection & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
77 SEM-05 & Semantic quotient classification by congruences & \StatusClassical & \nolinkurl{block17_semantic_quotients_final.tex}\\
78 SEM-06 & Semantic diamond and exact compatibility sequence & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
79 SEM-07 & Task-change exact sequence and extension-valued loss & \StatusInternal & \nolinkurl{block17_semantic_quotients_final.tex}\\
80 BRG-01 & Task-compatible bridge and five-term exact loss sequence & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
81 BRG-02 & Extension law for composite semantic loss & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
82 CAR-01 & Carrier factorization gate and joint semantic completion & \StatusClassical & \nolinkurl{block18_carrier_observer_change_final.tex}\\
83 CAR-02 & Carrier-indexed observer packet theorem & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
84 CAR-03 & Cancellation and idempotence barriers & \StatusClassical & \nolinkurl{block18_carrier_observer_change_final.tex}\\
85 OBC-01 & Observer base-change relation module & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
86 OBC-02 & Polyphase infinite-discrete versus finite-linear separation & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
87 CVX-01 & Observer-conditioned convex packet transport and provenance boundary & \StatusInternal & \nolinkurl{block18_carrier_observer_change_final.tex}\\
88 ADM-01 & Admissibility monotonicity and completion/gap/escape stratification & \StatusInternal & \nolinkurl{block19_admissibility_lifting_final.tex}\\
89 ADM-02 & Sharp convex-versus-quadratic packet separation & \StatusClassical & \nolinkurl{block19_admissibility_lifting_final.tex}\\
90 DOC-01 & Forgetful descent, enhancement lifting, and doctrine-indexed task fibers & \StatusFramework & \nolinkurl{block19_admissibility_lifting_final.tex}\\
91 \end{longtable}

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