Chapter status
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| Chapter | Page status | Claims | Claim types | Verification | Open issue |
|---|---|---|---|---|---|
| Australian construction inputs: Carson and OpenDSSDirect | source-backed Carson/OpenDSSDirect reproduction; overhead and underground reference matrices remain independently compared outputs, and the CS1035 construction mapping is explicitly unresolved. | 1 | empirical | independently-implemented | Recover the raw CS1035 conductor, screen, earth-return, frequency, and ordering provenance before claiming a faithful reconstruction. |
| BIM/BFM parallel lines: an expressiveness audit | literature-informed formulation case; the equations illustrate scope boundaries and are not a new executable certificate. | 0 | — | untracked | — |
| Building and changing a model you can check | three exact executable teaching witnesses with deliberate failures and transfer exercises; not a production importer, incremental network compiler, or OPF price validator. | 5 | theorem | self-checked | This counterexample does not prove general solver-cache behavior, correctness of arbitrary structural updates, nonlinear reuse, speed benefits, or physical adequacy.; This direct counterexample is not a general regularization-convergence theorem, an approximation bound for real switching equipment, or a result for arbitrary nonlinear or complex-impedance networks.; Independent review and complete versioned importer/exporter coverage remain outside the field-level teaching witness.; This disproves one update rule; it neither rules out source-aware incremental updates nor establishes general nonlinear, multiconductor or constrained update correctness.; No AC-OPF locational-price, generic solver dual convention, nonlinear sensitivity or uniqueness guarantee is established. |
| Check a converter operating point by hand | self-checked arithmetic tutorial for one supplied RMS operating point; no network solve or physical controller validation. | 0 | — | untracked | — |
| A coupled multi-voltage corridor | literature-backed representation and exact fixed-linear lowering case with an executable scalar certificate; a geometry-derived multi-voltage certificate and decision-preservation tests remain follow-on work. | 2 | proposal, theorem | self-checked | Obtain information-model and protection review; define a machine-readable coupling-group schema and test partial-overlap import round trips.; Independently review the sign/orientation convention; extend the result to block-valued full-pi and singular tableau targets; and separately test limit, state, protection, and optimization-decision preservation. |
| Executable running network | executable fixture, local solver evidence, and a derived state-conditioned radiality witness; claims are versioned and verification-scoped. | 2 | empirical | self-checked | Add an independent fixture reviewer.; Re-run with an independent solver where possible. |
| Four-wire impedance-model ladder | deterministic four-wire transformation witness; authored overhead and cable reproductions remain a follow-on case-study tranche. | 1 | empirical | self-checked | Reproduce authored overhead-line and underground-cable cases with geometry or linecode provenance, balanced and unbalanced load rows, grounding variants, and an external solver cross-check. |
| Non-proportional three-phase four-wire parallel case | guarded AC decision case with self-checked and independently reproduced numerical evidence; broader global claims remain open. | 1 | theorem | self-checked | TR-PAR-007 covers nonsingular nominal-pi primitives; the companion certificate now refuses singular and singular-shunted recovery maps. Extend from that refusal boundary to exact singular reductions, several retained members, state-dependent topology and controls, and obtain an independent global optimality bound where required. |
| Multiconductor parallel AC decision case | guarded multiconductor decision case with executable redundancy certificates; general state-dependent classification remains open. | 2 | empirical, theorem | self-checked | The 2026-08-15 automated independent re-derivation reproduces the closed-form values, relaxation, pruning, and binding-current interpretation but is not human peer review; extend the result to near-proportional/non-proportional members, global nonlinear optimality, and independently reviewed physical cases.; Extend from pairwise implications to constraints jointly implied by multiple retained limits, then condition certificates on topology, controls, outages, investments, and non-Euclidean thermal regions. |
| An explicit neutral does not make power limits current limits | self-checked exact two-conductor SI witness with a local native-package comparison; no general three-phase, dynamic-stability or thermal result. | 1 | theorem | self-checked | Independent scientific review, three-phase extensions and native internal pi-shunt coverage remain pending; no temperature, stability, or complete feeder-feasibility conclusion is established. |
| Four-wire nominal-pi parallel case | guarded nominal-$\pi$ decision case with executable certificates; singular shunted refusal and state/voltage-dependent recomputation are explicit, while global extensions remain open. | 5 | empirical, theorem | independently-implemented, self-checked | The certificate now includes singular-shunted refusal and voltage-dependent recomputation probes. Extend from these guards to exact singular reductions, voltage-dependent nonlinear decision models, several retained members, topology and control states, and global AC optimality bounds where required.; Extend the joint-support certificate to full nonlinear AC cases with several retained members, state-dependent maps, topology decisions, and global optimality bounds.; Extend beyond this fixed linear member relation to voltage-dependent shunts, topology/control states, several independently varying retained members, and global nonlinear AC optimality guarantees.; Extend from the finite scalar and phase-selective envelope to topology/control states, independently varying recovery maps, global nonlinear optimality, and external physical-model review.; Extend the reduced-coordinate treatment to singular shunted primitives, coupled conductor models, and global nonlinear AC decision bounds. |
| When may a null mode be removed? | self-checked algebraic lesson with exact rational witnesses; no automatic symmetry detector or native package capability is claimed. | 1 | theorem | self-checked | Independent scientific review and reader evaluation remain pending; no automatic quotient certification, arbitrary device-current freedom, native package capability or nonlinear uniqueness guarantee is established. |
| The running multiconductor network | semantic specification; numerical realization is versioned separately. | 0 | — | untracked | — |
| An end-to-end modelling study | draft capstone workbook over the existing running fixture; no new solved application is claimed. | 0 | — | untracked | — |
| Transformer tap AC decision case | solver-backed transformer-control case with independent local reproduction; broader control and global-optimality claims remain open. | 5 | empirical, theorem | independently-implemented, self-checked | TR-XFMR-007 independently reproduces the numerical branch search, and the certificate now includes a finite two-scenario tap-pair switching-cost ledger; extend the network-level contract to unbalanced downstream controls and richer multiwinding decisions.; The finite tap-pair ledger is branch-complete for its declared domain, but the continuous subproblems remain local Ipopt solutions; reproduce the case with an independently assembled transformer primitive or external power-system tool and establish global guarantees where required.; This is a finite local witness, not a global unbalanced OPF guarantee; extend the contract to richer multiwinding controls, topology decisions, and independently assembled physical models.; This remains a finite local path witness, not a global unbalanced multi-period OPF guarantee; extend to richer controls, topology decisions, switching operation limits, and independently assembled physical models.; Extend operation-count, dwell-time, deadband, and switching-cost semantics to richer multiwinding controls and globally certified multi-period OPF models. |
| When a model admits unintended solutions | self-checked exact scalar witnesses and pinned local-solver comparisons; no general AC uniqueness or dynamic-stability result. | 2 | theorem | self-checked | Independent review remains pending; nonlinear controls, variable taps, device capability curves and complete AC-OPF convexity require separate analysis.; Independent scientific review and general three-phase extensions remain pending; the separate controlled neutral/shunt witness does not establish arbitrary AC/OPF uniqueness, dynamic stability, or a complete equipment thermal model. |
| Circuit formulations and the lowering boundary | formulation guide and equivalence contract; the definitions and guards below are book conventions supported by circuit and power-system precedents. General equivalence theorems beyond the declared linear scopes remain future work. | 6 | definition, theorem | self-checked | The scalar identity does not establish nonsingularity or uniform conditioning of every network, grounding adequacy, nonlinear/control equivalence, or correctness of all package transformer subtypes.; This algebraic boundary neither invalidates all power-variable formulations nor verifies a complete network, equipment limits, or global optimality.; Add independent review and extend the witness to controlled, dynamic, and multi-terminal power-network factors.; Extend the failure-family witness to multiconductor, grounded, state-dependent, and nonlinear formulations with independent review.; Extend the rank guard to frequency-dependent, singular-shunt, dynamic, and state-dependent compound operators with independent review.; Obtain independent review of the source-factor versus study-operator distinction and extend the witness to a generator control and a non-OpenDSS formulation. |
| From source graphs to views and graph surgery | proposed architecture with a package-independent compiled-view, degeneracy, phase-selective switching, and state-conditioned zone-surgery witness; broader transformation algebra remains open. | 6 | proposal, theorem | self-checked | Add independent technical review of the house visual grammar and compare additional utility and manufacturer diagram conventions.; Add a full evaluated multiwinding factor lowerer and independently review equation-preservation conditions.; Extend the surgery contract to energized islands, protection states, n-terminal factors, and optimization decisions.; Extend port-selective surgery to coupled conductor bundles, grounding factors, and protection/energization states.; Connect diagnostics to standards-aware import remediation and quantify restricted-coordinate recovery policies.; Specify utility-data remediation policies for duplicate or indistinguishable switch assets. |
| Cycles, parallelism, and radial structure | representation-scoped graph definitions with executable invariant witnesses, including conductor-terminal and state-conditioned lifts; broader multi-terminal compilation families remain open. | 3 | empirical, theorem | self-checked | Extend the executable invariant checks to conductor-terminal incidence and state-indexed multi-terminal factors.; Extend the active-state witness to switching, outages, and energized-state uncertainty on the canonical multiconductor fixture.; Add active-state radiality certificates with open/closed switches, outages, and multi-terminal compilation choices. |
| Data-model crosswalk | versioned practice crosswalk with a checked running-fixture contract; external package imports and full round-trip adapters remain open. | 1 | practice | self-checked | The running-fixture contract is checked against pinned documentation profiles; external package imports and file-level round-trip provenance/rating checks remain open. |
| Earth, neutral, and reference model classes | scoped model-class taxonomy with a numerical E₂ explicit-earth/protection witness; asset-aware protection studies remain future work. | 4 | definition, empirical | self-checked | Extend the explicit-earth witness to relay curves, CT saturation, richer maintenance decisions, and independent reproduction.; Extend the explicit-earth comparison to relay curves, CT saturation, richer maintenance decisions, and independent reproduction.; Extend to relay curves, CT saturation, richer maintenance decisions, and independent reproduction.; Replace the illustrative functions with standards-aligned relay/CT models and quantify uncertainty and coordination margins. |
| Formal representation frameworks | formal framework definitions with a checked structural architecture witness; evaluated-factor coverage remains open. | 3 | empirical | self-checked | Lift the data witness to evaluated factor relations and independently review the architecture against a non-synthetic asset model.; Extend the lift to evaluated factor relations and compare its boundary semantics with the simple quotient and line-identity cycle basis.; Compare the scalar terminal lift with a full conductor-terminal factor evaluator and state-conditioned topology maps. |
| IBR power-factor, Volt-var and Volt-watt controls | self-checked control equations and examples for a local development candidate; physical controller validation remains open. | 1 | theorem | self-checked | Independent review remains pending; no dynamic controller compliance, authenticated native construction, scale-free PF-ratio accuracy or complete-network feasibility is certified. |
| From conductor geometry to impedance fidelity | physical-fidelity reference chapter; a geometry-derived running-network certificate remains future work. | 1 | practice | self-checked | Exercise the contract on source-backed overhead and underground construction records and obtain independent power-engineering review. |
| Load models and decision dependence | constitutive-model reference chapter with scoped numerical load-model, connection-map, and continuation witnesses plus independent reproduction; broader nonlinear and network-level certificates remain future work. | 5 | definition, empirical, theorem | independently-implemented, self-checked | This algebra does not certify arbitrary transformer/connection implementations, nonlinear operating-point feasibility, physical load adequacy, or source data provenance.; Add multiconductor connection maps and continuation to collapse points; the declared scalar CP/CI/CZ/ZIP fixture now has separately varying reactive coefficients and an independent reproduction.; Extend the definition and executable guardrail to arbitrary unbalanced terminal maps, nonstandard connection families, explicit unit provenance, and independently reviewed importer crosswalks.; Extend connection-map evidence to unbalanced multiconductor loads, explicit grounding, phase-specific ratings, and network-level decision solves.; Replace the iteration-failure boundary with a mathematically continued nose curve, add independent solver continuation, and extend to multiconductor/network-level decisions. |
| Multigraphs for expert modelers | normative mathematical conventions and literature-backed reference; core matrix identities have an executable finite witness; electrical adequacy remains representation- and query-dependent. | 7 | definition, theorem | self-checked | Obtain expert graph-theory review of the flag terminology and its relationship to the book's engineering specializations.; Obtain expert review and extend the executable witness to complex block stamps, transformer ratios, and coupled multi-terminal factors without calling the resulting operator a universal graph Laplacian.; Obtain independent proof review and add property-based checks over randomized finite multigraphs and application-specific weighted-query contracts.; Review the incidence/hypergraph/factor-graph terminology across mathematical modeling, circuit, and graph-theory communities and add evaluated n-port examples beyond the existing transformer witnesses.; Obtain independent terminology review across graph theory, circuit topology, and power-system modeling communities.; Review whether the book should add a dedicated loopy-Laplacian notation for grounded diagonal terms in future editions.; Extend and independently review the block-coordinate result for multiphase pi factors, transformer maps, singular primitives, and retained branch-current or rating queries. |
| Node–breaker, bus–breaker, and topology processing | scoped topology-processing definitions with a generated node–breaker switch-state and radiality witness; larger running-network topology lifts remain future work. | 1 | definition | self-checked | Add a generated node–breaker fixture with open, closed, and unknown switch states. |
| Notation and modelling conventions | maintained modelling convention; not a standalone empirical claim. | 0 | — | untracked | — |
| Numerical consequences of representation and reduction | generated structural, linearized, symbolic KKT, and package-level solver-diagnostics crosswalk witnesses; solver-internal nonlinear exports remain future work. | 5 | definition, empirical | self-checked | Extend the current five-bus structural witness to a pinned running-network benchmark with solver-exported Ybus/Jacobian sparsity, ordering-dependent fill, and recovered decision-margin checks.; Add an independent KKT/Jacobian export and compare ordering-dependent fill and decision margins across source and reduced views.; The public BMOPFTools checked-KKT callback now runs through DiffOpt on a minimal parameterized OPF and agrees with finite difference; a native JuMP/MOI Jacobian structure is now recorded, while solver-private KKT rows, ordering, and factorization statistics remain outside the public boundary.; Extend the initial bus-result contract to equation residuals, device limits, power balance, objective and global-optimality evidence, and independent solver reproduction.; Extend the witness schema with model-specific equation coverage, scaling/backward-error metadata, and independent recomputation adapters. |
| Orientation, terminal quantities, and power transfer | foundational definitions and terminology. | 0 | — | untracked | — |
| Preservation contracts | foundational definitions; certificate requirements are normative proposals. | 1 | definition | self-checked | Obtain independent review of the observation-indexed equivalence vocabulary and connect it to additional solver interfaces. |
| Rating and limit semantics | normative rating and limit vocabulary; utility-field mappings remain future implementation work. | 1 | definition | self-checked | Map selected utility and software rating fields into the typed limit record. |
| Maps between representation frameworks | formal vocabulary and scoped map definitions. | 1 | proposal | self-checked | Exercise the matrix against version-pinned external imports and independently review the cross-community API terminology. |
| Representation taxonomy | foundational taxonomy; categories are analytical, not a standards claim. | 0 | — | untracked | — |
| Scope and thesis | reader-facing scope contract and methodological thesis. | 1 | definition | self-checked | — |
| From source data to a canonical network model | worked exact resistive assembly lesson, followed by source-conversion guidance. | 1 | practice | self-checked | Compare the contract against additional utility, CIM/CGMES, OpenDSS, and solver-native adapters with external domain review. |
| Transformation semantics and register | normative vocabulary and first reader-facing transformation register. | 1 | definition | self-checked | Add independently reviewed formal signatures for closure and composition across larger transformation families. |
| Translation traps: graphs, circuits, and power-system language | reviewed explanatory synthesis and controlled vocabulary. | 1 | empirical | self-checked | Extend the negative cases to nominal-pi cascades, protection boundaries, nonlinear formulations, and independent reproduction. |
| Two topology levels and the nodal projection | literature-backed definitions with executable structural and recovery witnesses; inverse recovery is reported by explicit identifiability status and remains non-canonical without additional structure. | 7 | theorem | self-checked | Classify identifiable and bounded ambiguity families under realistic line, transformer, shunt, catalog, measurement, and state constraints.; Extend the support/stamp distinction to frequency-coupled, rectangular realified, Jacobian, and multi-terminal compiled operator families.; Characterize chordality and minimal fill under missing phases, sparse coupling blocks, parallel factors, multi-terminal devices, and meshed bus graphs.; Classify realistic catalog, measurement, grounding, transformer, and state-dependent recovery classes beyond the four finite witnesses.; Extend the augmented-observation criterion to multiconductor current measurements, nonlinear grounding, transformer controls, and partial observability.; Extend the rank and partial-observation criterion to noisy measurements, nonlinear operating-point data, coupled transformer ports, and experimental design.; Extend deterministic bounds to noisy partial observations, structured/passive uncertainty sets, nonlinear operating points, and experiment design. |
| When the general model collapses | controlled positive-sequence specialization with factor- and network-level executable witnesses; global decision equivalence and external review remain open. | 2 | empirical, theorem | self-checked | Extend the network witness to controls, phase-specific limits, contingencies, and an independent mathematical review before making a global decision-equivalence claim.; Extend the witness to controls, phase-specific limits, contingencies, and independent mathematical review. |
| Power-System Modelling for Computation | overview of the teaching draft and complete reference library. | 0 | — | untracked | — |
| Scientifically constrained agent benchmark | transparent benchmark substrate and controlled-pilot design; the first human review required corrections, those corrections are applied and await re-review, and no agent runs or condition effects are claimed. | 0 | — | untracked | — |
| Development research and decision log | maintained development record; not a scientific claims ledger. | 0 | — | untracked | — |
| Literature map | research record; coverage is provisional and not an exhaustive systematic review. Current matrix counts, checksums, search coverage, and coding status are published in the generated review protocol and evidence status page. | 0 | — | untracked | — |
| Representation implementation record | research and software record; implementation coverage is evidence about the current repository, not a claim that the architecture is complete. | 1 | practice | self-checked | Compare the implementation contract with an independently reviewed package boundary and broader source-data adapters. |
| Research agenda | proposal and open-work register. | 0 | — | untracked | — |
| Review protocol and evidence status | generated scoping-review snapshot and evidence-status record. | 0 | — | untracked | — |
| Search run: 2026-08-14 seed batch | generated search-run record. | 0 | — | untracked | — |
| Search run: 2026-08-15 formulation and graph-model landscape | generated search-run record. | 0 | — | untracked | — |
| Search run: 2026-08-15 information-model and software citation chase | generated search-run record. | 0 | — | untracked | — |
| Search run: multiphase formulations and practical reductions | generated search-run record. | 0 | — | untracked | — |
| Search run: coupled multi-voltage corridors | generated search-run record. | 0 | — | untracked | — |
| Evidence map and verification summary | generated reference navigation and evidence-gap summary. | 0 | — | untracked | — |
| Federated scientific knowledge: end-to-end trace | maintained cross-repository implementation trace and scope boundary. | 1 | empirical | self-checked | Rerun both pinned candidates on the current corpus and evaluate domain-adapted alternatives before making a current or general neural-retrieval comparison. |
| Device and bound audit reference | scoped local-candidate applicability reference; implementation comparisons, not external scientific review or a published-package API promise. | 1 | theorem | self-checked | Independent review remains pending; a numerical floor does not establish physical voltage quality, authenticated phase order or native package polynomial feasibility outside the ratio domain. |
| References | bibliography and source register. | 0 | — | untracked | — |
| Terminology | maintained glossary and translation aid. | 0 | — | untracked | — |
| Cross-community vocabulary indexes | generated bidirectional vocabulary index; not a standards crosswalk. | 0 | — | untracked | — |
| Use this resource with ChatGPT | reader-facing access and grounding guide. The repository's developer/operator details remain in llm/README.md. | 0 | — | untracked | — |
| Use this resource with Claude | reader-facing access and grounding guide. The repository's developer/operator details remain in llm/README.md. | 0 | — | untracked | — |
| Computational case guide | teaching guide to existing evidence and the scalar opening lesson. | 0 | — | untracked | — |
| A plausible model gives the wrong answer | introductory counterexample with executable scalar and multiconductor evidence; independent mathematical review remains open. | 4 | empirical, theorem | self-checked | Add an independent mathematical reviewer.; Molzahn2018 gives an exact scalar AC constraint-pruning test without asset aggregation; a general multiconductor classification remains open.; Establish necessary and sufficient redundancy tests for arbitrary multiconductor limits and for state- or decision-dependent line models.; The multiconductor mechanism is exercised in TR-PAR-004; add an independent reviewer for this linear case. |
| A five-bus multigraph: identities, cycles, and tree coordinates | generated worked graph example with hash-bound figures, BMOPFTools cross-checks, and companion conductor-terminal and multi-port lowering witnesses. | 1 | theorem | self-checked | Lift the executable incidence and cycle objects to conductor-terminal graphs, state-conditioned topology decisions, and compiled multi-terminal factors. |
| Five buses through a multi-port lowering | generated structural lowering example composed from the stable five-bus topology fixture and the checked three-winding transformer contract; it is not a complete transformer power-flow model. | 2 | empirical, theorem | self-checked | Independently review the layer interfaces and extend the witness to evaluated four- and n-winding factors, non-diagonal reference matrices, connection-specific shunts, controls, and decision-preserving edge realizations.; Independently review the four-winding equation-preservation conditions and extend the decision family to richer controls and non-diagonal coupled conductor blocks. |
| How to read power-network diagrams and equations | introductory translation bridge; the examples are deliberately small, while the terminology is used throughout the multiconductor chapters. | 1 | empirical | self-checked | Extend to mixed terminal counts, multi-terminal factors, and numerical-zero policies. |
| How to use this book | selective teaching route and reference-library guide. | 0 | — | untracked | — |
| One network, five languages | explanatory cross-community vocabulary bridge; not a standards crosswalk. | 1 | practice | self-checked | Obtain terminology review from representatives of power engineering, software and network data, mathematical modelling, graph theory, and graph machine learning. |
| One network, many graphs | explanatory synthesis introducing the representation landscape. | 0 | — | untracked | — |
| Why I wrote this book | draft author preface for Frederik Geth's review. | 0 | — | untracked | — |
| Reading guide: from simple graphs and transmission models to multiconductor networks | audience-specific route map; the formal definitions and executable evidence remain in the linked foundation and case chapters. | 0 | — | untracked | — |
| Certificate schema and composition | versioned certificate schema and composition contract; associativity and richer interface compatibility remain open. | 1 | theorem | self-checked | Prove associativity modulo certificate serialization and strengthen compatibility checks beyond object identity. |
| Circuit coordinate transformations: phase-to-neutral and phase-to-phase | guarded transformation definitions with executable witnesses. | 0 | — | untracked | — |
| Conductor-coordinate normalization | guarded exact coordinate transformation with an executable certificate; independent mathematical review remains open. | 1 | theorem | self-checked | Add an independent mathematical reviewer and extend coordinate actions to general input/output tensors. |
| Degree-two series elimination | guarded exact series transformation with positive and negative tests; physical line-class closure remains open. | 3 | theorem | self-checked | The 2026-08-15 automated independent re-derivation found and motivated the repaired coupling guard but is not human peer review; add a named mathematical reviewer for the uncoupled rule and its coupling boundary.; Formalize sufficient physical line-merge guards for selected line models.; Add an independent mathematical reviewer; determine model-specific reciprocity and physical line-class closure guards. |
| Fixed-linear transformer factor completion | guarded fixed-linear transformer completion with an executable anatomy witness; broader rating and control models remain open. | 1 | theorem | self-checked | Independently review the completion and test phase-angle controls, tap-dependent leakage, and total-current or apparent-power ratings. |
| Guarded normalization rules | candidate rule catalogue; individual rules require explicit certificates. | 1 | proposal | self-checked | Attach executable certificates to the remaining catalogue rows and review rewrite-system termination, critical-pair, and confluence conditions. |
| Kron, Ward, and optimized network equivalents | scoped reduction definitions, audited literature synthesis, and a package-independent Kron/Ward/scenario comparison; independent mathematical review and source-faithful Opti-KRON implementation remain open. | 13 | empirical, theorem | self-checked | The 2026-08-15 automated independent re-derivation verified dense partition actions, reciprocity distinctions, and the fixed-injection scope but is not human peer review; extend the fixture to randomized and terminal-permutation campaigns and obtain a named mathematical review.; Replace the illustrative target-selection family with a source-faithful Opti-KRON implementation and extend observations to voltage, constraints, decisions, and topology guards.; Extend the direct fixture check to non-pendant eliminations, retained branch limits, shunts, and multiconductor internal states.; Extend the fill-in witness to multiconductor blocks, retained branch limits, shunts, and ordering-dependent numerical factorization diagnostics.; Extend the neutral-current recovery contract from the linear shunt probe to nonlinear loads, explicit earth-return factors, and general neutral/grounding reductions; the series and shunt probes have independent reproductions.; Extend to nonlinear earth-return factors, multiple grounding points, protection observations, and independent physical-model review.; Extend to nonlinear and state-dependent grounding, grounding impedance uncertainty, protection observations, and physical-model review.; Extend to uncertainty sets, nonlinear/state-dependent grounding, protection observations, and physical-model review.; Extend to global continuation, multiple nonlinear grounding points, uncertainty sets, protection observations, and physical-model review.; Extend to global continuation, more nonlinear grounding points, uncertainty sets, protection observations, and physical-model review.; Extend to adaptive continuation, global branch tracking, uncertainty sets, protection observations, and physical-model review.; Extend local derivative bounds to adaptive/global continuation, nonlinear multi-point grounding, noisy observations, and physical-model review.; Extend the chain to a nonlinear AC decision model, parameter uncertainty, and independent error analysis before treating it as a general certification theorem. |
| Multiwinding leakage reference compilation | exact reference-compilation construction with executable round-trip evidence; independent transformer review remains open. | 1 | theorem | self-checked | Add an independent transformer-model review and establish compact serialization contracts that preserve the declared source and compilation references. |
| Multiwinding terminal leakage assembly | guarded exact terminal assembly with executable certificates; tap-dependent and excitation extensions remain open. | 1 | theorem | self-checked | Independently review the fixed and parameterized completions and test tap-dependent leakage or excitation models. |
| Parameterized transformer tap decisions | exact parameterized tap-factor construction with solver-backed evidence; broader control domains remain open. | 1 | theorem | self-checked | The first solver-backed network embedding is TR-XFMR-006; extend the contract to phase-angle, independent per-phase, mechanically coupled, and tap-dependent-loss controls. |
| Projection, compilation, and reduction | foundational transformation definitions and scope boundaries. | 0 | — | untracked | — |
| Transformer-winding coordinate normalization | guarded exact winding-coordinate normalization with executable round trips; compact serialization closure remains open. | 1 | theorem | self-checked | Prove which normalized factors can be serialized back into compact vector-group and delta-roll fields without loss. |
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