Chapter status

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ChapterPage statusClaimsClaim typesVerificationOpen issue
Australian construction inputs: Carson and OpenDSSDirectsource-backed Carson/OpenDSSDirect reproduction; overhead and underground reference matrices remain independently compared outputs, and the CS1035 construction mapping is explicitly unresolved.1empiricalindependently-implementedRecover the raw CS1035 conductor, screen, earth-return, frequency, and ordering provenance before claiming a faithful reconstruction.
BIM/BFM parallel lines: an expressiveness auditliterature-informed formulation case; the equations illustrate scope boundaries and are not a new executable certificate.0untracked
Building and changing a model you can checkthree exact executable teaching witnesses with deliberate failures and transfer exercises; not a production importer, incremental network compiler, or OPF price validator.3theoremself-checkedIndependent 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.
A coupled multi-voltage corridorliterature-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.2proposal, theoremself-checkedObtain 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 networkexecutable fixture, local solver evidence, and a derived state-conditioned radiality witness; claims are versioned and verification-scoped.2empiricalself-checkedAdd an independent fixture reviewer.; Re-run with an independent solver where possible.
Four-wire impedance-model ladderdeterministic four-wire transformation witness; authored overhead and cable reproductions remain a follow-on case-study tranche.1empiricalself-checkedReproduce 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 caseguarded AC decision case with self-checked and independently reproduced numerical evidence; broader global claims remain open.1theoremself-checkedTR-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 caseguarded multiconductor decision case with executable redundancy certificates; general state-dependent classification remains open.2empirical, theoremself-checkedThe 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.
Four-wire nominal-pi parallel caseguarded nominal-$\pi$ decision case with executable certificates; singular shunted refusal and state/voltage-dependent recomputation are explicit, while global extensions remain open.5empirical, theoremindependently-implemented, self-checkedThe 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.
The running multiconductor networksemantic specification; numerical realization is versioned separately.0untracked
An end-to-end modelling studydraft capstone workbook over the existing running fixture; no new solved application is claimed.0untracked
Transformer tap AC decision casesolver-backed transformer-control case with independent local reproduction; broader control and global-optimality claims remain open.5empirical, theoremindependently-implemented, self-checkedTR-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.
Circuit formulations and the lowering boundaryformulation 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.4definition, theoremself-checkedAdd 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 surgeryproposed architecture with a package-independent compiled-view, degeneracy, phase-selective switching, and state-conditioned zone-surgery witness; broader transformation algebra remains open.6proposal, theoremself-checkedAdd 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 structurerepresentation-scoped graph definitions with executable invariant witnesses, including conductor-terminal and state-conditioned lifts; broader multi-terminal compilation families remain open.3empirical, theoremself-checkedExtend 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 crosswalkversioned practice crosswalk with a checked running-fixture contract; external package imports and full round-trip adapters remain open.1practiceself-checkedThe 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 classesscoped model-class taxonomy with a numerical E₂ explicit-earth/protection witness; asset-aware protection studies remain future work.4definition, empiricalself-checkedExtend 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 frameworksformal framework definitions with a checked structural architecture witness; evaluated-factor coverage remains open.3empiricalself-checkedLift 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.
From conductor geometry to impedance fidelityphysical-fidelity reference chapter; a geometry-derived running-network certificate remains future work.1practiceself-checkedExercise the contract on source-backed overhead and underground construction records and obtain independent power-engineering review.
Load models and decision dependenceconstitutive-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.4definition, empiricalindependently-implemented, self-checkedAdd 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 modelersnormative mathematical conventions and literature-backed reference; core matrix identities have an executable finite witness; electrical adequacy remains representation- and query-dependent.7definition, theoremself-checkedObtain 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 processingscoped topology-processing definitions with a generated node–breaker switch-state and radiality witness; larger running-network topology lifts remain future work.1definitionself-checkedAdd a generated node–breaker fixture with open, closed, and unknown switch states.
Notation and modelling conventionsmaintained modelling convention; not a standalone empirical claim.0untracked
Numerical consequences of representation and reductiongenerated structural, linearized, symbolic KKT, and package-level solver-diagnostics crosswalk witnesses; solver-internal nonlinear exports remain future work.5definition, empiricalself-checkedExtend 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 transferfoundational definitions and terminology.0untracked
Preservation contractsfoundational definitions; certificate requirements are normative proposals.1definitionself-checkedObtain independent review of the observation-indexed equivalence vocabulary and connect it to additional solver interfaces.
Rating and limit semanticsnormative rating and limit vocabulary; utility-field mappings remain future implementation work.1definitionself-checkedMap selected utility and software rating fields into the typed limit record.
Maps between representation frameworksformal vocabulary and scoped map definitions.1proposalself-checkedExercise the matrix against version-pinned external imports and independently review the cross-community API terminology.
Representation taxonomyfoundational taxonomy; categories are analytical, not a standards claim.0untracked
Scope and thesisreader-facing scope contract and methodological thesis.1definitionself-checked
From source data to a canonical network modelworked exact resistive assembly lesson, followed by source-conversion guidance.1practiceself-checkedCompare the contract against additional utility, CIM/CGMES, OpenDSS, and solver-native adapters with external domain review.
Transformation semantics and registernormative vocabulary and first reader-facing transformation register.1definitionself-checkedAdd independently reviewed formal signatures for closure and composition across larger transformation families.
Translation traps: graphs, circuits, and power-system languagereviewed explanatory synthesis and controlled vocabulary.1empiricalself-checkedExtend the negative cases to nominal-pi cascades, protection boundaries, nonlinear formulations, and independent reproduction.
Two topology levels and the nodal projectionliterature-backed definitions with executable structural and recovery witnesses; inverse recovery is reported by explicit identifiability status and remains non-canonical without additional structure.7theoremself-checkedClassify 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 collapsescontrolled positive-sequence specialization with factor- and network-level executable witnesses; global decision equivalence and external review remain open.2empirical, theoremself-checkedExtend 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 Computationoverview of the teaching draft and complete reference library.0untracked
Scientifically constrained agent benchmarktransparent 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.0untracked
Development research and decision logmaintained development record; not a scientific claims ledger.0untracked
Literature mapresearch 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.0untracked
Representation implementation recordresearch and software record; implementation coverage is evidence about the current repository, not a claim that the architecture is complete.1practiceself-checkedCompare the implementation contract with an independently reviewed package boundary and broader source-data adapters.
Research agendaproposal and open-work register.0untracked
Review protocol and evidence statusgenerated scoping-review snapshot and evidence-status record.0untracked
Search run: 2026-08-14 seed batchgenerated search-run record.0untracked
Search run: 2026-08-15 formulation and graph-model landscapegenerated search-run record.0untracked
Search run: 2026-08-15 information-model and software citation chasegenerated search-run record.0untracked
Search run: multiphase formulations and practical reductionsgenerated search-run record.0untracked
Search run: coupled multi-voltage corridorsgenerated search-run record.0untracked
Evidence map and verification summarygenerated reference navigation and evidence-gap summary.0untracked
Federated scientific knowledge: end-to-end tracemaintained cross-repository implementation trace and scope boundary.1empiricalself-checkedRerun both pinned candidates on the current corpus and evaluate domain-adapted alternatives before making a current or general neural-retrieval comparison.
Referencesbibliography and source register.0untracked
Terminologymaintained glossary and translation aid.0untracked
Cross-community vocabulary indexesgenerated bidirectional vocabulary index; not a standards crosswalk.0untracked
Use this resource with ChatGPTreader-facing access and grounding guide. The repository's developer/operator details remain in llm/README.md.0untracked
Use this resource with Claudereader-facing access and grounding guide. The repository's developer/operator details remain in llm/README.md.0untracked
Computational case guideteaching guide to existing evidence and the scalar opening lesson.0untracked
A plausible model gives the wrong answerintroductory counterexample with executable scalar and multiconductor evidence; independent mathematical review remains open.4empirical, theoremself-checkedAdd 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 coordinatesgenerated worked graph example with hash-bound figures, BMOPFTools cross-checks, and companion conductor-terminal and multi-port lowering witnesses.1theoremself-checkedLift 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 loweringgenerated 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.2empirical, theoremself-checkedIndependently 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 equationsintroductory translation bridge; the examples are deliberately small, while the terminology is used throughout the multiconductor chapters.1empiricalself-checkedExtend to mixed terminal counts, multi-terminal factors, and numerical-zero policies.
How to use this bookselective teaching route and reference-library guide.0untracked
One network, five languagesexplanatory cross-community vocabulary bridge; not a standards crosswalk.1practiceself-checkedObtain terminology review from representatives of power engineering, software and network data, mathematical modelling, graph theory, and graph machine learning.
One network, many graphsexplanatory synthesis introducing the representation landscape.0untracked
Why I wrote this bookdraft author preface for Frederik Geth's review.0untracked
Reading guide: from simple graphs and transmission models to multiconductor networksaudience-specific route map; the formal definitions and executable evidence remain in the linked foundation and case chapters.0untracked
Certificate schema and compositionversioned certificate schema and composition contract; associativity and richer interface compatibility remain open.1theoremself-checkedProve associativity modulo certificate serialization and strengthen compatibility checks beyond object identity.
Circuit coordinate transformations: phase-to-neutral and phase-to-phaseguarded transformation definitions with executable witnesses.0untracked
Conductor-coordinate normalizationguarded exact coordinate transformation with an executable certificate; independent mathematical review remains open.1theoremself-checkedAdd an independent mathematical reviewer and extend coordinate actions to general input/output tensors.
Degree-two series eliminationguarded exact series transformation with positive and negative tests; physical line-class closure remains open.3theoremself-checkedThe 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 completionguarded fixed-linear transformer completion with an executable anatomy witness; broader rating and control models remain open.1theoremself-checkedIndependently review the completion and test phase-angle controls, tap-dependent leakage, and total-current or apparent-power ratings.
Guarded normalization rulescandidate rule catalogue; individual rules require explicit certificates.1proposalself-checkedAttach executable certificates to the remaining catalogue rows and review rewrite-system termination, critical-pair, and confluence conditions.
Kron, Ward, and optimized network equivalentsscoped reduction definitions, audited literature synthesis, and a package-independent Kron/Ward/scenario comparison; independent mathematical review and source-faithful Opti-KRON implementation remain open.13empirical, theoremself-checkedThe 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 compilationexact reference-compilation construction with executable round-trip evidence; independent transformer review remains open.1theoremself-checkedAdd an independent transformer-model review and establish compact serialization contracts that preserve the declared source and compilation references.
Multiwinding terminal leakage assemblyguarded exact terminal assembly with executable certificates; tap-dependent and excitation extensions remain open.1theoremself-checkedIndependently review the fixed and parameterized completions and test tap-dependent leakage or excitation models.
Parameterized transformer tap decisionsexact parameterized tap-factor construction with solver-backed evidence; broader control domains remain open.1theoremself-checkedThe 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 reductionfoundational transformation definitions and scope boundaries.0untracked
Transformer-winding coordinate normalizationguarded exact winding-coordinate normalization with executable round trips; compact serialization closure remains open.1theoremself-checkedProve which normalized factors can be serialized back into compact vector-group and delta-roll fields without loss.

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