TNFR theory: reading routes, mathematical owners and implementation

This is the maintained theory catalog. Use it to find definitions, proofs and their execution paths. The glossary classifies concepts; the strategy explains research dependencies and the portfolio classifies contributions. The execution plan alone owns tasks, status and reopening conditions. Engineering guidance belongs to the documentation map.

Choose the complete model before reusing a result. Registered operators, the native relational law and the normalized-sine comparison have different evolution laws and admission contracts. Shared storage or matching local derivatives do not make them interchangeable. The nodal identity alone selects none of them uniquely; formation, maintenance and physical identification retain their separate hypotheses.

Choose a question

Question	Start here
What are form, capacity, pressure, phase and time?	Foundations and parameter ledger
Which information and laws does interaction consume?	Relation foundations, constitutive information
What forms a pattern, and what maintains it?	Formation and identity, native exchange, sine patterns
How do internal motion, scale and memory survive composition?	Resonance, collective state, composition, memory
What do execution and observations guarantee?	Operators and grammar, diagnostics, theory to execution
What can be compared with physical observations?	Physical atlas, measurement protocols
What do arithmetic applications establish?	Arithmetic and applications, under their supplied mathematical premises

A definition specifies a model; a conditional theorem needs its hypotheses; finite evidence records particular checks; an auxiliary construction adds premises. These can coexist in one document. Research priority is separate from validity, and a filename is not evidence.

Directory responsibilities

Location	Responsibility
theory/*.md	Foundations, cross-cutting topics and collection entry points
theory/nodal/	Detailed form/phase, relational-pattern and reduction derivations; filenames and chapter premises distinguish models
theory/research/	The execution plan and supporting measurement protocols
theory/research/archive/	Deferred case studies, evaluated records and retirement provenance; historical instructions are inactive

Each maintained document has one primary row below. The catalog generates the website menu; scripts/check_documentation.py checks coverage and menu agreement. Preserve published section links when splitting an owner. After changing catalog rows or groups, run python scripts/check_documentation.py --write-generated.

State and laws

Mathematical owner	What it defines or establishes
Fundamental theory	EPI state space, nodal identity, chart/equivalence admission and derived trajectory properties under complete laws
Parameter foundations	Units, zero limits, cross-channel dependencies, capacity versus oscillation frequency, clocks and the threshold/constant ledger
Relation foundations	Support, conductance, distance and causal dependence; zero-relation limits, autonomous contact countermodels and undetermined relation storage
Pressure premises	Locality, covariance, phase-domain boundaries and what does not select a unique pressure law
Joint parameter response	Signed form, pressure derivatives, pressure-state closure and finite phase/capacity/source compatibility
Glossary	Uniform concept cards with checked classifications, dependencies, evidence links and a generated index; linked owners retain definitions and proofs

Form, phase and coherent patterns

Mathematical owner	What it establishes and what remains separate
Inherited form dynamics	Fine-to-coarse pushforwards, inherited pressure/metric, field reconstruction and changing support
Phase-to-form exchange	Causal-source matching, regional frames and response to a prescribed phase input
Primitive phase closure	Symmetry and closure obstructions, oriented response and the actual runtime phase-writer inventory
Derived form phase	Regional Cartesian/Gram geometry, fixed affine closure, derived angles and source-relative predictions
Relational law and chapter index	Native joint-law premises and routes to constitutive information, response identification, recovery and capture
Relational coefficient and capacity identification	Spectral and finite-amplitude discrimination, temporal coefficient acquisition and capacity-intervention records with their separate calibration and observation scopes.
Sine law and constitutive information boundaries	The complete global sine comparison; common exchange geometry, form balance, storage alternatives, first-moment restrictions and form-origin information premises.
Native local recovery and regional interaction	Full-law local recovery, regular-equilibrium stiffness, regional transmission and work accounting; interacting environments remain retained.
Native phase domains and capture	Regular-domain continuation, winding passage, reflected basins and the full-state acute-sector barrier, including capacity/storage-scale covariance and regularity margins.
Native validated transit and preparation controls	Validated continuous transit, bounded constitutive robustness and zero/reversed/consensus-form controls; frozen responses retain their original numerical verdicts.
Relational pattern composition	Native pattern interfaces, collective observations and composition premises
Effective mediated connections	Native retained intermediaries, effective interactions and their reduction premises
Native formation and its obstructions	Native preparation, formation obstructions and retained finite response controls
Smooth-sine pattern dynamics	Geometry, memory representations, positive-loss capture, prepared acquisition with an inherited receiver response and two formed attracting classes with common-probe discrimination, recovery and a central-contact invisibility obstruction; conservative source-directed acquisition, exact collective families, finite full-state retention and actual contact feedback. Formation and maintenance retain separate handoff obligations
Repeated probes of formed sine classes	Quantitative nonlinear return neighborhoods, per-cycle discrimination and cumulative supplied work under the fixed C9 hybrid protocol; no exact periodic-orbit, autonomous maintenance or practical-speed claim
Contact of actually formed sine classes	Uninterrupted source-to-contact recovery, class-dependent actual receiver response, support-event work and whole-joined winding retention under one supplied C9 bridge; no reset, autonomous contact selection or physical measurement bridge
Reduced ports of formed sine classes	Twenty-coordinate component surrogate with an exact nonlinear bridge, retained hidden-source uncertainty and a full-law error criterion for receiver transfer; distinct from an exact nonlinear quotient, physical identification or a runtime-speed claim
Network composition of reduced sine ports	Degree-aware assembly on simple unit central-contact graphs, exact surrogate charge/storage balances and uniform finite full-state error; actual source handoff, contact work and joined identity remain separate obligations
Acquired mediator class and a transmitted form response	Finite class-dependent receiver response to a paired donor probe on a three-C9 path, with full source histories, exact degree normalization, nonlinear errors, work and retained identities; no autonomous event or physical-property identification
Effective memory of an acquired sine-class mediator	Exact tangent source/kernel and retained nonlinear residual for the full two-contact mediator, source-matched finite errors, stationary-comparator separation and an acquired-family closure obstruction; no hidden-state reset or physical identification
Two-probe superposition on an acquired sine composite	Matched four-history form-input response, symmetry and nonlinear onset, finite scalar-noise cancellation and four-endpoint record overlap with the same-source tangent law; carried event work and collective identity remain explicit
Finite separation of a nonlinear class-mediated response	Exact heat-cubic prediction and its retained full-law evaluation separate nonlinear/tangent four-record sets; source association, shared prefixes, exact events and partial-failure evidence remain distinct from acquisition or sensor precision
Organization dependence of nonlinear interaction	Exact cancellation of common heat channels isolates the mediator-class contribution; full nonlinear/source bounds identify an unresolved contrast and a limitation of the independent-remainder estimate, without asserting response equality or record overlap
Complete cubic-amplitude mediator response	Full tangent feedback and quadratic internal recoupling, fixed time-polynomial enclosures and a holomorphic higher-amplitude bound; actual-source uncertainty, true sign and scalar observation resolution remain separate
Spatial observation of nonlinear class interaction	Reflection-odd receiver form difference, complete quadratic feedback and a class-sensitive higher-amplitude bound; independent source residuals and sixteen scalar reading errors remain explicit
Feasible amplitudes for class discrimination	Common-scale homogeneity of the retained cubic coefficient, uniform finite-error discrimination and a spectral bound on delayed event work; original source, sensor and identity budgets remain fixed
Independent full-law class comparison protocol	Fixed scaled intervention, complete nonlinear references and independent actual-source transfer; retained finite class contrast under explicit width, consistency and noise criteria
Repeated joined class interaction	Finite common return on the full joined support, carried branch means and residuals, repeated work and separation from a persistent tangent comparator
Nonlinear collective interface	Six central port coordinates with causal cubic memory, retained hidden initialization, nonlinear source-error bounds and pressure/work observations on the fixed joined support
Changed-input collective prediction	Independent causal port computation for a mediator impulse, with source, numerical, work and identity budgets and a grounded tangent port comparator
Independent changed-input full-law protocol	Complete 54-coordinate producer and retained changed-input comparison, with absolute-phase source association, separate actual-family transport and fixed numerical, consistency and comparator criteria
Causal composition of acquired sine-class interfaces	Exact two-channel component feedback, conditional output-map substitution and an explicit cubic full-state residual bound preserving the admitted memory distinction on the existing support
Causal nonadditivity of distinct neighbor interventions	Mixed donor/receiver response of the mediator, complete cubic memory and a static edge bound separating matched additive response functionals with retained source, work, identity and recording budgets
Independent distinct-neighbor protocol	Shared complete-state observation at distinct input ports, nonlinear common-source transfer and the retained finite comparison against separately matched additive responses
Nonlinear excess storage and loss	Exact full/tangent event and loss balance, finite signed rectangular storage excess from static edge bounds, complete amplitude/source errors and a separate storage observation requirement
Uniform tracking of reduced sine ports	All-time full/surrogate comparison on trapped charts, exact normalized-gap admission, parity-separated defects and conserved-mean floors; form and phase resolution retain separate verdicts
Form tracking by ordered heat comparison	Sharper all-time form estimates for the unchanged surrogate, retaining noncommuting diffusion/stiffness, nonlinear bridge perturbation, initial exchange and mean uncertainty; the earlier phase-only evidence remains unchanged
Two-port compatibility of sine classes	Joint acute equilibrium of the existing C9 winding classes through two distinct ports, with forced deformation, balanced interface circulation and local recovery; an exact boundary witness excludes direct scalar-storage capture certification for undeformed unequal classes, without deciding their trajectories or support selection
Finite transit of two-port sine classes	Full-law directional deformation from an independently supplied undeformed C9 pair, with whole-window acute admission and storage-based slow-reference error control; finite transit does not establish final capture or support selection
Prepared capture of two-port sine classes	Conditional full-family capture from the unchanged two-port preparation, combining a fixed-budget validated nominal reference, acute full-law error bounds and analytic form relaxation; validation and complete-state basin premises remain explicit
Supplied probe of the acquired two-port composite	Conditional finite receiver transmission after a donor form pulse, with an unjoined control, explicit event work and post-pulse identity recovery; the pure-heat countermodel prevents a winding-specific or constitutive-selection interpretation
Interior phase probe of acquired two-port deformation	Finite degree-metric warmup and identical local phase intervention/readout on joined and unjoined supports, with nonlinear response errors, a separate phase-blind control and post-event identity; local geometry does not remove global support dependence
Two-port geometry from a calibrated local response	Conditional outer inference on an explicit nonstationary full-state family, with remote-port leakage, full-flow and observation errors; nominal coordinates, actual arc means and joint realizability remain distinct
Geometry and gain from two successive phase inputs	Conditional joint outer constraints from one uninterrupted complete trajectory, with retained intermediate state, a nonsingular leading response map and correlated three-reading errors; finite resolution is distinct from exact identifiability or physical calibration
Geometry, sensor gain and a declared uncertain clock	Necessary geometry and gain/clock marginals under one bounded positive observation-clock conversion, reusing a uniform full-flow envelope; exact common-rate/clock equivalence is separate from gain/clock agreement of the leading response and its curvature counterexample
Finite curvature from one additional reading	Necessary clock/gain refinement from four associated readings on the same full-state trajectory, with original-source and third-derivative error bounds; exact local information gain on an ideal fixed-source subfamily is distinct from noisy global identification
Clock drift, sampled exposure and robust mean-rate inference	Exact finite-sample exposure equivalence and necessary first-window mean-rate/gain bounds with a positive varying clock, held sensor and complete-law reading-transfer error; instantaneous profile recovery and physical clock identification remain unsupported
Finite-aperture observations and mean-clock inference	Necessary geometry, gain and first-window mean-rate bounds from four fixed interval averages, with exact quadratic moments and separate observation errors; validated forward averages under an explicit affine clock retain complete state/event history, while the kernel remains an independently supplied premise
Finite-noise and horizon resolution for the four boxcar observations	Response-free sufficient width budgets under the unchanged complete observation model, with separate horizon limitations of the method and a complete-history bounded-noise ambiguity; declared errors do not establish physical attainability
Exact and controlled form-phase reductions	Equivalent form/phase/memory representations, controlled slow-time comparison and its full-state capture handoff; hidden initialization and transient errors remain explicit.
Conservative regional formation and its barriers	Finite winding entry, regional channel balance, distributed source geometry, retention barriers and a robust finite passage under the full conservative environment.
Collective phase families and live contact feedback	Exact phase-offset partitions, nearby full-state moving windows, contact/storage exchange and complete receiver-rigidity conditions.
Conservative source preparation and finite retention	Energy-speed retention, reverse-source certification, sign/reflection saddle reduction, nonlinear corridors, source-to-target construction and its finite operational and constitutive limitations.
Native reduction and memory index	Native symmetry reduction and conditional memory; chapter routes separate mediated dynamics, environmental memory, recovery and archived receiver studies
Native mediated pattern dynamics	Native one-, two- and three-port mediator reduction, fast-limit scope, memory clocks and the frozen causal-response control; no boundary source is installed.
Sine environmental state and causal memory	Complete sine mediator geometry, cancellation, conserved hidden inventory, exact causal elimination and conditional state/capacity inference with its sampling boundaries.
Return-path geometry and collective response	Native return-path equilibrium and causal oscillatory response, with separately declared sine/cubic storage-family geometry and its inverse response.
Retained phase records and finite contact readout	Native isolated-pattern recovery, retained phase offset, finite contact and removal budgets and the receiver mean record.
Sine relative state, recovery and conservative identity	Exact relative coordinates and bracket, whole-set recovery with a live environment, and the separate zero-loss protection and recurrence result.
Resonance foundations	Reciprocal response and its same-type port boundary, reversible pulses and almost-everywhere nonlinear recurrence; complete-generator spectral scope, dissipation, conservative memory and boundaries of pulse stability and formation
Emergence and ontology	Which formation/identity claims are supported, which mechanisms can be reused, and which ontological claims remain open

Transport, memory and clocks

Mathematical owner	Domain and reuse boundary
EPI diffusion stability	Reversible and restricted time-varying diffusion, metric/solver bounds and finite executor evidence; not full-runtime stability
Directed nonnormal dynamics	Directed transport, transient amplification and clock changes; eigenvalue decay alone is insufficient
Derived EPI memory	Linear/affine hidden-state elimination, initial sources, observation closure and error propagation
Capacity and localization	Held-capacity balance, release and admission of proposed form/capacity laws
Cycle support dynamics	Joint cycle budgets and finite reorganization clocks under the stated phase/capacity laws
Cycle memory relaxation	Restricted delayed REMESH/history contraction; distinct from eliminating hidden phase/form state
Forced support balance	Held-source restoration, reference changes, event work and distinct charge/mean accounting under prescribed capacity, clock and support changes
Forced regional response and environmental readouts	Regional balances, represented phase reduction and environmental-input geometry.
Forced-source closure and phase clocks	Phase/capacity tangency, source constraints and the limits of synchronization as a clock.
Conditional phase locking and circulation geometry	P2 and network locking, capacity adaptation, circulation and cycle periods.
Winding generation and native writer boundaries	Acute winding retention, chart escape and native Mutation/capacity writer obstructions.
Geometric identity and capacity-feedback bounds	Local restoring response, geometric identity and prospective capacity tubes.
REMESH fixed-delay models	History companion systems, filters and runtime defects; no unrestricted infinite-runtime theorem
Scale, geometry and collective-state index	Pure-EPI coarse-graining and field geometry; chapter routes to pair state, pulse, grouping, mobility and interaction
Sufficient unordered pair state	Realizable pair invariants, internal-state reconstruction, unequal-capacity correlations and support-symmetry boundaries; global cancellation uses the declared fixed conservative doubled C5.
Internal replica pulses and their perturbations	The prepared internal pulse, complete variational law, small-amplitude splitting and persistent constituent activity under the same conservative doubled-cycle model.
Phase and joint form-phase grouping	State-derived pair observations, fully acute equilibrium geometry, finite grouping windows and joint-identity episodes; observation does not create support.
Pair geometry under alternative reciprocal mobility	The distinct complete positive-mobility law, grouping discriminator and protected relative geometry; old waveform, mean and volume claims do not transfer automatically.
Pair actions, regional exchange and cancellation	Local and whole-pair actions, autonomous regional form exchange, zero-resultant restoration, receiver law/orientation ambiguity, two-time discrimination with unknown coefficients and bounded continuous defects; joint geometric persistence and internal-allocation response.

Operators, grammar and support events

Mathematical owner	Domain and reuse boundary
Structural operators	Named transformations and their interpretation; registered catalog size does not prove mathematical completeness
Unified grammar	U1–U6 word and live-state contracts, with configured policy premises
Diagnostic and grammar scope	Counterexamples, constitutive closure audit and limits of grammar/diagnostic claims
Coupling and winding	Restricted cycle gap diffusion, winding retention and event/runtime exclusions
Relational support events	Native attachment, removal, event accounting and occurrence-law boundaries
Coherent pattern contact	Prepared contact, two-port recovery and formation barriers under its stated event/phase laws
THOL pressure feedback	History-driven pressure, refresh order and disconnected-child limitations
THOL birth and transport	Configured child creation, admitted transport and source/event accounting; not spontaneous substrate creation
Child coupling feedback	Child-target Coupling, changes of reference and comparison with the original profile

Diagnostics and geometry

Mathematical owner	Domain and reuse boundary
Minimal structural degrees	Complementary tetrad observations and counterexamples to complete-state reconstruction
Structural conservation diagnostics	Actual temporal balance, currents and residuals; a field energy needs its own monotonicity proof
Stability and dynamics diagnostics	Operational stability/lifecycle observations and their implementation boundaries
Extended fields	Algebraic derived quantities, availability and emergent-property audit; static statistics are not temporal laws

Auxiliary models and physical comparisons

Mathematical owner	Added premises and open bridge
Variational and exchange models	Auxiliary action/Hamiltonian read-outs, exact restricted diffusion bridges and conditional cotangent closure
Dissipative/open-system models	Specified forcing and dissipative constructions with their neutral-mode boundaries
Gauge and polarization constructions	Classical auxiliary symmetries; no engine-wide gauge or particle-unification theorem
Physical phenomena atlas	Conditional reductions and measurement prerequisites; shared collective-property comparison with geometry, charge/magnetic-response and quantum obligations

Arithmetic and applications

These are scoped mathematical constructions and application references, not parallel active campaigns or evidence that arithmetic nodes are physical NFRs. Historical R identifiers remain searchable here; their proofs own the claims.

Mathematical owner	Contribution and boundary
Number theory	Arithmetic encodings, pressure and primality criterion; supplied divisor information is explicit
Structural observability — R1	Symmetry sectors, nonlinear counterexamples and finite operator/selector scope
Arithmetic dynamics — R2	Pulse recurrence for the declared residue-network construction
CRT composition — R3	Chinese-remainder transport/product synthesis
p-adic dynamics — R4	Projective transport; a static lift is not a temporal REMESH echo
Algebraic number fields — R5	Finite/algebraic-field extensions and classification limits
Additive dynamics — R6	Controlled Fourier construction; no demonstrated TNFR-specific excess
Arithmetic pressure — R7	Channel independence and redundancy for primality; completeness remains open
Arithmetic operators — R8	Synthetic effect comparisons, not actual glyph/grammar execution
Riemann scope	Arithmetic/spectral constructions, reproduction entry points and unresolved analytic bridge; not a proof of RH

Research, measurement and parked evidence

Owner	Responsibility
Execution plan	Sole active F1–F4 task queue; supporting P1–P5 admission gates
Research strategy	Scientific rationale, premise review and reuse boundaries; scheduling belongs to the execution plan
Passive transport protocol	Independent measurement and clock mapping, calibration/evaluation separation
Regional phase/amplitude protocol	Collective observation map, uncertainty and data-source admission
Physical admission of the delayed digital-PLL realization	Source-specific complete-law and measurement audit, with a scoped delayed-history mapping obstruction; the published realization is not admitted to the fixed sine inference
TCLab comparison boundary	Short scope and archive route for the evaluated thermal comparison; no admitted physical validation
Parked C6 evidence boundary	Archive route and scope of the retained C6 certification evidence

Theory to execution

This map routes a model or responsibility to shared code and representative checks. The linked mathematical owner retains definitions, hypotheses and result-specific evidence; this page does not repeat its theorem inventory. Architecture owns dispatch, Testing owns test selection and commands, and the SDK guide owns usage.

Detached reports, exact prepared-family assessments and validated forecasts have different inputs and guarantees. Sine readers do not change native execution. Tangent, nonlinear and finite-response evidence remain distinct; an SDK adapter is not another law or a complete checkpoint. Case-study links provide access to retained evidence without reopening their campaigns.

Execution and constitutive foundations

Mathematical owner or model	Shared execution and admission	Representative checks
Nodal pressure and continuous flow	dnfr; canonical; form geometry; source relative form; relational	core-physics checks; form geometry; phase resultant chamber
Operator-word studies	SDK study; CLI study	SDK study; CLI study commands
Sine comparison admission	relational; sine admission; sine preparation; sine comparison	sine admission; sine comparison
Exchange, storage and information premises	relational; sine mediation; sine comparison; forced support; phase response	locality selection; exchange execution

Observation and constitutive discrimination

Mathematical owner or model	Shared execution and admission	Representative checks
Native coefficient and capacity response	observations; rational interval; SDK reports; capacity discriminator; interval taylor; acquisition	coefficient identification; coefficient scope; capacity sampling; capacity sampling response
Pressure and environmental observations	relational	pressure state
Declared-law and clock comparisons	sine resonance; linear observation; bridge discrimination	sine bridge channels; orthogonal form loss observation; bridge finite discrimination; bridge clock discrimination
Storage-family discrimination	phase storage	phase storage discriminator; phase storage discriminator dynamics

Native patterns, support and exchange

Mathematical owner or model	Shared execution and admission	Representative checks
Pattern composition and observations	observations; support transport; capture; transit	pattern observation; phase response
Support and event accounting	observations; selector symmetry	attachment; SDK reports
Native formation premises and obstructions	capture; formation robustness; reflected transit; validated taylor	formation admission; capture
Recovery, domains and capture	reflected transit; reflected equilibria; regularity; reflected boundary	reflected barrier; seeded response; regularity; resultant kinematics
Rhythm and precontact locking	See the linked owner.	local recovery; contact admission

Sine comparison, environmental state and recovery

Mathematical owner or model	Shared execution and admission	Representative checks
Complete sine response	sine resonance; linear observation	sine resonance; linear observation
Retained environment and exact causal memory	sine bridge memory; linear observation; sine comparison; sine mediation	sine bridge memory; sine bridge memory kernel
Hidden-state and capacity observation	sine observation	sine observation; sine capacity observation
Sample admission and reserved forecasts	sine forecast; sine prior forecast; observations; sine sampling	sine forecast; sine prior protocol; sample jet; sine sampling
Relative state and recovery	sine pattern; sine recovery	sine pattern; environment response; sine recovery; sine pattern recovery

Collective state, geometry and constitutive alternatives

Mathematical owner or model	Shared execution and admission	Representative checks
Sufficient pair state and cancellation	sine pair	phase moment information; sine global pair state; sine pair cancellation observation
Pair actions and form exchange	al sha stage proposals; sine comparison; sine scale; sine pair	pair emission; pair emission observation; regional transfer observation; finite pair exchange; receiver readout; receiver constitutive ambiguity; two-time receiver discrimination; two unknown law coefficients; continuous receiver defects; persistent internal-allocation response
Internal pulse, variation and work response	replica pulse	sine replica stiffness trace curve; sine replica pulse work response; sine replica pulse finite work response
Pair grouping and identity observations	sine scale	joint grouping; joint grouping observation; joint identity observation
Alternative reciprocal mobility	sine comparison	sine comparison

Formation, memory and remaining integration paths

Mathematical owner or model	Shared execution and admission	Representative checks
Exact and controlled reductions	sine forecast; sine reduction; sine preparation; sine recovery	sine exchange equivalence; sine form reconstruction; sine sector storage intersection
Sine preparation, composition and capture	sine budget; sine preparation; sine symmetry; phase cycle geometry; sine recovery; sine sector boundary; sine composition; sine entry; formation response; formed classes and probe	sine budget; sine symmetry; acute cycle periods; sine sector capture; preparation reuse; formation response; formed class pair; formed class response; central contact controls
Repeated probes of formed classes	formed class maintenance	formed class maintenance
Strict nonlinear recovery on an admitted acute chart	shared sine Lyapunov bounds, consumed by maintenance and unprobed contact handoffs	independent Lyapunov bounds and reuse
Actual formed-class contact	formed class contact	formed class contact; central contact controls
Reduced formed-class ports	reduced class ports; shared actual-family contact handoff	reduced class ports; retained full contact; retained bundle integrity
Degree-aware port-network composition	network assembly and bounds; shared unit-contact geometry; actual-family handoff	port-network composition; retained two-component reduction; retained bundle integrity
Class-mediated collective response	paired full-family assessment; shared actual-source handoff; joined identity bounds; retained first assessment	primitive admission and source availability; independent full-support response and work algebra; read-only frozen-evidence audit; SDK projection
Acquired-mediator effective memory	full spatial factors and conditional nonlinear-error bound; shared rational coordinate partition; shared class-response coefficients	admission, parameter provenance and conditional bounds; independent full-law kernel, stationary map and closure controls; unchanged frozen-response audit; SDK projection
Two-probe nonlinear superposition	conditional response and event bounds; shared complete-support coefficients	primitive admission and separated conditional guards; independent symmetry, mixed onset and noise-overlap algebra; unchanged frozen-response audit; SDK projection
Finite nonlinear interaction protocol	exact heat-polynomial coefficient and remainder; validated four-history producer; shared held sine field; prospective frozen evaluation; retained first outcome; shared event admission	conditional separation controls; independent coefficient/error algebra; producer admission and partial failure; independent full-state/source/prefix controls; held-field controls; retained Taylor arithmetic; read-only freeze integrity; retained full-response arithmetic audit; independent protocol arithmetic; shared box Taylor; unchanged frozen-response audit; SDK projection
Organization-dependent nonlinear interaction	common-channel contrast and full error budget; shared heat and remainder owner; shared event bounds	admission, unresolved bounds and exact margins; independent class-channel, onset and error algebra; unchanged source evidence; SDK projection
Complete cubic-amplitude class contrast	triangular coefficient and full-law remainder; shared exact contrast decisions; shared event bounds	coefficient admission and carried events; independent hierarchy, parity and tail algebra; retained evidence reconstruction; exact observation decisions; SDK projection
Spatial nonlinear class observation	receiver projection and full-law bound; shared full-coordinate coefficients	admission and observation controls; independent locality and amplitude algebra; compact evidence reconstruction; shared reading-count decisions
Common-scale amplitude feasibility	conditional interval calculator; shared carried-event ledger	primitive and domain admission; independent homogeneity and event algebra; retained coefficient association; SDK projection
Independent class comparison protocol	two-source full-state composition; shared evidence reconstruction; source transfer and protocol arithmetic; retained comparison	source admission, first failure and evidence controls; independent source, width and noise algebra; read-only freeze association; retained full-response audit; source restoration
Repeated joined class interaction	conditional exact bounds; shared modified-energy kernels	joined geometry, carried means, work and return; reconstructed reference association
Nonlinear collective interface	port structure and conditional error bounds; shared amplitude-tail owner; repeated work and return	port, memory, work and source controls; reconstructed cubic premise
Changed-input collective prediction	causal grounded-path evaluator; fixed admission and observation policy	causal coefficient and source controls; independent work and strict comparison controls; retained prediction audit
Independent changed-input full-law protocol	two-source complete-flow producer; retained step and endpoint reconstruction; source transport, inspected prediction and fixed assessment	producer admission, complete-state carry and partial evidence; independent source and observation policy; freeze association without response execution; retained first comparison with read-only response audit; shared box Taylor arithmetic
Causal component composition	degree-aware factorization and primitive residual bounds; shared coordinate-memory partition	independent row, balance, source and residual controls; substitution of the reconstructed retained observation
Distinct-neighbor nonadditivity	static edge bounds, mixed response and event admission; shared source fidelity; shared event ledger	independent onset, finite bounds, observation and event controls
Independent distinct-neighbor protocol	shared four-history producer; full evidence reconstruction; source transport and prospective decisions	selector, state carry and failure controls; independent source and observation policy; read-only freeze association; synthetic evaluator wiring; retained response reconstruction
Nonlinear excess storage and loss	static onset, adjoint cones and complete error accounting; shared phase cones; common-source fidelity; prepared passive-loss observer and arithmetic reader	independent balances, exact edge algebra, finite sign and observation bounds; prepared observer wiring, field algebra and unrelated reference
All-time reduced-port tracking	uniform tracking assessment; shared joined-state bounds; degree-aware surrogate	parity tracking and channel resolution; retained finite composition; retained bundle integrity
Ordered heat form tracking	form comparison assessment; fresh baseline admission	heat gains, initial exchange and preserved channel criteria; retained bundle integrity
Two-port C9 compatibility and storage handoff obstruction	joint equilibrium and handoff assessments; shared cycle geometry	two-port equilibrium and null controls; handoff boundary-witness controls; retained bundle integrity
Finite two-port directional transit	full-law transit assessment	directional transit and complete-state controls
Prepared two-port capture	validated reference and full-state capture; shared retained-metric Taylor kernel	reference geometry and capture controls; retained evidence
Supplied two-port probe and maintenance	conditional endpoint probe assessment; retained finite source handoff	finite response, work and recovery controls; source-handoff admission; retained evidence
Interior phase-dipole response	finite warmup and response assessment; shared modified-energy kernels; retained source handoff	dipole, heat-control and recovery controls; modified-energy kernel controls; source-handoff admission; retained evidence
Calibrated two-port geometry inference	local response inverse; independent full-law readout; shared source-box Taylor step; shared affine family	geometry and inverse admission; full-law readout; source-box Taylor; SDK projection
Two-pulse geometry and gain inference	joint outer inverse; shared source geometry; complete-flow producer; outward angle and norm arithmetic	paired response, memory, observation correlation and admission; retained two-input bundle with read-only evidence audit; SDK projection
Geometry and gain with an uncertain clock	constant-clock adapter and marginal projections; shared two-input constraint envelope	clock domains, scale reduction, projections and equivalence boundaries; joint-inverse controls; SDK projection
Finite-curvature information and refinement	four-reading constraint and marginal projection; shared clock envelope; retained software evaluation	source/derivative error, observation association and necessary refinement; clock controls; read-only frozen-bundle audit; SDK projection
Clock drift and sampled exposure	mean-rate adapter and reading transfer; fresh reference curvature constraints; retained nonconstant-clock evaluation	exposure equivalence, drift transfer, reduction and admission; curvature controls; read-only frozen-bundle audit; SDK projection
Finite-aperture observation	boxcar moment and error adapter; validated affine-clock average producer; retained software evaluation	moment exactness and necessary projections; full-state integral carry and partial failure; read-only frozen-record audit; shared source-box Taylor controls; SDK projection
Finite-noise and horizon resolution	response-free rational budget	independent moment/error budgets, guard boundaries and noise-overlap controls; SDK projection
Archived eleven-node receiver case	sine formation; receiver barrier; phase cycle geometry; sine equilibria	sine formation; sine formation barrier; sine receiver protocol; sine forecast

Conservative acquisition, feedback and finite maintenance

Mathematical owner or model	Shared execution and admission	Representative checks
Source admission and regional entry	sine regional; sine partition; sine entry; sine comparison	sine cycle barrier; sine contact averaging; sine conservative passage; sine regional forecast; sine regional forecast integrity; sine phase accessibility; conservative regional organization protocol
Conservative saddle and corridor preparation	sine symmetry; sine resonance; sine corridor; sine sensitivity	sine involution reduction; sine c5 leaf saddle; sine saddle corridor; sine saddle corridor integrity; sine saddle preparation; sine saddle sensitivity
Metric forecasts and frozen preparation records	validated metric; sine metric forecast; sine metric connection; sine constitutive robustness	validated metric taylor; sine saddle metric forecast; sine metric connection protocol; sine constitutive robustness
Collective phase families and finite retention	sine entry; sine partition; sine regional	sine conservative handoff; SDK reports; sine phase offset partition; sine phase offset partition dynamics; sine moving pattern window; sine reversible preparation; sine reversible preparation protocol
Collective contact feedback	sine partition	sine collective pulse balance; sine collective pulse balance dynamics; collective pulse organization protocol

Memory and inverse response

Mathematical owner or model	Shared execution and admission	Representative checks
Retained native phase records	cycle memory; memory contact	cycle memory; cycle memory mechanism
Native mediator and memory reduction	linear observation	linear observation; mediation; memory response
Return geometry and native response	phase cycle geometry; relational	phase cycle geometry; return geometry; return path geometry protocol; uniform tangent; SDK uniform tangent
Effective mediated connections	relational	effective link; mediation

Other runtime boundaries

Mathematical owner or model	Shared execution and admission	Representative checks
Fields and diagnostic provenance	fields; SDK study	field readout consistency; SDK study
Operator events and relation admission	operator contracts; network stage; neighbor differences; dnfr; edge semantics	operator event runtime; stable neighbor pressure
Delayed digital-PLL physical admission	primary-methods source receipt; no physical execution or fixed-sine adapter admitted	exact detector, history and phase-map controls
Arithmetic applications	See the linked owner.	See the linked owner.

Historical aliases and maintenance

The former S1–S16 labels covered stability, state/reduction, support, observation and identity questions now routed by subject above. R identifiers remain on their arithmetic owners. Neither those labels nor the old B0–B11 catalog audit prove universal operator completeness or constitute a task queue.

The archive owns recovery records and retired programme boundaries. Retain frozen model, preparation, source, precision and verdict; corrections require separate evidence. Archived instructions do not activate work.

Update this catalog when ownership, scope or navigation changes. Update definitions and affected implementation/tests together; task status belongs only to the execution plan.