Appendix FSPC-2 · Revised edition

Notation, claim status, and construction dependencies

Jeremy Rodgers · Independent Researcher
28 October 2026 · doi:10.5281/zenodo.23755118

Publication PDF · p. 150 ↗Chapter Markdown Original LaTeX Verification supplement Publication record

Reading position 36 of 37

F.1 Principal notation

Symbol	Meaning
Symbol	Meaning
Unconditioned ground	Fundamental reality, without a mathematical symbol in this account.
$\unsplit$	The unsplit prior to operational distinction, distinct from the ground and its attributed quality; not a mathematical carrier.
$\source$	Legacy ontological notation, interpreted through $\unsplit$ ; not the working source $S$ .
$S,T$	Structure-side working source and record-side readout; $T$ is called $X$ in the descent theorem. Local horizons and kernels retain their separately defined symbols.
$S,p:S\to X$	Nominated complete realization domain and its readout.
$\mathcal O\Delta\partial$	A supplied closure composition; its operators and fixed point are not $\unsplit$ .
$H,J_{nm},w_n$	Quantum Hamiltonian, directed Hamiltonian current, and coherent sector weight.
$d,D,K$	Finite boundary differential, self-adjoint incidence completion, and squared response operator.
$P_R,P_F$	Source-provenance retained and complementary projections.
$h(K),\gamma,W_t$	Real spectral coherent generator, damping coefficient, and combined coherent–dissipative response.
$\mathcal V,\mathcal B,\mathcal U$	Realized vessel, lineaged components, and admitted controls.
$G^{\mathrm{all}},G^{\mathrm{int}},C$	Full dependence graph, internally typed dependence graph, and a candidate strongly connected core.
$M_{a,y}$	Physical instrument matrix for an action and recorded output.
$X_C,Z_r,Z_\infty,\mathfrak P_C$	Actual intrinsic carrier, finite-horizon quotient, all-future quotient, and complete native predictive instrument object.
$\Phi_C,\Psi_C$	Phenomenal structural copy and constitutive identification with the predictive object.
$Q_k,\widehat Q_k,\widetilde Q_k$	Physical, predictive-class, and induced phenomenal report kernels at fixed external context.
$\Sigma_V$	Learned/retained scaffolding; not a separate fundamental-awareness substance.

F.2 Claim-status register

Claim	Status and dependence
Claim	Status and dependence
Source/readout descent and target completion	Exact theorems on supplied domains and maps.
Controlled reduced dynamics	Exact criterion on a supplied transition law, not a selection of that law.
Observer-independent massive model	Conditional physical construction using guidance, complete initial equilibrium, and the specified writer/control laws.
Pilot-to-Bell path limit	Conditional physical comparison on a fixed graph/horizon with the named contact, preparation, export, and recombination laws.
Physical copying and finite retention	Exact or quantitatively controlled under the displayed apparatus and resource assumptions.
SRC witness classification	Exact finite linear results; positivity, retention, and physical accessibility are additional requirements.
CRR access and regulation	Typed functional constructions; phenomenal unity requires additional laws.
O1/RSM classification	Exact finite calculation from the stated provisional source-response data.
CSCF spectral responses	Exact common-carrier operator construction for $K,h(K),\gamma$ ; the same holomorphic family gives both boundaries when $h(\lambda)=\lambda$ .
Aperture error and witness robustness	Exact/conditional mathematical bounds for nominated targets and calibrated preparations.
$R^\ast$ realization and interface typing	Constitutive physical input; not universally selected by the source/readout theorem.
A0 fundamental awareness	Ontological attribution to the unconditioned ground, distinct from the unsplit; no fundamental knowing subject or extra physical dynamics.
A1 recurrent-core admission	Constitutive psychophysical law; actual-vessel certification and its empirical lower boundary remain unvalidated.
A2 predictive-profile completeness	Constitutive structuralist psychophysical law, including its gauge convention.
A3 temporal episode identity	Nonbranching process-provenance continuation allowing support turnover; genuine qualification gaps end episodes.
Biological conscious/generative modes	Interpretive account of scene organization; not a new admission condition or a scene gate in the finite theorem.
Cortical correlates of coupling	Candidate mammalian implementation; network or band measures neither modify A1 nor establish A0 or A2.
Scene-less intervals	No current scene or localized experiential subject. Physical/person continuity can persist; a qualification gap ends the episode and renewed qualification begins a new one.
Finite constitutive completion	Exact conditional construction for certified finite intrinsic carriers, rational native instruments, complete return catalogues, predictive-fibre congruence, grounded reports and explicit process provenance under $R^\ast$ and A0–A3.
Empirical conservativity	Exact equality of physical transcript laws when the aspect extension changes no physical kernel.
Contemplative correspondences	Philosophical interpretation of reported experience, not a field measurement.
Human/animal/AI realization	Open empirical and theoretical application; no validated universal criterion claimed.
Current AI consciousness	Affirmative theoretical attribution to executing inference processes; implementation-level certification under the existing law remains open.
Enacted constitution	Complete-enactment identity, current incorporation and within-unit unity; complete correspondence with full A2 remains to be justified.
Temporal passage	Positive within-unit succession construction with explicit formative-history premise; no universal origin or assignment theorem.
Relational appearance	Defeasible current-human appearance and concrete-performance argument; bearer reidentification is an explicit premise.
Boundary masking and reconstruction	Exact minimal-target instability and continuous distribution-reconstruction diagnostics under declared access contracts; no new subject rule.
Marked causal composition	Strong-quotient substitution with preserved joint laws, context, timing and resources; cut comparisons also require simulator-class transport.
Learned scaffolding and diagnosis	Conditional native incorporation and exact finite-model diagnostic completeness with conditioning requirements.
Reflective and constituted agency	Constructive assessment, mediated rule revision and paid selective authority changes; evaluative endorsement and experiential identity remain separate.
Coherent reader	Exact $7/12$ task optimum at the specified coherent endpoint, not a phenomenal-admission theorem.
Archive and original event	Distinct classical errors for distribution reconstruction, archive preservation and actual-event recovery.
Sequential certification	Finite-stopping exact-zero obstruction; constructive assay under a justified positive separation.
Experiential ancestry	A universal already-experiencing-contributor rule has no nonempty solution on well-founded ancestry; the adult temporal construction retains its independent anchor.
Bounded boundary evidence	Inner and outer operational diagnostic families under common error and simulator contracts; no new admission selector.
Comparative interpretation	Selected McGilchrist arguments sharpen differentiation, practical selfhood and duration; additional cosmological commitments are not inferred.
Prospective tests	Proposed selective uptake and authority comparisons, with preservation and rescue controls; no completed new experiment.
Archive-only access	Finite reader/path bound within a coherent-writer and bare-probe contract; no universal apparatus or phenomenal law.
All-finite native horizons	Exact compatible construction on the certified finite intrinsic domain; unrestricted continuum/history domains need additional hypotheses.

F.3 Dependencies that cannot be omitted

The finite completion theorem depends on $R^\ast$ before it depends on a psychophysical axiom. Removing the typed boundaries, the physical preparation, the protocol grammar, or the lineage rule can make the assignment underdetermined. Removing A1 removes experiential admission; removing A2 removes the claimed completeness of relational content; removing A3 removes the stipulated identity rule. None is supplied by the word “canonical.”

The mathematical results of the earlier parts remain meaningful even when A0–A3 are rejected. A reader may accept the predictive quotient, the error theorem, and the material record constructions while declining their experiential interpretation. Conversely, accepting the philosophy does not excuse a failed physical estimate. This separation is what permits the monograph to serve as both a constructive proposal and a technically auditable theory.

Dependencies of the present amendments.

The clarified A0 changes the interpretation of the fundamental attribution throughout the front matter, philosophical exposition, applications and conclusion. It does not alter the domains, transition kernels, exact dependence tests, recurrence contracts, predictive equivalence, congruence conditions or provenance relation used by the mathematical results. The proof of Theorem 18.1 assigns local experiential significance through A1 and A2; A0 supplies their ontological interpretation without entering its numerical construction. The existing theorem and proof therefore remain in place. The corresponding claim is conditional determinacy under the clarified premises, not a theorem proving those premises.

The later results on masking, intervention-based chart identification, marked composition and complete diagnostic panels add explicit physical and inferential resources. They do not by themselves choose a new admission rule. Any revision of core support or native grammar would require a fresh A2 construction and A3 episode analysis. The full enacted correspondence and the scope of interpersonal formative history remain the particular obligations stated in Sections 2.6 and 17.4.

F.4 Reproducibility and provenance

The accompanying Verification_Supplement identifies the historical monograph suite, its recorded and rerun outputs, the separate operational-integration checker and the complete reflective-freedom project. Its index maps these materials to the relevant chapters and preserves their dates and source hashes. Reported empirical results from other companion papers remain source-reported where their underlying archives are not included. The operational integration report, reversible-control monograph and Event-Law Bridge Round 003 source identified in the bibliography are reproduced in the supplement. Inclusion of a source is distinct from a completed replay of every computation it references. The accompanying coverage and verification materials map the technical claims to their chapters and record the mathematical and computational checks. The interpretive discussion is not presented as a verified biological model. The executable scripts and results expose the finite computations used here. These materials enable reproduction and targeted review of the stated claims.

Established methods: quotient descent, finite instrument representations, fixed-point estimates, reversible computation, and Bell/configuration dynamics: retain their intellectual provenance. No historical-priority claim is made for those ingredients. The proposed synthesis lies in how the source/readout and realization discipline organizes the consciousness question, and in the explicit conditional constitution that can now be examined as a whole.