Appendix FSPC-2 · Version 2

Notation, claim status, and construction dependencies

Jeremy Rodgers · Independent Researcher
20 September 2026 · doi:10.5281/zenodo.22853774

Publication PDF · p. 127 ↗Chapter Markdown Original LaTeX Publication record

Reading position 36 of 37

F.1 Principal notation

Symbol	Meaning
Symbol	Meaning
$\unsplit$	Reality prior to operational distinction; an ontological notation, 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 source-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 primitive awareness	Ontological hypothesis: awareness as the knowing aspect of $\unsplit$ ; no 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.
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.

F.4 Reproducibility and provenance

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.