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Shadow Theory

The technical companion

Choose the question. Follow the inference.

The supplement’s purpose, conventions and dependency guide explain how the ten modules support distinct parts of the investigation.

A technical companion to the current-act account

The ten modules develop the full mathematical, empirical and philosophical depth behind From Physical Comparison to Relational Appearance: A Defeasible Current-Act Account. They belong to the same publication, Jeremy Rodgers, Version 1.4, 16 October 2026, DOI 10.5281/zenodo.23408737.

The supplement is organised by inference rather than research chronology. Module A develops adequate-source and calibration constraints; B treats occurrence, inclusion and ownership; C distinguishes finalisation, access, sampling and resource contracts; D studies retention, reset and return; E constructs and tests exact native causal fields; F develops metric and realisation-identification diagnostics; G records empirical methods and the retrospective application; H preserves typed constitutive alternatives and countermodels. Each module states which conclusion its result can support and which connecting premise remains separate.

Follow the argument

Readers assessing the main conclusion should begin with the corrected concrete-performance argument in §§8.10–8.12, the actual archive and its interpretive limits in §§7.2–7.5, and the presented-form and basing distinctions in §9.1 and §9.5. These develop the premises used by the main argument. The content-signature theorem in §§9.2–9.4 is a separate conditional constraint on content laws, not a proof of actual occurrence or bearer identity.

For the main objections, §§8.3–8.5 separate causal, epistemic and bearer claims, and §8.6 develops the mixed-act alternative. The pair/common-witness distinction in §2.2 and the current-source counterexamples in §9.5 explain why separate successful reports or faithful transmission need not establish one operative current field. Empirical provenance, exposure and supplementary analyses are in Module G; Module J provides selected further applications and the fixed predictive failure, with reproduction limits stated at the end.

Modules A and C–F provide optional technical investigations of adequate descriptions, access, retention, native causal structures and metric recovery. Their full assumptions and proofs remain available without being premises of every main-paper inference. In particular, §§3.1–3.2 distinguish abstract common finalisation from a fixed passive apparatus’s early marking ability; their difference does not determine phenomenal onset. Readers pursuing those technical questions can follow their internal dependencies without treating the supplement’s order as a cumulative proof of a universal manifestation law.

Notation and evidential conventions

The physical nomination PP and experience-inclusive act AA follow the main paper. QQ denotes a qualitative mode except in explicitly subscripted probability kernels Qb(⋅∣h)Q_b(\cdot\mid h). HH is a causal-prefix history, CC a nominated final content, and μ\mu a prefix law. Total variation is

TV⁡(ν,ν′)=sup⁡E∣ν(E)−ν′(E)∣. \operatorname{TV}(\nu,\nu')=\sup_E|\nu(E)-\nu'(E)|.

Finite models use sums; extensions to general spaces require the stated measurability and disintegration conditions and are not presumed by notation alone. In the parity construction qq is the correct-update probability, η=1−q\eta=1-q, and Lq=log⁡2(2q)L_q=\log_2(2q); a graph Laplacian is written LL.

Formal examples with assigned phenomenal labels are countermodels or tests of proposed laws, not observations of appearance. Published experimental findings are attributed to their original authors. The principal actual application is an already exposed archive reanalysis; data hashes certify provenance and decoding rather than QQ. Established mathematical machinery is cited where it enters, and scope-sensitive corrections are carried into the derivations.

The publication describes an accompanying public reproducibility archive that separates directly runnable finite checks from empirical analyses requiring external public data. Its README specifies acquisition instructions, schemas, hashes and expected outputs. Recorded outputs are supplied for comparison; they do not replace the proofs or the stated empirical and constitutive warrants. The website preserves these source-reported claims; implementing this web edition does not constitute a rerun of those experiments.

Module I develops the presented-form argument, the exact target-specific content-signature theorem and the separation of current sensory basing from physical-port constitution. Module J places selected empirical extensions and a failed fixed predictive assay beside the claims they constrain. Module B distinguishes occurrence, recognition, personal appropriation and retrospective interpretation. These materials extend the argument without changing the original archive into a fresh validation study or treating the open general manifestation law as resolved.

The complete technical sequence

Module Investigation Source sections
A: Adequate sources, quotients and calibrated identification What a physical source preserves, what a decoder can recover, and what calibration identifies 1.1–1.6
B: Occurrence, inclusion and ownership Faithful tokens, common witnesses, ownership, constitutive alternatives and the SPC-2 bridge 2.1–2.16
C: Finalization, selection and physical access Common finalisation, passive marking, sampling and information bounds 3.1–3.9
D: Retention, reset, recurrence and return Physical retention, erasure, access windows and native return 4.1–4.7
E: A selected native parity structure and its limits Exact native parity, distinctions, relations and symmetry 5.1–5.7
F: Spatial response, native equivalence and relational events Metric response, native interventions, clocks and optical geometry 6.1–6.7
G: Empirical application, measurement and temporal scope Ebbinghaus archive, calibrated interpretation and other empirical applications 7.1–7.12
H: Typed epistemic and constitutive arguments Countermodels, mixed acts, identity and the corrected performance principle 8.1–8.12
I: Presented form, content signatures and current sensory basing One-form relational content, exact symmetry constraints and basing 9.1–9.6
J: Presented form, empirical tests and the limits of transfer Further applications and the failed fixed neural predictive assay 10.1–10.5

Publication references retain the source attribution for both the main article and this technical companion.