# References
## Bibliography
[1] J. Rodgers. *Shadow Theory and Consciousness: Awareness, Perspectival Realization, and the Source-to-Experience Problem*. Version 2, 20 September 2026. doi:[10.5281/zenodo.22853774](https://doi.org/10.5281/zenodo.22853774). Author's public publication listing checked 30 September 2026; the exact source snapshot used here is indexed in the supporting package.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-1) · [Supporting material and release status](/consciousness/research/paper-4/supporting-material-and-release-status#citation-32)
[2] J. Rodgers. *Relational Boundaries and Awareness Localization: Robustness, Composition, and Identification Limits*. Paper 2, version 1.0, 29 September 2026. doi:[10.5281/zenodo.23075822](https://doi.org/10.5281/zenodo.23075822). Preserved source version: supporting-deposit item P2 in reference [[20](/consciousness/research/paper-4/references#bib-support)].
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-1)
[3] J. Rodgers. *Learning Effective Interfaces from Opaque Stochastic Systems: Capacity, Selection, and Validation Limits*. Paper 3, revised version 2 with post-hoc optimization sensitivity, 29 September 2026. doi:[10.5281/zenodo.23075824](https://doi.org/10.5281/zenodo.23075824). Preserved source version: supporting-deposit item P3 in reference [[20](/consciousness/research/paper-4/references#bib-support)].
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-2)
[4] J. Rodgers. *Assignment Determinacy without Unique Componentization: A Finite Realization Doctrine and Exact Logical Application*. FRD-1 report, 30 September 2026. Sections 2–4 (FRD-01–FRD-04); doctrine, proofs, and extractor. Supporting-deposit item FRD1 in reference [[20](/consciousness/research/paper-4/references#bib-support)]; public location pending.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-3) · [Section 2](/consciousness/research/paper-4/inherited-benchmark-and-conditional-assignment#citation-8)
[5] J. Rodgers. *Register-Local Preservation and a State-Recoding Obstruction for Finite SPC-2 Realizations*. FRD-2 report, 30 September 2026. Section 3.2 (P2–P3) and Section 4 (P4). Supporting-deposit item FRD2 in reference [[20](/consciousness/research/paper-4/references#bib-support)]; public location pending.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-3) · [Section 2](/consciousness/research/paper-4/inherited-benchmark-and-conditional-assignment#citation-7) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-25)
[6] J. Rodgers. *Native Implementation and Formalism Sensitivity in a Frozen SPC-2 and IIT Comparison*. Completed CCI-1 technical note, 30 September 2026, Sections 2–4. Supporting-deposit item CCI1 in reference [[20](/consciousness/research/paper-4/references#bib-support)]; public location pending. This is the executed result, not the earlier preparation checkpoint.
Cited in: [Section 2](/consciousness/research/paper-4/inherited-benchmark-and-conditional-assignment#citation-10) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-30)
[7] A. Hyvärinen, H. Sasaki, and R. E. Turner. Nonlinear ICA using auxiliary variables and generalized contrastive learning. *Proceedings of Machine Learning Research* 89, 859–868 (2019). [https://proceedings.mlr.press/v89/hyvarinen19a.html](https://proceedings.mlr.press/v89/hyvarinen19a.html).
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-23)
[8] I. Khemakhem, D. P. Kingma, R. P. Monti, and A. Hyvärinen. Variational autoencoders and nonlinear ICA: A unifying framework. *Proceedings of Machine Learning Research* 108, 2207–2217 (2020). [https://proceedings.mlr.press/v108/khemakhem20a.html](https://proceedings.mlr.press/v108/khemakhem20a.html).
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-23)
[9] A. Yeredor. Independent component analysis over Galois fields of prime order. *IEEE Transactions on Information Theory* 57(8), 5342–5359 (2011). doi:10.1109/TIT.2011.2145090. Accessible antecedent version: *Independent Component Analysis Over Galois Fields*, arXiv:1007.2071v1 (2010).
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 5](/consciousness/research/paper-4/which-stochastic-continuations-remain-common#citation-13) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-26)
[10] A. Painsky, S. Rosset, and M. Feder. Generalized independent component analysis over finite alphabets. *IEEE Transactions on Information Theory* 62(2), 1038–1053 (2016). doi:10.1109/TIT.2015.2510657. Accessible preprint: arXiv:1508.04934v1 (2015).
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-24)
[11] P. K. Rubenstein, S. Weichwald, S. Bongers, J. M. Mooij, D. Janzing, M. Grosse-Wentrup, and B. Schölkopf. Causal consistency of structural equation models. *Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence* (2017). Accepted manuscript: arXiv:1707.00819v1.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-27)
[12] S. Beckers and J. Y. Halpern. Abstracting causal models. *AAAI* 33, 2678–2685 (2019). doi:10.1609/aaai.v33i01.33012678.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-4) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-27)
[13] W. Hoeffding. Probability inequalities for sums of bounded random variables. *Journal of the American Statistical Association* 58, 13–30 (1963). doi:10.1080/01621459.1963.10500830.
Cited in: [Section 4](/consciousness/research/paper-4/a-constructive-diagnostic-for-the-frozen-implementations#citation-11)
[14] L. Albantakis et al. Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. *PLoS Computational Biology* 19, e1011465 (2023). doi:10.1371/journal.pcbi.1011465.
Cited in: [Section 6](/consciousness/research/paper-4/executed-official-intrinsic-grain-comparison#citation-14) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-28)
[15] W. Marshall, G. Findlay, L. Albantakis, and G. Tononi. Intrinsic units: identifying a system's causal grain. *Neuroscience of Consciousness*, niag013 (2026). doi:10.1093/nc/niag013. Equations 16–17 and intrinsic-unit construction.
Cited in: [Section 1](/consciousness/research/paper-4/question-scope-and-relation-to-previous-work#citation-5) · [Section 6](/consciousness/research/paper-4/executed-official-intrinsic-grain-comparison#citation-18) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-28)
[16] W. G. P. Mayner, W. Marshall, and G. Tononi. Intrinsic cause–effect power: The tradeoff between differentiation and specification. *Entropy* 28(4), 410 (2026). doi:10.3390/e28040410. Accessible authors' preprint: arXiv:2510.03881v1. The preprint, publication metadata, and pinned executable are distinguished; the full final publisher text was not retrieved in this repair.
Cited in: [Section 6](/consciousness/research/paper-4/executed-official-intrinsic-grain-comparison#citation-17) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-29)
[17] W. G. P. Mayner et al. PyPhi: A toolbox for integrated information theory. *PLoS Computational Biology* 14(7), e1006343 (2018). doi:10.1371/journal.pcbi.1006343. Executed source revision: `2b98c1d5bba246c042fd1c65618ebad86196342a`; archived distribution `2.0.0rc3.dev6+g2b98c1d5b`.
Cited in: [Section 5](/consciousness/research/paper-4/which-stochastic-continuations-remain-common#citation-12)
[18] Official PyPhi documentation. *Conditional independence*. [https://pyphi.readthedocs.io/en/latest/theory/conditional-independence.html](https://pyphi.readthedocs.io/en/latest/theory/conditional-independence.html). Accessed 30 September 2026.
Cited in: [Section 5](/consciousness/research/paper-4/which-stochastic-continuations-remain-common#citation-12)
[19] Official PyPhi documentation. *Searching across grains*. [https://pyphi.readthedocs.io/en/latest/howto/grain-search.html](https://pyphi.readthedocs.io/en/latest/howto/grain-search.html). Accessed 30 September 2026. Executed definitions are pinned by the archived source rather than a moving documentation endpoint.
Cited in: [Section 6](/consciousness/research/paper-4/executed-official-intrinsic-grain-comparison#citation-15)
[20] J. Rodgers. *Paper 4 supporting research: frozen FRD-1, FRD-2, and completed CCI-1 reports, source, results, and review evidence*. Planned public supporting deposit, package version 1.1-RC1, 30 September 2026. Public supporting-deposit DOI not supplied. Exact items MONO, P2, P3, FRD1, FRD2, CCI1, P4, and REVIEW are located in `publication/PUBLICATION_DEPENDENCY_MAP.md` in the accompanying package. No public supporting-deposit DOI was supplied for this web edition.
Cited in: [Section 2](/consciousness/research/paper-4/inherited-benchmark-and-conditional-assignment#citation-9) · [Section 6](/consciousness/research/paper-4/executed-official-intrinsic-grain-comparison#citation-16) · [Section 7](/consciousness/research/paper-4/novelty-limitations-and-verification-status#citation-31) · [Supporting material and release status](/consciousness/research/paper-4/supporting-material-and-release-status#citation-33) · [References](/consciousness/research/paper-4/references#citation-38)