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Shadow Theory

Certified Target-Sufficient Readout Design and Exact Finite-Model Reduction

References

Jeremy RodgersSection 11 of 11Original PDF ↗Publication DOI ↗

References

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[3] Claude. A 2o(n) time algorithm for 3-sat, 2026. URL https://github.com/anthropics/fo rmal-math/blob/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth/paper.pdf. Supplied manuscript dated 26 October 2026; Anthropic affiliation.

[4] Frank R. Kschischang, Brendan J. Frey, and Hans-Andrea Loeliger. Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory, 47(2):498–519, 2001. doi: 10.1109/18.910572. URL https://www.isiweb.ee.ethz.ch/papers/arch/aloe-2001-1.pdf.

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[6] Ryan O’Donnell. Analysis of Boolean Functions. Cambridge University Press, 2014. doi: 10.1017/ CBO9781139814782. URL https://arxiv.org/abs/2105.10386.

[7] OpenAI. The exponential time hypothesis is false, 2026. URL https://github.com/openai/ma th/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-202 6/paper.pdf. Dated 17 October 2026, revised 25 October 2026; supplied manuscript.

[8] OpenAI. Scope of the lean formalization: The exponential time hypothesis is false, 2026. URL

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[9] OpenAI. Working with academic communities to build scientific understanding, October 2026. URL https://openai.com/index/building-scientific-understanding-with-academic-c ommunities/.

[10] Jeremy Rodgers. Target-relative necessity of completion: When readout loss obstructs, and what a sufficient extension must retain, 2026.

[11] Jeremy Rodgers. Canonical minimal source completion: The coarsest readout extension on which a nominated family of source relations becomes well defined, 2026.

[12] Jeremy Rodgers. Observable quotients and exact projected dynamics: Closure, memory, minimal dynamical completion, and effective field operators, 2026.

[13] Alexander D. Scott and Gregory B. Sorkin. Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function. ACM Transactions on Algorithms, 5(4):45:1–45:27, 2009. doi: 10.1145/1597036.1597049. URL https://people.maths.ox.ac.uk/scott/Papers/c ounting.pdf.

[14] Sukhwinder Singh and Guifre Vidal. Global symmetries in tensor network states: Symmetric tensors versus minimal bond dimension. Physical Review B, 88:115147, 2013. doi: 10.1103/Phys RevB.88.115147.

[15] Sukhwinder Singh, Robert N. C. Pfeifer, and Guifre Vidal. Tensor network decompositions in the presence of a global symmetry. Physical Review A, 82:050301, 2010. doi: 10.1103/PhysRevA.82. 050301.

[16] Armando Solar-Lezama. Program Synthesis by Sketching. PhD thesis, University of California, Berkeley, 2008. URL https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-1 77.html.

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