No Primary Source Found on Page Value Saturation in Random Hybrid Circuits — E8 Intelligence Research

FINDING: Search returned only secondary/lecture-level sources (YouTube talks, seminar reviews) on entanglement entropy; no primary paper on "Page value saturation in random hybrid quantum circuits" was retrieved, so no new mathematical result can be extracted from these items alone. | MATH: The relevant canonical results the domain implies (not derived from these links): Page curve S_A = min(|A|,|B|)·ln d − (d^{2|A|−2|B|})/(2 ln d) for random states; volume-law saturation S ∝ ln d · min(|A|,|B|); hybrid-circuit transition at critical measurement rate p_c with S ~ L (volume) for pp_c. | CONNECTION: No geometric-harmony ratio (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic/root-system structure is supported by the retrieved evidence. | DEPTH: 2 Notes on precision: - The five URLs are: (1) a general explainer video, (2) a Qiskit how-to, (3) a QIP2023 talk on topological entanglement entropy lower bounds (Ranard et al.), (4) a lecture s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23939031
Primary Topic
Quantum many-body systems
Type
preprint
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No Primary Source Found on Page Value Saturation in Random Hybrid Circuits — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum many-body systems
preprint

No Primary Source Found on Page Value Saturation in Random Hybrid Circuits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned only secondary/lecture-level sources (YouTube talks, seminar reviews) on entanglement entropy; no primary paper on "Page value saturation in random hybrid quantum circuits" was retrieved, so no new mathematical result can be extracted from these items alone. | MATH: The relevant canonical results the domain implies (not derived from these links): Page curve S_A = min(|A|,|B|)·ln d − (d^{2|A|−2|B|})/(2 ln d) for random states; volume-law saturation S ∝ ln d · min(|A|,|B|); hybrid-circuit transition at critical measurement rate p_c with S ~ L (volume) for pp_c. | CONNECTION: No geometric-harmony ratio (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic/root-system structure is supported by the retrieved evidence. | DEPTH: 2 Notes on precision: - The five URLs are: (1) a general explainer video, (2) a Qiskit how-to, (3) a QIP2023 talk on topological entanglement entropy lower bounds (Ranard et al.), (4) a lecture s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quantum many-body systems
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No Primary Source Found on Page Value Saturation in Random Hybrid Circuits — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS