PRH | Essay | 7.4 • No Free Information | Zenodo Skip to main Communities My dashboard Log in Sign up Post Riemann Hypothesis Helson-Blur Program Published April 28, 2026 | Version v3 Preprint Restricted PRH | Essay | 7.4 • No Free Information Authors/Creators Perisic, Aleksandar Description We propose no free information as an operational principle: every certified bit available to a finite observer has a nonzero resource price. The purpose of this essay is not to prove a new physical law, nor to present a completed mathematical theory, but to build a formal language around that intuition and explore what it suggests when pushed to its limit. The Euler product for the Riemann zeta function is used as an arithmetic archetype: global multiplicative structure is accessed through irreducible local factors, and refinement requires staged work. We then introduce an inverse-budget information-resource scaling as a convenient normalization, not as a universal theorem. A Landauer-type expression is used as a thermodynamic accounting scale for irreversible recording and certification, not as a microscopic speed limit for all information processing. Finally, we develop a principle-driven meromorphic pole model in which black holes are treated as pole-like entries in a cosmic catalogue and smooth dark sectors are interpreted as unresolved blur. This model is intended as a symbolic and back-of-the-envelope framework: a way to ask what the universe would look like if information-price accounting were treated as a guiding principle from arithmetic to cosmology. Files Restricted The record is publicly accessible, but files are restricted. Log in to check if you have access. Additional details References R. Landauer, "Irreversibility and heat generation in the computing process," IBM Journal of Research and Development 5 (1961), 183–191. C. H. Bennett, "The thermodynamics of computation—A review," International Journal of Theoretical Physics 21 (1982), 905–940. J. D. Bekenstein, "Black holes and entropy," Physical Review D 7 (1973), 2333–2346. G. W. Gibbons and S. W. Hawking, "Cosmological event horizons, thermodynamics, and particle creation," Physical Review D 15 (1977), 2738–2751. R. W. Hellings and G. S. Downs, "Upper limits on the isotropic gravitational radiation background from pulsar timing analysis," Astrophysical Journal Letters 265 (1983), L39– L42. G. Agazie et al. (NANOGrav Collaboration), "The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background," Astrophysical Journal Letters 951 (2023), L8. S. Burke-Spolaor et al., "The astrophysics of nanohertz gravitational waves," The Astronomy and Astrophysics Review 27 (2019), 5. E. S. Phinney, "A practical theorem on gravitational wave backgrounds," (2001). J. L. Synge, Relativity: The General Theory, North-Holland, 1960. S. M. Voronin, "A theorem on the universality of the Riemann zeta-function," Izvestiya AN SSSR. Ser. Mat. 39 (1975), 475–486; English translation: Math. USSR Izvestija 9 (1975), 443–453. J. Steuding, Value-Distribution of L-Functions, Lecture Notes in Mathematics 1877, Springer, 2007. H. M. Edwards, Riemann's Zeta Function, Academic Press, 1974. H. Iwaniec and E. Kowalski, Analytic Number Theory, AMS Colloquium Publications, Vol. 53, 2004. B. Ja. Levin, Distribution of Zeros of Entire Functions, revised edition, American Mathe- matical Society, 1996. J. B. Conway, Functions of One Complex Variable, Graduate Texts in Mathematics, Springer, 1978. 99 Views 60 Downloads Show more details All versions This version Views Total views 99 35 Downloads Total downloads 60 24 Data volume Total data volume 33.1 MB 10.4 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19849559 Markdown [](https://doi.org/10.5281/zenodo.19849559) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19849559.svg :target: https://doi.org/10.5281/zenodo.19849559 HTML <a href="https://doi.org/10.5281/zenodo.19849559"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19849559.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19849559.svg Target URL https://doi.org/10.5281/zenodo.19849559 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created April 28, 2026 Modified June 21, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies