{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:58:07Z","timestamp":1776851887805,"version":"3.51.2"},"reference-count":55,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T00:00:00Z","timestamp":1776643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The weak-field, quasi-static regime of gravity is commonly described by the Newton\u2013Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1\u2013AX5 (including conservation) and standard DEC refinement, the Newton\u2013Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency\u2013wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source\u2013potential relation characterized by a power-law kernel wker(k)=1+C(k0\/k)\u03b1 in Fourier space. The kernel exponent \u03b1=12(1\u2212\u03c6\u22121)\u22480.191, where \u03c6=(1+5)\/2, is derived from self-similarity of the discrete ledger closure; the amplitude C=\u03c6\u22122\u22480.382 is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed M\/L=1, no per-galaxy tuning, conservative \u03c3tot), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves median(\u03c72\/N)=3.06 over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization\/screening.<\/jats:p>","DOI":"10.3390\/e28040477","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:57:21Z","timestamp":1776758241000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Discrete Informational Framework for Classical Gravity: Ledger Foundations and Galaxy Rotation Curve Constraints"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9457-7019","authenticated-orcid":false,"given":"Megan","family":"Simons","sequence":"first","affiliation":[{"name":"Recognition Physics Institute, Austin, TX 78701, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7212-4713","authenticated-orcid":false,"given":"Elshad","family":"Allahyarov","sequence":"additional","affiliation":[{"name":"Recognition Physics Institute, Austin, TX 78701, USA"},{"name":"Institut f\u00fcr Theoretische Physik II: Weiche Materie, Heinrich-Heine Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstrasse 1, 40225 D\u00fcsseldorf, Germany"},{"name":"Theoretical Department, Joint Institute for High Temperatures, Russian Academy of Sciences (IVTAN), 13\/19 Izhorskaya Street, Moscow 125412, Russia"},{"name":"Department of Physics, Case Western Reserve University, Cleveland, OH 44106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8868-7497","authenticated-orcid":false,"given":"Jonathan","family":"Washburn","sequence":"additional","affiliation":[{"name":"Recognition Physics Institute, Austin, TX 78701, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Will, C.M. (1993). Theory and Experiment in Gravitational Physics, Cambridge University Press.","DOI":"10.1017\/CBO9780511564246"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wald, R.M. (1984). General Relativity, University of Chicago Press.","DOI":"10.7208\/chicago\/9780226870373.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1086\/158003","article-title":"Rotational properties of 21 SC galaxies with a large range of luminosities and radii","volume":"238","author":"Rubin","year":"1980","journal-title":"Astrophys. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"L109","DOI":"10.1086\/508162","article-title":"A Direct Empirical Proof of the Existence of Dark Matter","volume":"648","author":"Clowe","year":"2006","journal-title":"Astrophys. J."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Planck Collaboration (2020). Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys., 641, A6.","DOI":"10.1051\/0004-6361\/201832909"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1086\/377252","article-title":"First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission","volume":"148","author":"Bennett","year":"2003","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1146\/annurev-astro-091916-055313","article-title":"Small-Scale Challenges to the \u039bCDM Paradigm","volume":"55","author":"Bullock","year":"2017","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1002\/andp.201200212","article-title":"Dark matter and cosmic structure","volume":"524","author":"Frenk","year":"2012","journal-title":"Ann. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12249","DOI":"10.1073\/pnas.1308716112","article-title":"Cold dark matter: Controversies on small scales","volume":"112","author":"Weinberg","year":"2015","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1093\/mnras\/stu1536","article-title":"Introducing the Illustris Project: Simulating the coevolution of dark and visible matter","volume":"444","author":"Vogelsberger","year":"2014","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1146\/annurev-astro-082812-140951","article-title":"Physical Models of Galaxy Formation in a Cosmological Framework","volume":"53","author":"Somerville","year":"2015","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1086\/307643","article-title":"Where Are the Missing Galactic Satellites?","volume":"522","author":"Klypin","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"L40","DOI":"10.1111\/j.1745-3933.2011.01074.x","article-title":"Too big to fail? The puzzling darkness of massive Milky Way subhaloes","volume":"415","author":"Bullock","year":"2011","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"L19","DOI":"10.1086\/312287","article-title":"Dark Matter Substructure within Galactic Halos","volume":"524","author":"Moore","year":"1999","journal-title":"Astrophys. J. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1086\/161130","article-title":"A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis","volume":"270","author":"Milgrom","year":"1983","journal-title":"Astrophys. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.12942\/lrr-2012-10","article-title":"Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions","volume":"15","author":"Famaey","year":"2012","journal-title":"Living Rev. Relativ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"201101","DOI":"10.1103\/PhysRevLett.117.201101","article-title":"The Radial Acceleration Relation in Rotationally Supported Galaxies","volume":"117","author":"McGaugh","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"152","DOI":"10.3847\/1538-4357\/836\/2\/152","article-title":"One Law to Rule Them All: The Radial Acceleration Relation of Galaxies","volume":"836","author":"Lelli","year":"2017","journal-title":"Astrophys. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1046\/j.1365-8711.2003.06596.x","article-title":"Clusters of galaxies with modified Newtonian dynamics (MOND)","volume":"342","author":"Sanders","year":"2003","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2012.01.001","article-title":"Modified Gravity and Cosmology","volume":"513","author":"Clifton","year":"2012","journal-title":"Phys. Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2014.12.002","article-title":"Beyond the LambdaCDM model: Dark energy and modified gravity","volume":"568","author":"Joyce","year":"2015","journal-title":"Phys. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"065020","DOI":"10.1103\/PhysRevD.81.065020","article-title":"Nonlocal Modification of Newtonian Gravity","volume":"81","author":"Blome","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"111301","DOI":"10.1103\/PhysRevLett.99.111301","article-title":"Nonlocal Cosmology","volume":"99","author":"Deser","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4","DOI":"10.12942\/lrr-2014-4","article-title":"The Confrontation between General Relativity and Experiment","volume":"17","author":"Will","year":"2014","journal-title":"Living Rev. Relativ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"041501","DOI":"10.1103\/PhysRevD.97.041501","article-title":"GW170817 Falsifies Dark Matter Emulators","volume":"97","author":"Boran","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1007\/BF02733251","article-title":"General Relativity Without Coordinates","volume":"19","author":"Regge","year":"1961","journal-title":"Nuovo C."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"R53","DOI":"10.1088\/0264-9381\/21\/15\/R01","article-title":"Background independent quantum gravity: A status report","volume":"21","author":"Ashtekar","year":"2004","journal-title":"Class. Quantum Gravity"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Thiemann, T. (2007). Modern Canonical Quantum General Relativity, Cambridge University Press.","DOI":"10.1017\/CBO9780511755682"},{"key":"ref_29","unstructured":"Rovelli, C. (2004). Quantum Gravity, Cambridge University Press. Cambridge Monographs on Mathematical Physics."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1103\/PhysRevLett.59.521","article-title":"Space-Time as a Causal Set","volume":"59","author":"Bombelli","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","unstructured":"Sorkin, R.D. (2003). Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School). arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s41114-019-0023-1","article-title":"The causal set approach to quantum gravity","volume":"22","author":"Surya","year":"2019","journal-title":"Living Rev. Relativ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.physrep.2012.03.007","article-title":"Nonperturbative Quantum Gravity","volume":"519","author":"Jurkiewicz","year":"2012","journal-title":"Phys. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"013002","DOI":"10.1088\/1361-6382\/ab57c7","article-title":"Quantum gravity from causal dynamical triangulations: A review","volume":"37","author":"Loll","year":"2020","journal-title":"Class. Quantum Gravity"},{"key":"ref_35","unstructured":"Hirani, A.N. (2003). Discrete Exterior Calculus. [Ph.D. Thesis, California Institute of Technology]."},{"key":"ref_36","unstructured":"Desbrun, M., Hirani, A.N., Leok, M., and Marsden, J.E. (2005). Discrete Exterior Calculus. arXiv."},{"key":"ref_37","unstructured":"Bossavit, A. (1998). Computational Electromagnetism, Academic Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1103\/PhysRevLett.75.1260","article-title":"Thermodynamics of Spacetime: The Einstein Equation of State","volume":"75","author":"Jacobson","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6377","DOI":"10.1063\/1.531249","article-title":"The World as a Hologram","volume":"36","author":"Susskind","year":"1995","journal-title":"J. Math. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4310\/ATMP.1998.v2.n2.a1","article-title":"The Large N Limit of Superconformal Field Theories and Supergravity","volume":"2","author":"Maldacena","year":"1998","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"029","DOI":"10.1007\/JHEP04(2011)029","article-title":"On the Origin of Gravity and the Laws of Newton","volume":"2011","author":"Verlinde","year":"2011","journal-title":"J. High Energy Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"016","DOI":"10.21468\/SciPostPhys.2.3.016","article-title":"Emergent Gravity and the Dark Universe","volume":"2","author":"Verlinde","year":"2017","journal-title":"SciPost Phys."},{"key":"ref_43","unstructured":"Wheeler, J.A. (1990). Information, physics, quantum: The search for links. Complexity, Entropy, and the Physics of Information, CRC Press."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"046901","DOI":"10.1088\/0034-4885\/73\/4\/046901","article-title":"Thermodynamical Aspects of Gravity: New Insights","volume":"73","author":"Padmanabhan","year":"2010","journal-title":"Rep. Prog. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"157","DOI":"10.3847\/0004-6256\/152\/6\/157","article-title":"SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves","volume":"152","author":"Lelli","year":"2016","journal-title":"Astron. J."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"A3","DOI":"10.1051\/0004-6361\/201732547","article-title":"Fitting the radial acceleration relation to individual SPARC galaxies","volume":"615","author":"Li","year":"2018","journal-title":"Astron. Astrophys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"5451","DOI":"10.1093\/mnras\/stz2700","article-title":"The universal rotation curve of low surface brightness galaxies\u2014IV. The interrelation between dark and luminous matter","volume":"490","author":"Salucci","year":"2019","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_48","unstructured":"Pardo-Guerra, S., Simons, M., Thapa, A., and Washburn, J. (2026). Coherent Comparison as Information Cost: A Cost-First Ledger Framework for Discrete Dynamics. arXiv."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Washburn, J., and Rahnamai Barghi, A. (2026). Reciprocal Convex Costs for Ratio Matching: Axiomatic Characterization. Axioms, 15.","DOI":"10.3390\/axioms15020151"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(00)00070-3","article-title":"The random walk\u2019s guide to anomalous diffusion","volume":"339","author":"Metzler","year":"2000","journal-title":"Phys. Rep."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Mainardi, F. (2010). Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press.","DOI":"10.1142\/p614"},{"key":"ref_52","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press."},{"key":"ref_53","unstructured":"Washburn, J. (2024). Gap-45 Synchronization Certificates for Ledger Calculus, Recognition Physics Institute. Technical Report RPI-TR-2024-07."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1038\/nature01997","article-title":"A test of general relativity using radio links with the Cassini spacecraft","volume":"425","author":"Bertotti","year":"2003","journal-title":"Nature"},{"key":"ref_55","unstructured":"Acz\u00e9l, J. (1966). Lectures on Functional Equations and Their Applications, Academic Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/4\/477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:08:26Z","timestamp":1776848906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/4\/477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,20]]},"references-count":55,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["e28040477"],"URL":"https:\/\/doi.org\/10.3390\/e28040477","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,20]]}}}