Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble | Paper Citation Record

Observation 5602cb79-c9a5-45a7-8852-a5d4aa181005 · outbound

This paper cites The same result follows directly from the ultraviolet thermodynamic functions.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble The same result follows directly from the ultraviolet thermodynamic functions

Reference 1

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Quantum-corrected finite entropy of noncommutative acoustic black holes

Reference 2

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP

Reference 3

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This paper cites Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries

Reference 4

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Tests of quantum gravity from observations of gamma-ray bursts

Reference 5

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble High-energy tests of lorentz invariance

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This paper cites Doubly-special relativity: First results and key open problems.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Doubly-special relativity: First results and key open problems

Reference 8

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This paper cites Lorentz invariance with an invariant energy scale.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Lorentz invariance with an invariant energy scale

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This paper cites Modern tests of lorentz invariance.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Modern tests of lorentz invariance

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This paper cites Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Quantum gravity at a lifshitz point

Reference 12

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This paper cites Minimal length scale scenarios for quantum gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Minimal length scale scenarios for quantum gravity

Reference 13

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This paper cites Testing local lorentz invariance with gravitational waves.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Testing local lorentz invariance with gravitational waves

Reference 14

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This paper cites Theoretical physics implications of the binary black-hole mergers gw150914 and gw151226.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Theoretical physics implications of the binary black-hole mergers gw150914 and gw151226

Reference 15

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This paper cites Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee Field.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee Field

Reference 16

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This paper cites Radiative corrections in metric-affine bumblebee model.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Radiative corrections in metric-affine bumblebee model

Reference 17

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This paper cites Lorentz-violating dimension-five operator contribution to the black body radiation.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Lorentz-violating dimension-five operator contribution to the black body radiation

Reference 18

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This paper cites Lorentz-violating extension of scalar QED at finite temperature.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Lorentz-violating extension of scalar QED at finite temperature

Reference 19

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This paper cites The Lorentz-violating real scalar field at thermal equilibrium.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble The Lorentz-violating real scalar field at thermal equilibrium

Reference 20

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This paper cites Fermionic quantum gas at finite temperature within a Lorentz- violating background.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Fermionic quantum gas at finite temperature within a Lorentz- violating background

Reference 21

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This paper cites CP-violating non-linear electrodynamics and cor- rections to blackbody radiation thermal laws.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble CP-violating non-linear electrodynamics and cor- rections to blackbody radiation thermal laws

Reference 22

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This paper cites Non-commutative correction of ideal gas thermodynamics.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Non-commutative correction of ideal gas thermodynamics

Reference 23

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Higher-derivative Lorentz-breaking dispersion relations: a thermal description

Reference 24

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This paper cites Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity

Reference 25

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This paper cites Particle motion and thermal effects around a Kalb–Ramond black hole.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Particle motion and thermal effects around a Kalb–Ramond black hole

Reference 26

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This paper cites Exploring the thermodynamics of non-commutative scalar fields.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Exploring the thermodynamics of non-commutative scalar fields

Reference 27

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This paper cites Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking

Reference 28

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This paper cites Power spectra and circular polarization of primordial gravitational waves with parity and lorentz violations.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Power spectra and circular polarization of primordial gravitational waves with parity and lorentz violations

Reference 29

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Gravitational waves in metric-affine bumblebee gravity

Reference 30

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This paper cites Modified gravitational wave propagations in linearized gravity with lorentz and diffeomorphism violations and their gravitational wave constraints.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Modified gravitational wave propagations in linearized gravity with lorentz and diffeomorphism violations and their gravitational wave constraints

Reference 31

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This paper cites Propagation effects of Lorentz violation in gravita- tional waves.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Propagation effects of Lorentz violation in gravita- tional waves

Reference 32

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Gravitational waves in a minimal gravitational SME

Reference 33

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Signals for lorentz violation in gravitational waves

Reference 34

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Gravitational waves effects in a Lorentz–violating scenario

Reference 35

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Observation of gravitational waves from a binary black hole merger

Reference 36

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This paper cites Tests of general relativity with gw150914.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Tests of general relativity with gw150914

Reference 37

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Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

Reference 38

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This paper cites What gravity waves are telling about quantum spacetime.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble What gravity waves are telling about quantum spacetime

Reference 39

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This paper cites Tests of general relativity with the binary black hole signals from the ligo-virgo catalog gwtc-1.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Tests of general relativity with the binary black hole signals from the ligo-virgo catalog gwtc-1

Reference 40

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This paper cites Tests of general relativity with gwtc-3.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Tests of general relativity with gwtc-3

Reference 41

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Observation 0ec11dab-514d-491d-9fe1-a5d05e3bb59e · outbound

This paper cites Fractal universe and quantum gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Fractal universe and quantum gravity

Reference 43

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This paper cites Geometry of fractional spaces.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Geometry of fractional spaces

Reference 44

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This paper cites Multi-scale gravity and cosmology.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Multi-scale gravity and cosmology

Reference 45

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This paper cites Multiscale spacetimes from first principles.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Multiscale spacetimes from first principles

Reference 46

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Observation dfa4b2f2-eff8-4ac0-be72-0d9e0a33f461 · outbound

This paper cites The spectral dimension of the universe is scale dependent.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble The spectral dimension of the universe is scale dependent

Reference 47

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Observation 4742837b-1fe6-4660-870f-7a3ab5db115e · outbound

This paper cites Fractal spacetime structure in asymptotically safe gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Fractal spacetime structure in asymptotically safe gravity

Reference 48

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Observation cb4821cd-45fc-4c21-a582-ab873e44f5a8 · outbound

This paper cites Fractal structure of loop quantum gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Fractal structure of loop quantum gravity

Reference 49

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Observation 439d5d3e-8ff3-4b03-ada7-25288ccc5a84 · outbound

This paper cites Dimension and dimensional reduction in quantum gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Dimension and dimensional reduction in quantum gravity

Reference 50

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Observation 42bd0735-a121-485e-9e56-a8e6270fad5b · outbound

This paper cites Multifractional theories: an unconventional review.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Multifractional theories: an unconventional review

Reference 51

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Observation ed0f6ae0-d58f-4e0e-9c57-9d90893876dd · outbound

This paper cites Thermodynamics of a photon gas and deformed dispersion relations.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Thermodynamics of a photon gas and deformed dispersion relations

Reference 52

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Observation 05ad31f7-830e-4645-8d68-d50b320247fa · outbound

This paper cites Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.997504Z

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Observation 59ce1b93-47c0-460d-b56b-5fc576e507e0 · outbound

This paper cites The effect of modified dispersion relations on the thermodynamics of black-body radiation.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble The effect of modified dispersion relations on the thermodynamics of black-body radiation

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.971177Z

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Observation fb654a32-bfa4-4d97-82b2-7583a0f9ee9f · outbound

This paper cites Modified dispersion relation, photon’s velocity, and unruh effect.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Modified dispersion relation, photon’s velocity, and unruh effect

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.884287Z

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Observation e7b4a297-7379-4be1-9e08-7af62c469c98 · outbound

This paper cites Dsr-gup, maximally localized state, and black hole thermody- namics.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Dsr-gup, maximally localized state, and black hole thermody- namics

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.963673Z

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Observation 4417e5bd-0d76-4fc5-8a38-63e65fff9d5f · outbound

This paper cites Black hole corrections due to minimal length and modified dispersion relation.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Black hole corrections due to minimal length and modified dispersion relation

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.959516Z

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Observation 96fee08d-928e-4c1e-a3d7-cd1ecf5ecfd5 · outbound

This paper cites Thermal analysis of photon-like particles in rainbow gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Thermal analysis of photon-like particles in rainbow gravity

Reference 58

Resolution: verified exact; arxiv_id, observed 2026-05-20T20:43:43.387177Z

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Observation 6299f926-0b6e-43d8-9cd8-da9515f9f149 · outbound

This paper cites an unresolved cited work.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-05-20T20:43:43.945304Z

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Observation 751dbf44-fcc2-4bda-b153-f63ebd36a60e · outbound

This paper cites Huang,Statistical Mechanics.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Huang,Statistical Mechanics

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.972976Z

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Observation 1e3d5078-5f3b-4ed5-a610-9c5274bc30ea · outbound

This paper cites Kardar,Statistical Physics of Particles.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Kardar,Statistical Physics of Particles

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.946389Z

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Observation 3f9e0707-e1c2-4726-89be-4627ef1c144f · outbound

This paper cites an unresolved cited work.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-05-20T20:43:43.930071Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fa47f45f-2553-474f-8af7-17e06d4f28e0 · outbound

This paper cites Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.975134Z

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Observation b181769d-efc1-4d1b-8311-f63fedce8abb · outbound

This paper cites Theoretical physics implications of the binary black-hole mergers gw150914 and gw151226.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Theoretical physics implications of the binary black-hole mergers gw150914 and gw151226

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.836591Z

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Observation 59be88de-68a6-4c76-935a-f1870f03fdfe · outbound

This paper cites What gravity waves are telling about quantum spacetime.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble What gravity waves are telling about quantum spacetime

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.841544Z

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Observation c22753b4-4079-4021-bfe9-78ab9c6f3289 · outbound

This paper cites Quantum gravity at a lifshitz point.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Quantum gravity at a lifshitz point

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.843468Z

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Observation d1993ab5-af50-49a7-a357-91f3fe1310cd · outbound

This paper cites Testing local lorentz invariance with gravitational waves.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Testing local lorentz invariance with gravitational waves

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.847740Z

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Observation 3b1b7286-bdf6-4330-967a-133ef47ba2f3 · outbound

This paper cites Fractal universe and quantum gravity.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Fractal universe and quantum gravity

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.845390Z

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Observation e660e872-7f49-4695-a772-fc175ddc371e · outbound

This paper cites Geometry of fractional spaces.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Geometry of fractional spaces

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.856217Z

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Observation cbd5ac29-0aa9-4bfe-9a5a-81e16e3e5014 · outbound

This paper cites Lorentz violations in multifractal spacetimes.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Lorentz violations in multifractal spacetimes

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.839070Z

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Observation 166ebcfd-0dd1-4160-8e75-c9d6e7aa0062 · outbound

This paper cites Relativistic particle in multiscale spacetimes.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Relativistic particle in multiscale spacetimes

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.849785Z

Source-reported events for the cited work

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Observation 07122a92-f564-4b47-959b-4eff49cedb5b · outbound

This paper cites Symmetries and propagator in multifractional scalar field theory.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Symmetries and propagator in multifractional scalar field theory

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.858087Z

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Observation 4e032cad-c6cc-43dc-9e9e-22b47d0e2d00 · outbound

This paper cites Abc of multi-fractal spacetimes and fractional sea turtles.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Abc of multi-fractal spacetimes and fractional sea turtles

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.862042Z

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Observation 4787b7a8-fca8-42ec-8b84-4530cb3ae172 · outbound

This paper cites Geometry and field theory in multi-fractional spacetime.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Geometry and field theory in multi-fractional spacetime

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T20:43:43.853935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2a896e7c-ec5f-4cc8-a27a-700fc274d729 · outbound

This paper cites an unresolved cited work.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

Reference 75

Resolution: unresolved; raw_fallback, observed 2026-05-20T20:43:43.860040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b0ad92e7-b44c-46bb-b0e6-84054c7df2ea · outbound

This paper cites an unresolved cited work.

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-05-20T20:43:43.851724Z

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