On the statistical nature of Betti numbers and Euler characteristic of smooth random fields | Paper Citation Record

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This paper cites An example is a power law form with spectral index α.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields An example is a power law form with spectral index α

Reference 1

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This paper cites Such exam- ples arise when some physical process erases small and/or lager scale fluctuations.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Such exam- ples arise when some physical process erases small and/or lager scale fluctuations

Reference 2

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This paper cites For this purpose, we simulate 104 Gaussian CMB temperature fluctuation maps whose pixel resolution is set by the Healpix parame- ter Nside = 512.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields For this purpose, we simulate 104 Gaussian CMB temperature fluctuation maps whose pixel resolution is set by the Healpix parame- ter Nside = 512

Reference 3

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This paper cites For this purpose let us reca- pitulate the central limit theorem (CLT) for statistically independent discrete random variables [63, 64].

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields For this purpose let us reca- pitulate the central limit theorem (CLT) for statistically independent discrete random variables [63, 64]

Reference 4

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This paper cites In this case, for resolution q, the variable having the largest (finite) support is mjmax , and it satisfies the bound mjmax ≤ jmax.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields In this case, for resolution q, the variable having the largest (finite) support is mjmax , and it satisfies the bound mjmax ≤ jmax

Reference 5

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This paper cites We now take a different approach and focus on the nature of mj’s.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields We now take a different approach and focus on the nature of mj’s

Reference 6

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This paper cites Specifically we focus on Gaussian random fields, for which the closed form analytic formula for ⟨χ⟩ is available.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Specifically we focus on Gaussian random fields, for which the closed form analytic formula for ⟨χ⟩ is available

Reference 7

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Observation 9bbfccfd-832f-40be-bc9b-2e86751fea4b · outbound

This paper cites Robust Morphological Measures for Large-Scale Structure in the Universe.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Robust Morphological Measures for Large-Scale Structure in the Universe

Reference 12

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Observation 17faed1f-236c-49a4-a0e9-8e6c1a787042 · outbound

This paper cites Beyond genus statistics: a unifying approach to the morphology of cosmic structure.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Beyond genus statistics: a unifying approach to the morphology of cosmic structure

Reference 13

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Observation 2cd7e5e6-be93-4df2-846f-879eab117b56 · outbound

This paper cites Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps

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This paper cites Non Gaussianity and Minkowski Functionals: forecasts for Planck.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Non Gaussianity and Minkowski Functionals: forecasts for Planck

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Observation 9c9b99cf-619f-4af6-a5de-b1d00f7bb68e · outbound

This paper cites Betti numbers of Gaussian fields.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Betti numbers of Gaussian fields

Reference 17

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Observation d425a08d-9128-4ea0-b5ed-8f112a3daf29 · outbound

This paper cites Pranav, H.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Pranav, H

Reference 18

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Observation a6bd4f23-223f-4807-8309-5bbae53b3cd9 · outbound

This paper cites Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals

Reference 19

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Observation 38f5a8da-9e37-4d33-8d5a-76c55c3a61f4 · outbound

This paper cites Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams

Reference 20

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Observation 7fa0e158-3d15-4f86-bff2-e17cd2a391ef · outbound

This paper cites Edelsbrunner and J.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Edelsbrunner and J

Reference 21

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Observation f7aabe1b-0082-4796-8d7f-52fe6d9ee473 · outbound

This paper cites Sousbie, C.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Sousbie, C

Reference 22

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Observation 288a8d8a-9858-468f-a50d-5c8d89624d7d · outbound

This paper cites Van De Weygaert, G.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Van De Weygaert, G

Reference 23

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This paper cites Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

Reference 24

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This paper cites Topological bias: How haloes trace structural patterns in the cosmic web.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Topological bias: How haloes trace structural patterns in the cosmic web

Reference 25

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This paper cites Hot and cold spots counts as probes of non-Gaussianity in the CMB.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Hot and cold spots counts as probes of non-Gaussianity in the CMB

Reference 26

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This paper cites Persistent Homology and Non-Gaussianity.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Persistent Homology and Non-Gaussianity

Reference 27

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This paper cites The Persistence of Large Scale Structures I: Primordial non-Gaussianity.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields The Persistence of Large Scale Structures I: Primordial non-Gaussianity

Reference 28

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This paper cites Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Shape of the Matter Power Spectrum.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Shape of the Matter Power Spectrum

Reference 29

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This paper cites Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?

Reference 30

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Probing massive neutrinos with the Minkowski functionals of large-scale structure

Reference 31

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This paper cites Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\texttt{NPIPE}$ and $\texttt{FFP10}$ data releases.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\texttt{NPIPE}$ and $\texttt{FFP10}$ data releases

Reference 33

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Homology reveals significant anisotropy in the cosmic microwave background

Reference 34

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This paper cites Local patch analysis of ACT DR6 convergence map using morphological statistics.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Local patch analysis of ACT DR6 convergence map using morphological statistics

Reference 35

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This paper cites Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Non-Gaussianity of diffuse Galactic synchrotron emission at 408 MHz

Reference 37

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This paper cites The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map

Reference 38

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Statistical properties of Galactic synchrotron temperature and polarization maps -- a multi-frequency comparison

Reference 39

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This paper cites Morphological Analysis of the Polarized Synchrotron Emission with WMAP and Planck.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Morphological Analysis of the Polarized Synchrotron Emission with WMAP and Planck

Reference 40

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This paper cites A novel probe of bubble size statistics and time scales of the epoch of reionization using the contour Minkowski Tensor.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields A novel probe of bubble size statistics and time scales of the epoch of reionization using the contour Minkowski Tensor

Reference 41

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields The Shape and Size distribution of HII Regions near the percolation transition

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This paper cites Morphology of 21cm brightness temperature during the Epoch of Reioinization using Contour Minkowski Tensor.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Morphology of 21cm brightness temperature during the Epoch of Reioinization using Contour Minkowski Tensor

Reference 43

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This paper cites Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers

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This paper cites Measuring the topology of reionization with Betti numbers.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Measuring the topology of reionization with Betti numbers

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This paper cites Persistent homology of the cosmic web. I: Hierarchical topology in $\Lambda$CDM cosmologies.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Persistent homology of the cosmic web. I: Hierarchical topology in $\Lambda$CDM cosmologies

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This paper cites Persistent topology of the reionization bubble network. II: Evolution & Classification.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Persistent topology of the reionization bubble network. II: Evolution & Classification

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This paper cites Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams

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This paper cites Topology of Neutral Hydrogen Within the Small Magellanic Cloud.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Topology of Neutral Hydrogen Within the Small Magellanic Cloud

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This paper cites The HI-halo mass relation at redshift $z \sim 1$ from the Minkowski functionals of 21 cm intensity maps.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields The HI-halo mass relation at redshift $z \sim 1$ from the Minkowski functionals of 21 cm intensity maps

Reference 50

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Observation d421477a-fd47-404c-835d-f6a685fc79e8 · outbound

This paper cites On the evolution of Betti curves in the Cosmic web.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields On the evolution of Betti curves in the Cosmic web

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This paper cites Betti Functionals as a Probe for Cosmic Topology.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Betti Functionals as a Probe for Cosmic Topology

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This paper cites Comparing Mass Mapping Reconstruction Methods with Minkowski Functionals.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Comparing Mass Mapping Reconstruction Methods with Minkowski Functionals

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Observation 0672b3e6-2b38-4a65-a0e8-147392f8a88e · outbound

This paper cites Tomita, Progress of Theoretical Physics 76, 952 (1986).

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Tomita, Progress of Theoretical Physics 76, 952 (1986)

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This paper cites Coles, MNRAS 234, 509 (1988).

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Coles, MNRAS 234, 509 (1988)

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Observation c440e7be-15aa-418b-b0b6-ed8f26e001e9 · outbound

This paper cites Coles and M.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Coles and M

Reference 56

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Observation 210d04bb-f0b5-4203-80d7-11cd551118f0 · outbound

This paper cites General Statistical properties of the CMB Polarization field.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields General Statistical properties of the CMB Polarization field

Reference 57

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Observation dd040c6d-864e-4a1d-9819-94c0aeb212a5 · outbound

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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Matsubara, Astrophys

Reference 58

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Observation 9aef2215-02dc-41a0-90c4-df7fbb8c57e6 · outbound

This paper cites Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-06T19:49:49.399017Z

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This paper cites Weakly non-Gaussian formula for the Minkowski functionals in general dimensions.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Weakly non-Gaussian formula for the Minkowski functionals in general dimensions

Reference 60

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This paper cites Non-Gaussian statistics of critical sets in 2 and 3D: Peaks, voids, saddles, genus and skeleton.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Non-Gaussian statistics of critical sets in 2 and 3D: Peaks, voids, saddles, genus and skeleton

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T19:49:49.677832Z

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This paper cites Minkowski Functionals for composite smooth random fields.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Minkowski Functionals for composite smooth random fields

Reference 62

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Observation d21bfdf7-5fd9-48b8-be6d-2a842eabbea6 · outbound

This paper cites Owada and A.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Owada and A

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:49:58.488719Z

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Observation 80efc753-555c-429c-b66b-eb75110acb09 · outbound

This paper cites Owada and G.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Owada and G

Reference 64

Resolution: verified exact; raw_fallback, observed 2026-08-06T19:49:52.377514Z

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Observation dbfcfda4-39e7-4371-acd5-0db1a31e440e · outbound

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Reference 65

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:49:58.222722Z

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Observation ad359053-306b-4ad1-b595-36f1210edc07 · outbound

This paper cites an unresolved cited work.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Unresolved cited work

Reference 66

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:49:57.980338Z

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Observation d5fd4df5-201e-4cf8-8164-8acb9ddebb0f · outbound

This paper cites We are not considering scaling transformations of the manifold.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields We are not considering scaling transformations of the manifold

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:49:57.738703Z

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Observation 1c824f71-70b2-46ae-9570-cb9fe4296088 · outbound

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Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:49:57.378222Z

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Reference 69

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:49:56.975076Z

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This paper cites Lindeberg, Mathematische Zeitschrift.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Lindeberg, Mathematische Zeitschrift

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:49:56.773020Z

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Observation c36f9f35-7b9d-4828-b708-c4c62c8c606e · outbound

This paper cites Feller, Bull.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Feller, Bull

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:49:56.580773Z

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Observation 593d4ddd-9517-4e03-adf6-efa3e0a76510 · outbound

This paper cites Dvoretzky, Actes.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Dvoretzky, Actes

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:49:56.399317Z

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Observation cf6c0a43-2a85-45cf-894d-fe44f1d79968 · outbound

This paper cites The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method

Reference 73

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:49:52.102229Z

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Observation 1b096505-a25d-45a1-84d4-a11e5d473f79 · outbound

This paper cites an unresolved cited work.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Unresolved cited work

Reference 74

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Observation 62b8c4cd-984f-4bd9-828f-79bdd2b56b97 · outbound

This paper cites Hatcher, Algebraic Topology (Cambridge University Press, 2002).

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Hatcher, Algebraic Topology (Cambridge University Press, 2002)

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-06T19:49:51.288025Z

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This paper cites Feller, An Introduction to Probability The- ory and Its Applications.

On the statistical nature of Betti numbers and Euler characteristic of smooth random fields Feller, An Introduction to Probability The- ory and Its Applications

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-06T19:49:51.421679Z

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