Paper Citation Record · LEDGER

Reducible Iterated Graph Systems: multiscale-freeness and multifractals

As of 18 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2506.18073.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.18073 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T08:12:44.029481Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T10:52:14.961955Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-05-21T10:54:07.986296Z

Reference resolution

41 of 41 outbound references displayed

verified exact4
verified fuzzy36
unresolved1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 73dd2f7d-e7f3-40a1-b7f7-9fe98d643bc4 · outbound

This paper cites On the scale-freeness of random colored substitution networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals On the scale-freeness of random colored substitution networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.092725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7d4531bd-4200-4521-9022-ca6ac3c580e2 · outbound

This paper cites Fractal dimensions for iterated graph systems.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Fractal dimensions for iterated graph systems

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.116957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d57735c7-9ac7-4bde-ae51-9f6311fc2ccb · outbound

This paper cites Recursion equations in gauge field theories.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Recursion equations in gauge field theories

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.120401Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0c19dc67-540e-4d69-990c-6bb1ce8601b3 · outbound

This paper cites Notes on migdal’s recursion formulas.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Notes on migdal’s recursion formulas

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.128998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 014d83a9-f3ea-4bd3-809f-91c5769b1d26 · outbound

This paper cites Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.061234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 849af381-199c-4219-9798-9a8affc8e278 · outbound

This paper cites Renormalisation-group calculations of finite systems: order parameter and specific heat for epitaxial ordering.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Renormalisation-group calculations of finite systems: order parameter and specific heat for epitaxial ordering

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.148167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 57fc3f02-9998-4b7f-9842-504dc2de206e · outbound

This paper cites Exactly soluble ising models on hierar- chical lattices.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Exactly soluble ising models on hierar- chical lattices

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.140284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d9377ea8-aae1-46da-a550-c52c5d881a03 · outbound

This paper cites Density of states on fractals: fractons.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Density of states on fractals: fractons

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.136642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6b4b4097-556a-4157-ac76-34688d1041b4 · outbound

This paper cites Phase transitions on fractals. ii. sierpinski gaskets.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Phase transitions on fractals. ii. sierpinski gaskets

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.052352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f03785d5-f4b7-44bd-b484-797485d9b9b9 · outbound

This paper cites Particle-antiparticle annihilation in diffusive motion.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Particle-antiparticle annihilation in diffusive motion

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.168452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 49f0a89f-a313-4659-bc59-a8f6d344259f · outbound

This paper cites Flow in porous media: The.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Flow in porous media: The

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.087576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 65fb8b1a-acc9-4e9f-950f-6af537a411f7 · outbound

This paper cites Fractal structure of zeros in hierarchical models.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Fractal structure of zeros in hierarchical models

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.157750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 15fdf7c0-6864-483c-a84e-3fb0b856f95e · outbound

This paper cites Self-similarity of complex networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Self-similarity of complex networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.047616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 36dcb52e-aefa-40ab-b689-435f4821c2ac · outbound

This paper cites Collective dynamics of ‘small- world’networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Collective dynamics of ‘small- world’networks

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.164837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f34ff879-90ec-46d9-9e69-5644b84b104c · outbound

This paper cites Emergence of scaling in random networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Emergence of scaling in random networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.172520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cd50547f-7084-408e-883c-1e27b3f3522c · outbound

This paper cites Hierarchical organization in complex net- works.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Hierarchical organization in complex net- works

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.097067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 274dee77-69b6-445f-9d60-5a52b01eafc2 · outbound

This paper cites Epidemic spreading in scale-free networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Epidemic spreading in scale-free networks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.043194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 605bcbda-6102-4569-b9c7-e0f0b8c16b7a · outbound

This paper cites Brownian motion on the sierpinski gas- ket.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Brownian motion on the sierpinski gas- ket

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.056961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8bef0228-d5f5-4cea-8f1a-65cda7da9312 · outbound

This paper cites Transition density estimates for brow- nian motion on scale irregular sierpinski gaskets.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Transition density estimates for brow- nian motion on scale irregular sierpinski gaskets

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.112656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 87bcf8ae-9ac9-4fb9-9e08-2775f51e037a · outbound

This paper cites Brownian motion and harmonic analysis on sierpinski carpets.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Brownian motion and harmonic analysis on sierpinski carpets

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.022516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 28e64162-3cc9-4c72-b9ab-142361ea2760 · outbound

This paper cites A harmonic calculus on the sierpinski spaces.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals A harmonic calculus on the sierpinski spaces

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.038672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ee0fb2c2-4cd8-499f-b55b-c0f833384c6c · outbound

This paper cites Harmonic calculus on pcf self-similar sets.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Harmonic calculus on pcf self-similar sets

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.034143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7bb066f4-a1f7-40ea-9023-eae5a6229c55 · outbound

This paper cites Kigami, Analysis on Fractals.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Kigami, Analysis on Fractals

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.080445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c1e5f3b-8356-4f2d-90b5-308f81685540 · outbound

This paper cites Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.105644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 410afe26-c722-44dd-a861-dabb27a4570a · outbound

This paper cites Asymptotics for functions associated with heat flow on the sierpinski carpet.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Asymptotics for functions associated with heat flow on the sierpinski carpet

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.152848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation beaac7b6-6ed6-42cb-ba41-de4a61ad2f9f · outbound

This paper cites On the dichotomy in the heat kernel two sided estimates.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals On the dichotomy in the heat kernel two sided estimates

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.028263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dea42b45-3906-41f7-b5a2-2c2e5d4a3468 · outbound

This paper cites Heat kernels on metric measure spaces and an application to semilinear elliptic equations.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Heat kernels on metric measure spaces and an application to semilinear elliptic equations

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.109367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 44e9af7f-a143-49a3-9a82-8f0e18f3adf5 · outbound

This paper cites Self-similar k-graph c*-algebras.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Self-similar k-graph c*-algebras

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.144384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4215592c-65c1-4d44-b380-60054ca65483 · outbound

This paper cites Gradient estimate for the heat kernel on some fractal-like cable systems and quasi-riesz transforms.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Gradient estimate for the heat kernel on some fractal-like cable systems and quasi-riesz transforms

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.101231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 425cc721-ecbe-4062-8fc0-e88d36ac1c24 · outbound

This paper cites Fractality and scale-free effect of a class of self-similar networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Fractality and scale-free effect of a class of self-similar networks

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.123782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e91bf039-e095-462e-a5a2-43ea0411ed46 · outbound

This paper cites Average distance of substitution networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Average distance of substitution networks

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.064762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0517f5c3-8183-4408-b35c-cbc366fce0aa · outbound

This paper cites Scale-free effect of substitution networks.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Scale-free effect of substitution networks

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.077140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 055b665c-9d5f-4bb9-aa4d-b8071ab60f7d · outbound

This paper cites On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-19T08:13:01.523671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7d76cdb3-5522-47a3-a99c-3d0489bc8797 · outbound

This paper cites Iterated graph systems and the combi- natorial loewner property.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Iterated graph systems and the combi- natorial loewner property

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-19T08:13:01.510445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d52dc4af-3020-48b1-adfa-a0e0a8467369 · outbound

This paper cites Fractal Graph Contrastive Learning.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Fractal Graph Contrastive Learning

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-05-19T08:13:01.503753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6d2ffff2-4466-4b17-a084-8c8050dc0464 · outbound

This paper cites Renormalization Group Approach to Percolation in Hierarchical Lattices.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Renormalization Group Approach to Percolation in Hierarchical Lattices

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-19T08:13:01.516051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e1dddb4f-729c-4680-af39-d4b3cb618448 · outbound

This paper cites Percolation on fractal networks: A survey.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Percolation on fractal networks: A survey

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.133453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0601416b-9738-4348-a651-7cea1cec425f · outbound

This paper cites Perron-frobenius theory and frequency con- vergence for reducible substitutions.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Perron-frobenius theory and frequency con- vergence for reducible substitutions

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.083925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation acb94d94-857c-4caa-8912-ff2dc85820ac · outbound

This paper cites Unzerlegbare, nicht negative matrizen.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Unzerlegbare, nicht negative matrizen

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.073017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2c3a69de-fdf8-461a-8030-73e22c6c97ca · outbound

This paper cites an unresolved cited work.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-05-19T08:13:02.069339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d4c46c77-e376-4dd9-bf50-76b593b60bfa · outbound

This paper cites Falconer, Fractal Geometry: Mathematical Foundations and Applica- tions.

Reducible Iterated Graph Systems: multiscale-freeness and multifractals Falconer, Fractal Geometry: Mathematical Foundations and Applica- tions

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T08:13:02.161366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 84a94a0b-fb85-4dc5-8e19-cad26d847db7 · inbound

Iterated Graph Systems (I): random walks and diffusion limits cites this paper.

Iterated Graph Systems (I): random walks and diffusion limits Reducible Iterated Graph Systems: multiscale-freeness and multifractals

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-05-21T10:54:07.988026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.