Paper Citation Record · LEDGER

Exact renormalisation for patch frequencies in inflation systems

As of 17 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2507.07753.

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

pith.paper-citation-record.v1
2507.07753 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:43:01.415601Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T18:37:29.397128Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T02:59:26.051278Z

Reference resolution

30 of 30 outbound references displayed

verified exact10
verified fuzzy14
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c5c2434b-66b6-4270-abc5-792535eca801 · outbound

This paper cites Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples.

Exact renormalisation for patch frequencies in inflation systems Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:57.526851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db6ce76b-480e-4479-9c6c-fb55814a97ca · outbound

This paper cites Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction.

Exact renormalisation for patch frequencies in inflation systems Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:57.625687Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25aca5e7-fbe4-4a3f-b35a-4ad8a6b63741 · outbound

This paper cites Baake and U.

Exact renormalisation for patch frequencies in inflation systems Baake and U

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:07.614195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 308c43fa-c7ff-4e24-8ed7-c1cf31f45559 · outbound

This paper cites Baake, M.

Exact renormalisation for patch frequencies in inflation systems Baake, M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:07.332584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 25f98af6-fd45-4ce3-a99d-ed17084cbfe6 · outbound

This paper cites Factor frequencies in languages invariant under more symmetries.

Exact renormalisation for patch frequencies in inflation systems Factor frequencies in languages invariant under more symmetries

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:03.944160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f4ef82ec-013c-45a2-b253-bd1799353314 · outbound

This paper cites Invariant Measures on Stationary Bratteli Diagrams.

Exact renormalisation for patch frequencies in inflation systems Invariant Measures on Stationary Bratteli Diagrams

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:03.746661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b6512ef4-2996-44d4-ae23-20125f3bbe32 · outbound

This paper cites A spectral cocycle for substitution systems and translation flows.

Exact renormalisation for patch frequencies in inflation systems A spectral cocycle for substitution systems and translation flows

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:58.305879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8d16f10-7df9-4841-b687-f149e7687f9f · outbound

This paper cites When size matters: subshifts and their related tiling spaces.

Exact renormalisation for patch frequencies in inflation systems When size matters: subshifts and their related tiling spaces

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:03.493069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4e03423d-2615-48ef-b0a2-6a93257908c7 · outbound

This paper cites Clark and L.

Exact renormalisation for patch frequencies in inflation systems Clark and L

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:58.590670Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82334817-16d2-4d34-bb1e-d5f7ce560454 · outbound

This paper cites Cornfeld, S.V.

Exact renormalisation for patch frequencies in inflation systems Cornfeld, S.V

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:07.097601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2486f298-b5f0-4f5f-86cf-b5dc91089ec4 · outbound

This paper cites Invariant measures for non-primitive tiling substitutions.

Exact renormalisation for patch frequencies in inflation systems Invariant measures for non-primitive tiling substitutions

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:03.150565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a9341145-9eff-42c7-a55a-b2eb9fb8ee71 · outbound

This paper cites Dekking, On the Thue–Morse measure, Acta Univ.

Exact renormalisation for patch frequencies in inflation systems Dekking, On the Thue–Morse measure, Acta Univ

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:06.836326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7f3387b3-7fe9-4cdc-802e-870b2d5edcce · outbound

This paper cites How model sets can be determined by their two-point and three-point correlations.

Exact renormalisation for patch frequencies in inflation systems How model sets can be determined by their two-point and three-point correlations

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:02.908779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4d14c344-d780-45d2-9240-92f1a6d55f92 · outbound

This paper cites Weighted model sets and their higher point-correlations.

Exact renormalisation for patch frequencies in inflation systems Weighted model sets and their higher point-correlations

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:02.671164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a49521ca-302e-47f8-a5fd-2de20ad7081d · outbound

This paper cites Einsiedler and T.

Exact renormalisation for patch frequencies in inflation systems Einsiedler and T

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:06.591525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8000b5f3-fcc2-4022-8948-5f15ded73b20 · outbound

This paper cites Frid, On the frequency of factors in a D0L word, J.

Exact renormalisation for patch frequencies in inflation systems Frid, On the frequency of factors in a D0L word, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:06.343648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4fbc4cd4-b505-48af-a2cb-7b6acc3dd753 · outbound

This paper cites Gantmacher, Matrizentheorie, Springer, Berlin (1986).

Exact renormalisation for patch frequencies in inflation systems Gantmacher, Matrizentheorie, Springer, Berlin (1986)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:06.077698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2c02c977-5e88-452d-a166-de89ff5d989d · outbound

This paper cites Hollander and B.

Exact renormalisation for patch frequencies in inflation systems Hollander and B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:05.820165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6d40ee59-3e62-4406-ba9d-0ad5c24e611d · outbound

This paper cites Tiling deformations, cohomology, and orbit equivalence of tiling spaces.

Exact renormalisation for patch frequencies in inflation systems Tiling deformations, cohomology, and orbit equivalence of tiling spaces

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:02.389393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f74335a9-89c3-4132-8402-32cc737bada1 · outbound

This paper cites Pattern equivariant functions, deformations and equivalence of tiling spaces.

Exact renormalisation for patch frequencies in inflation systems Pattern equivariant functions, deformations and equivalence of tiling spaces

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:02.153519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d6132e13-8aa2-41a8-88ed-9ab64d3aa6e2 · outbound

This paper cites Lothaire, Combinatorics on Words , 2nd ed., Cambridge University Press (1997).

Exact renormalisation for patch frequencies in inflation systems Lothaire, Combinatorics on Words , 2nd ed., Cambridge University Press (1997)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:05.585168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 43d63feb-198e-4fdf-8c13-5cf9a52029e5 · outbound

This paper cites an unresolved cited work.

Exact renormalisation for patch frequencies in inflation systems Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:43:05.331574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation eb6ad7c5-e494-4ace-81ff-115260a34c45 · outbound

This paper cites Maz´ aˇ c,Fractal and Statistical Phenomena in Aperiodic Order , PhD Thesis, Bielefeld University, in preparation.

Exact renormalisation for patch frequencies in inflation systems Maz´ aˇ c,Fractal and Statistical Phenomena in Aperiodic Order , PhD Thesis, Bielefeld University, in preparation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:05.082068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 351d7fc9-f20e-40b1-a7cb-685d495f1662 · outbound

This paper cites Moody, Uniform distribution in model sets, Can.

Exact renormalisation for patch frequencies in inflation systems Moody, Uniform distribution in model sets, Can

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:04.817273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c548fcf9-8e2e-4563-a302-ed12d158a741 · outbound

This paper cites Complexity and invariant measure of the period-doubling subshift.

Exact renormalisation for patch frequencies in inflation systems Complexity and invariant measure of the period-doubling subshift

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:01.894803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6fb5b852-5089-4b8c-8de5-b55bfdfbf702 · outbound

This paper cites Queff´ elec, Substitution Dynamical Systems—Spectral Analysis , LNM 1294, 2nd ed., Springer, Berlin (2010).

Exact renormalisation for patch frequencies in inflation systems Queff´ elec, Substitution Dynamical Systems—Spectral Analysis , LNM 1294, 2nd ed., Springer, Berlin (2010)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:04.606936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7c899f51-1320-4973-a5e4-494628dbbe37 · outbound

This paper cites Sing, Pisot Substitutions and Beyond , PhD Thesis, Universit¨ at Bielefeld (2006), available electronically at urn:nbn:de:hbz:361-11555.

Exact renormalisation for patch frequencies in inflation systems Sing, Pisot Substitutions and Beyond , PhD Thesis, Universit¨ at Bielefeld (2006), available electronically at urn:nbn:de:hbz:361-11555

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:04.373424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cdb9e26c-7158-40a5-aeb5-1361f865c1c7 · outbound

This paper cites Solomyak, Dynamics of self-similar tilings, Ergod.

Exact renormalisation for patch frequencies in inflation systems Solomyak, Dynamics of self-similar tilings, Ergod

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:43:04.116589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ba527167-6377-4954-b023-9590c99c1c57 · outbound

This paper cites Spectral cocycle for substitution tilings.

Exact renormalisation for patch frequencies in inflation systems Spectral cocycle for substitution tilings

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T18:43:01.236537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0939e5ff-3c3e-4c53-895b-701381459cdf · outbound

This paper cites Uniformly distributed orbits in $\mathbb{T}^d$ and singular substitution dynamical systems.

Exact renormalisation for patch frequencies in inflation systems Uniformly distributed orbits in $\mathbb{T}^d$ and singular substitution dynamical systems

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:43:01.633235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation 9414c634-0822-4719-a007-9c8dd3ac70f5 · inbound

Renormalisation techniques for inflation systems and some of their applications cites this paper.

Renormalisation techniques for inflation systems and some of their applications Exact renormalisation for patch frequencies in inflation systems

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-07-04T02:59:26.053478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.