Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T20:04:53.943349Z
Paper Citation Record · LEDGER
On finitely many base $q$ expansions
As of 19 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2501.09582.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T20:00:56.122298Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T20:00:57.114897Z
Reference resolution
21 of 21 outbound references displayed
- verified exact0
- verified fuzzy20
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1ee4097b-80d4-435a-9760-3f7122ba0d31 · outbound
This paper cites Entropy, topological transitivity, and dimensional properties of unique q-expansions.
On finitely many base $q$ expansions Entropy, topological transitivity, and dimensional properties of unique q-expansions
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.391382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 07e38147-05b4-488b-abee-77471f1c7171 · outbound
This paper cites Generalized golden ratios over integer alphabets.
On finitely many base $q$ expansions Generalized golden ratios over integer alphabets
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.376691Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6b46a64b-a87c-446b-adc0-0f52b277ecfc · outbound
This paper cites On small bases which admit countably many expansions.
On finitely many base $q$ expansions On small bases which admit countably many expansions
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.362389Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6b82b56f-27d0-417b-9bf9-0664252d9226 · outbound
This paper cites On the cardinality and dimension of the slices of Okamoto’s functions.
On finitely many base $q$ expansions On the cardinality and dimension of the slices of Okamoto’s functions
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.348107Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7cd22b8e-f6cc-43b4-8b09-03e530d5092f · outbound
This paper cites Expansions in non-integer bases: lower order revisited.
On finitely many base $q$ expansions Expansions in non-integer bases: lower order revisited
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.333565Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 07bedafb-46d5-450f-b019-a01615046483 · outbound
This paper cites Metric results for numbers with multiple q-expansions.
On finitely many base $q$ expansions Metric results for numbers with multiple q-expansions
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.319606Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 613ea0ca-beda-44b1-b8bd-d97c85585e6c · outbound
This paper cites On the structure of univoque numbers.
On finitely many base $q$ expansions On the structure of univoque numbers
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.304960Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 49cf697d-8c74-4a83-9c5f-36212db2ce0e · outbound
This paper cites On the uniqueness of the expansions 1 =P q−ni.
On finitely many base $q$ expansions On the uniqueness of the expansions 1 =P q−ni
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.290589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 39ade22b-03e7-496b-89f1-18d8c1f5054a · outbound
This paper cites On the number of expansions 1 =P q−ni.
On finitely many base $q$ expansions On the number of expansions 1 =P q−ni
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.274581Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 905691f4-bf79-4c5e-8316-107bd0770dfb · outbound
This paper cites Characterization of the unique expansions 1 =P∞ i=1 q−ni and related problems.
On finitely many base $q$ expansions Characterization of the unique expansions 1 =P∞ i=1 q−ni and related problems
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.151021Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9f9a7baa-9d5e-4596-9c76-5bb0b083b0a5 · outbound
This paper cites Intersections of thick compact sets in Rd.
On finitely many base $q$ expansions Intersections of thick compact sets in Rd
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.136051Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e5a9a0b6-88b2-411c-9990-0465ee17a248 · outbound
This paper cites Unique representations of real numbers in non-integer bases.
On finitely many base $q$ expansions Unique representations of real numbers in non-integer bases
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.120092Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 03662442-fa1e-440a-84c9-f0bbae838c5a · outbound
This paper cites Hausdorff dimension of univoque sets and devil’s staircase.
On finitely many base $q$ expansions Hausdorff dimension of univoque sets and devil’s staircase
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.105157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ce636a7c-6ebe-4f66-a3d9-4958d88051d2 · outbound
This paper cites Unique developments in non-integer bases.
On finitely many base $q$ expansions Unique developments in non-integer bases
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.090136Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ce73d408-a8d3-4a87-9bf7-355dca5586c4 · outbound
This paper cites Newhouse.
On finitely many base $q$ expansions Newhouse
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.075293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8738dacf-8c69-49a2-bc89-c1761779bef5 · outbound
This paper cites On the β-expansions of real numbers.
On finitely many base $q$ expansions On the β-expansions of real numbers
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.043388Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fe3a4440-d298-4f57-8cee-d3aa35261e2b · outbound
This paper cites Representations for real numbers and their ergodic properties.Acta Math.
On finitely many base $q$ expansions Representations for real numbers and their ergodic properties.Acta Math
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.028243Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a22fb27b-300f-43df-82cd-a8c962274e1e · outbound
This paper cites Almost every number has a continuum of β-expansions.
On finitely many base $q$ expansions Almost every number has a continuum of β-expansions
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:54.012770Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e9ba9a69-eb0a-4c97-8e34-4bdd3ac281ea · outbound
This paper cites Expansions in non-integer bases: lower, middle and top orders.
On finitely many base $q$ expansions Expansions in non-integer bases: lower, middle and top orders
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:53.997037Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c03364be-b96e-464d-80b4-1a0b919e0296 · outbound
This paper cites Ergodic properties of the Erd¨ os measure, the entropy of the golden shift, and related problems.
On finitely many base $q$ expansions Ergodic properties of the Erd¨ os measure, the entropy of the golden shift, and related problems
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:04:53.980723Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 74444321-697a-4edf-804e-bcd507dcc7b1 · outbound
This paper cites an unresolved cited work.
On finitely many base $q$ expansions Unresolved cited work
Reference 202
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:04:54.059937Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
Observation 7c14efe1-9a2b-4d3c-9528-d51aa39b077e · inbound
The matrix potential game and structures of self-affine sets cites this paper.
The matrix potential game and structures of self-affine sets On finitely many base $q$ expansions
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T20:00:57.178555Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.