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Paper Citation Record · LEDGER

Spectral gaps, additive energy, and a fractal uncertainty principle

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1504.06589.

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

pith.paper-citation-record.v1
1504.06589 v3

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 1 of 1 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T16:33:55.213773Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

0 of 0 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved0
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 5c291ee7-82b1-4d11-b61e-c82a8be6cf6c · inbound

Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$ cites this paper.

Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$ Spectral gaps, additive energy, and a fractal uncertainty principle

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-01T16:33:55.213773Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T16:33:55.213773Z digest=sha256:f845217ee532553e1b57b4cb6e8c62a5ba64146f671404b5d87bde5ece8b816e