Paper Citation Record · LEDGER

A Dynamical Criterion Equivalent to the Riemann Hypothesis

As of 11 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2509.10588.

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

pith.paper-citation-record.v1
2509.10588 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:21:47.723207Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

20 of 20 outbound references displayed

verified exact0
verified fuzzy0
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 90de23bf-7f8c-4db4-a6aa-e7b44636ca99 · outbound

This paper cites Sur la distribution des nombres premiers,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Sur la distribution des nombres premiers,

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.646701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23d22b53-2f98-4849-88d7-8049fc8026bc · outbound

This paper cites Trajectory system: start atn >3, applya(m) =m+π(m) if composite,a(m) =m−prevprime(m) if prime; sequence of terms,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Trajectory system: start atn >3, applya(m) =m+π(m) if composite,a(m) =m−prevprime(m) if prime; sequence of terms,

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.651713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd320cc5-121d-44e4-926e-c57a2ffdd0e3 · outbound

This paper cites First occurrence of 2 in the trajectory system (if it occurs),.

A Dynamical Criterion Equivalent to the Riemann Hypothesis First occurrence of 2 in the trajectory system (if it occurs),

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.655749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0625d7c7-fdbe-4d3c-a291-ff3b613a4ecf · outbound

This paper cites Maximum value reached in a trajectory starting fromn(under the same system),.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Maximum value reached in a trajectory starting fromn(under the same system),

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.659698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3518c2c2-69b1-4e6e-955c-969ed00f08f2 · outbound

This paper cites Estimates of Some Functions Over Primes without R.H..

A Dynamical Criterion Equivalent to the Riemann Hypothesis Estimates of Some Functions Over Primes without R.H.

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.663938Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14d4c224-dcbd-484a-862a-9b020f780ac8 · outbound

This paper cites Updating the error term in the prime number theorem.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Updating the error term in the prime number theorem

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.668363Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 055a0e03-8243-4b19-ab7c-b1a0a4601cbc · outbound

This paper cites Iwaniec and E.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Iwaniec and E

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.672881Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 001cb9f9-a30d-4cc5-aa15-758a9a14c13d · outbound

This paper cites an unresolved cited work.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.676930Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9165699f-d8ba-4faf-8613-e71542392356 · outbound

This paper cites an unresolved cited work.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.680439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0805278f-da37-49d8-88b5-0cda2b5098ce · outbound

This paper cites ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse,

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.684502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79fd025b-9cb0-4121-bbdd-01dbdf671edb · outbound

This paper cites an unresolved cited work.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.688187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0fac30d-3e8a-4658-ba56-b3667d8ac0a8 · outbound

This paper cites The Riemann Hypothesis,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis The Riemann Hypothesis,

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.691864Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c6a7edc-71ad-4d6f-b163-254a9b521ecf · outbound

This paper cites An Elementary Problem Equivalent to the Riemann Hypothesis,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis An Elementary Problem Equivalent to the Riemann Hypothesis,

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.695583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 651d3dc5-f681-42f0-be3a-439bd264c73a · outbound

This paper cites A strengthening of the Nyman–Beurling criterion for the Riemann hy- pothesis,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis A strengthening of the Nyman–Beurling criterion for the Riemann hy- pothesis,

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.699288Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfedcd4b-f2c4-46e2-a5f0-7d8cab3344a1 · outbound

This paper cites On some approximative Dirichlet polynomials in the theory of the zeta-function of Riemann,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis On some approximative Dirichlet polynomials in the theory of the zeta-function of Riemann,

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.703359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3fa033c-783c-4c79-a3d5-8e83df1ac903 · outbound

This paper cites On some groups and semigroups of translations,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis On some groups and semigroups of translations,

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.707895Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10ce0615-e0d7-4076-80cc-8eb1b1b64fdb · outbound

This paper cites A closure problem related to the Riemann zeta function,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis A closure problem related to the Riemann zeta function,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.711763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 555b0272-4473-4e41-802f-b8e5b1735504 · outbound

This paper cites ¨Uber die Nullstellen der Zetafunktion,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis ¨Uber die Nullstellen der Zetafunktion,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.715706Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8ee5cde-97b2-42c9-b02d-fa53abf280d6 · outbound

This paper cites ¨Uber die Nullstellen der Zetafunktion,.

A Dynamical Criterion Equivalent to the Riemann Hypothesis ¨Uber die Nullstellen der Zetafunktion,

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.719463Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5639ed16-e22d-4a84-9bd1-8bcd5674a571 · outbound

This paper cites an unresolved cited work.

A Dynamical Criterion Equivalent to the Riemann Hypothesis Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T18:21:47.723207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.