Paper Citation Record · LEDGER

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell

As of 19 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2505.23238.

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

pith.paper-citation-record.v1
2505.23238 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:57:12.318568Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:57:10.562744Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T12:57:12.389570Z

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy22
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ad2eb320-c3f4-4bbf-b4a4-981b6c61af93 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:16.714258Z

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 1ad7bef1-f8b2-424c-824a-b5c15a393a14 · outbound

This paper cites Die Methode istmethodisch unabhängigvon spektralen, statistischen oder nume- rischen Ansätzen und benötigt keine Kenntnis der exakten Nullstellen.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Die Methode istmethodisch unabhängigvon spektralen, statistischen oder nume- rischen Ansätzen und benötigt keine Kenntnis der exakten Nullstellen

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:16.573809Z

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 25741d31-34f9-4db6-a716-fff43b4a2136 · outbound

This paper cites Da das Flächenmaß in einer Umgebung vonL einer Produktmenge entspricht, gilt auch im komplexen Raum die lokale Integrabilität.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Da das Flächenmaß in einer Umgebung vonL einer Produktmenge entspricht, gilt auch im komplexen Raum die lokale Integrabilität

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:15.723591Z

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 1e4184a4-2121-4526-b90f-74bd47591357 · outbound

This paper cites Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-07T12:57:12.475728Z

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 a572dbcf-8b77-4af9-a21e-45bc4f248e50 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:16.397698Z

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 7600e9c9-5e8a-4f4e-950f-6b7729271f1b · outbound

This paper cites The method ismethodologically independentof spectral, statistical, or numerical approaches and does not require knowledge of the exact zeros.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell The method ismethodologically independentof spectral, statistical, or numerical approaches and does not require knowledge of the exact zeros

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:16.314055Z

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 6b35af3f-c8f0-4e88-8cb2-e557a71ca0bd · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:16.175508Z

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 deac2931-a8a6-494d-a4e8-08f43eb61f83 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:16.077128Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 17fdde1e-b97c-4f3f-bf38-d1c81b9ff3cd · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:15.970329Z

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 89c3ee9c-e5a5-4281-8f6a-80feb2fd9279 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:15.839471Z

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 8caea130-9177-4c73-875b-7c2b0dbf75be · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:15.543581Z

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 1244c307-6995-4fc7-a7fe-11c4e79da83b · outbound

This paper cites • Symmetrische Viererpaarbildung von Nullstellen.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell • Symmetrische Viererpaarbildung von Nullstellen

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:15.420678Z

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 12053631-86e3-43e4-8db8-a83ce05bdd3f · outbound

This paper cites Betrachte die vier zugehörigen Punkte im kritischen Streifen: β±iγ und (1−β)±iγ.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Betrachte die vier zugehörigen Punkte im kritischen Streifen: β±iγ und (1−β)±iγ

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:15.291652Z

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 a032825c-fa32-4436-ab99-fc5304ebf35a · outbound

This paper cites Diese Nullstellen liegen somit nicht auf der kritischen Linie und erfüllenβ̸= 1 2.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Diese Nullstellen liegen somit **nicht** auf der kritischen Linie und erfüllenβ̸= 1 2

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:15.173539Z

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 f06bd427-cb84-4b66-8046-7f3fe4c55232 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:15.038295Z

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 16a28adb-cf07-40b0-98ef-285399ac474f · outbound

This paper cites Diese Repräsentationen besitzen unterschiedliche analytische Eigenschaften und Gültigkeitsbereiche, sind aber sämtlich geeignet, um das IntegralmodellW(R) konkret auszuwerten.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Diese Repräsentationen besitzen unterschiedliche analytische Eigenschaften und Gültigkeitsbereiche, sind aber sämtlich geeignet, um das IntegralmodellW(R) konkret auszuwerten

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.943768Z

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 ab896aec-82df-4856-b9ca-2ff21295aa7a · outbound

This paper cites Wir definieren wie zuvor: Dreg R :={s =σ +it∈ C|σ∈ [δ, 1−δ], t∈ [−R,R ]}\ N(R)⋃ k=1 B(ρk,εk).

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Wir definieren wie zuvor: Dreg R :={s =σ +it∈ C|σ∈ [δ, 1−δ], t∈ [−R,R ]}\ N(R)⋃ k=1 B(ρk,εk)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.818429Z

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 3d160825-1870-4ef1-92c3-3674fe1ac915 · outbound

This paper cites Lemma 5.4.1 (Untere Schranke).

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Lemma 5.4.1 (Untere Schranke)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.742120Z

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 51d4fead-f47d-4890-8d94-13a203591588 · outbound

This paper cites Da|ζ(s)|≥ mR, folgt für den Integran- den: JC(s) = 1 |ζ(s)|λ·|σ− 1 2|p≤ 1 mλ R · 1 |σ− 1 2|p.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Da|ζ(s)|≥ mR, folgt für den Integran- den: JC(s) = 1 |ζ(s)|λ·|σ− 1 2|p≤ 1 mλ R · 1 |σ− 1 2|p

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.650982Z

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 a444ba4b-1782-4f09-915e-1167e58f4ff5 · outbound

This paper cites Die Fläche des Rechtecks ist Fläche(Dreg R )≤ (1− 2δ)· 2R.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Die Fläche des Rechtecks ist Fläche(Dreg R )≤ (1− 2δ)· 2R

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.504145Z

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 84470145-fc3f-4b77-bc63-784b35ec06e0 · outbound

This paper cites W(R)≤ 1 2R· 1 mλ R · ∫R −R dt· ∫1−δ δ 1 |σ− 1 2|pdσ = 1 mλ R · ∫1−δ δ 1 |σ− 1 2|pdσ.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell W(R)≤ 1 2R· 1 mλ R · ∫R −R dt· ∫1−δ δ 1 |σ− 1 2|pdσ = 1 mλ R · ∫1−δ δ 1 |σ− 1 2|pdσ

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.415329Z

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 ef63d96d-12a1-4f88-83dc-517a8946d651 · outbound

This paper cites Wir betrachten den kritischen Teilbereich des In- tegrationsstreifens entlang der reellen Achse, wobei nur die Nähe zur kritischen Linie σ = 1 2 problematisch ist.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Wir betrachten den kritischen Teilbereich des In- tegrationsstreifens entlang der reellen Achse, wobei nur die Nähe zur kritischen Linie σ = 1 2 problematisch ist

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:14.275303Z

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 405eb79d-7cd1-4eed-a605-42695019f15d · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:14.144918Z

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 240a48c5-86a4-4d17-b078-3018a49341bb · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:13.998204Z

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 437d1475-1be9-4409-90d7-bd31b32eb995 · outbound

This paper cites Die Funktion|Γ(s)| ist aufσ∈ [δ, 1−δ], |t|≤ R, holomorph und dort nach unten beschränkt: |Γ(s)|≥ γR > 0 ⇒ |ζ(s)|≤ C γR =:MR.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Die Funktion|Γ(s)| ist aufσ∈ [δ, 1−δ], |t|≤ R, holomorph und dort nach unten beschränkt: |Γ(s)|≥ γR > 0 ⇒ |ζ(s)|≤ C γR =:MR

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:13.896730Z

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 a329649b-31fd-400d-96e5-37829126ab44 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:13.717073Z

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 4b2cc753-7d9c-43c8-bd36-c7ee2e9c016e · outbound

This paper cites AufDreg R gilt: JC(s) = 1 |ζ(s)|λ·|σ− 1 2|p≤ 1 mλ R · 1 |σ− 1 2|p.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell AufDreg R gilt: JC(s) = 1 |ζ(s)|λ·|σ− 1 2|p≤ 1 mλ R · 1 |σ− 1 2|p

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:13.609434Z

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 7d58f0a8-fea8-4d5d-9f75-fe155c42eb48 · outbound

This paper cites Die Fläche des Streifens beträgt höchstens2R· (1− 2δ), und der Gewichtsfaktor ist fürp< 1 integrierbar: ∫1−δ δ 1 |σ− 1 2|pdσ <∞.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Die Fläche des Streifens beträgt höchstens2R· (1− 2δ), und der Gewichtsfaktor ist fürp< 1 integrierbar: ∫1−δ δ 1 |σ− 1 2|pdσ <∞

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:13.445290Z

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 426012d7-74f9-4d4a-923f-fccde5eb55ae · outbound

This paper cites Da die Abschätzung unabhängig vonR ist, folgt: lim R→∞ W(R)<∞.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Da die Abschätzung unabhängig vonR ist, folgt: lim R→∞ W(R)<∞

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:13.324200Z

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 08d18348-5920-45b1-8ca2-2bd7afc56e6e · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:13.215300Z

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 8ce16983-c26d-4e07-be39-b8980414e713 · outbound

This paper cites Edwards.Riemann’s Zeta Function.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Edwards.Riemann’s Zeta Function

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:13.065964Z

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 c1ecd960-e86e-4eff-8f10-bb8f7a831dc2 · outbound

This paper cites Variae observationes circa series infinitas.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Variae observationes circa series infinitas

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:12.958825Z

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 058ae7aa-7a0c-4d3e-92fc-dbef6ef4c5ca · outbound

This paper cites Folland.Real Analysis: Modern Techniques and Their Applications.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Folland.Real Analysis: Modern Techniques and Their Applications

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:12.807360Z

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 ad2fff8c-b32b-4d42-9989-ea64befed504 · outbound

This paper cites Analytic Number Theory, volu- me 53 ofAmerican Mathematical Society Colloquium Publications.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Analytic Number Theory, volu- me 53 ofAmerican Mathematical Society Colloquium Publications

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:12.729838Z

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 dc5947db-8ab4-4e77-915b-a30f6aef79d5 · outbound

This paper cites Über die anzahl der primzahlen unter einer gegebenen größe.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Über die anzahl der primzahlen unter einer gegebenen größe

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:57:12.626722Z

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 bd0e1431-4385-4cf3-b7b1-3841711ff445 · outbound

This paper cites an unresolved cited work.

Beweis der Riemannschen Vermutung \"uber ein reguliertes normiertes Integralmodell Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:57:12.561610Z

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 1e4184a4-2121-4526-b90f-74bd47591357 · inbound