Paper Citation Record · LEDGER

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds

As of 8 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2607.11069.

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

pith.paper-citation-record.v1
2607.11069 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T07:16:58.614647Z

measured 17 of 17 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 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

17 of 17 outbound references displayed

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verified fuzzy0
unresolved17
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d146bc28-8bcc-4cbc-a8c1-09715edc07f8 · outbound

This paper cites Cambridge University Press, 2014.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Cambridge University Press, 2014

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87d7720a-841e-4df9-adb4-b77a0e737df7 · outbound

This paper cites Allaart and Kiko Kawamura.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Allaart and Kiko Kawamura

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25bee0d2-6d69-4b0f-b024-dd5067637c11 · outbound

This paper cites Numeration, Liège 2023.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Numeration, Liège 2023

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

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Observation 00d978ed-347b-4757-a93a-78ec76c09fb1 · outbound

This paper cites Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16602e7e-df5b-4a3e-9018-42dcb988e476 · outbound

This paper cites On sharp isoperimetric inequalities on the hypercube, 2023.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds On sharp isoperimetric inequalities on the hypercube, 2023

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58acbd7a-6547-4e7f-8186-70c8b3b00785 · outbound

This paper cites A class of functional inequalities and the takagi function.Journal of Inequalities and Applications, 6(4):379–393, 2001.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds A class of functional inequalities and the takagi function.Journal of Inequalities and Applications, 6(4):379–393, 2001

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6a92cd4-b4bb-4185-b9a0-9594060933e3 · outbound

This paper cites an unresolved cited work.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 639574fc-8fd7-460d-970e-dc2ada7b2b34 · outbound

This paper cites an unresolved cited work.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48ca1e71-055a-4eb4-aea3-f865d2ced391 · outbound

This paper cites On thelp norms of stochastic integrals and other martingales.Duke Mathematical Journal, 43(4):697–704, 1976.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds On thelp norms of stochastic integrals and other martingales.Duke Mathematical Journal, 43(4):697–704, 1976

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bb16c68-4d8b-4357-883a-573806f5dc4f · outbound

This paper cites Sharp isoperimetric inequalities on the hamming cube near the critical exponent, 2024.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Sharp isoperimetric inequalities on the hamming cube near the critical exponent, 2024

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb195e71-2507-415b-8bee-db89ebd7e499 · outbound

This paper cites A note on the edges of then-cube.Discrete Mathematics, 14(2):157–163, 1976.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds A note on the edges of then-cube.Discrete Mathematics, 14(2):157–163, 1976

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a5ec300-b9aa-445a-b93f-6f937d1ac3dd · outbound

This paper cites A note on the edges of the n-cube.Discrete Mathematics, 14(2):157–163, 1976.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds A note on the edges of the n-cube.Discrete Mathematics, 14(2):157–163, 1976

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a2fbaf2-905d-4e08-a8d6-17efd0fb323a · outbound

This paper cites Ein beispiel einer nicht analytischen funktion.Mathematische Zeitschrift, 3(1–2):93–97, 1919.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Ein beispiel einer nicht analytischen funktion.Mathematische Zeitschrift, 3(1–2):93–97, 1919

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbd2dbe9-b83f-4398-a2f4-408d295ea3d9 · outbound

This paper cites Frauds Bargain Attack: Generating Adversarial Text Samples via Word Manipulation Process.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Frauds Bargain Attack: Generating Adversarial Text Samples via Word Manipulation Process

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7449aef-45f9-41d4-b8cb-49758b37b246 · outbound

This paper cites A simple example of a continuous function without derivative.Proc.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds A simple example of a continuous function without derivative.Proc

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db948b02-37f7-4797-ae0e-0c2fbf29dc18 · outbound

This paper cites Sharp inequalities for the conditional square function of a martingale.The Annals of Probability, 19(4):1679–1688, 1991.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Sharp inequalities for the conditional square function of a martingale.The Annals of Probability, 19(4):1679–1688, 1991

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd2b0008-2a7e-4af7-b8f1-555388e59076 · outbound

This paper cites Sharp square-function inequalities for conditionally symmetric martingales.Transactions of the American Mathematical Society, 328(1):393–419, 1991.

Sharp Ternary Martingale Isoperimetry and $n$-adic Takagi-Type Lower Bounds Sharp square-function inequalities for conditionally symmetric martingales.Transactions of the American Mathematical Society, 328(1):393–419, 1991

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T07:16:58.614647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.