Paper Citation Record · LEDGER

Minimizing Lattice Energy and Hexagonal Crystallization

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2411.17199.

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

pith.paper-citation-record.v1
2411.17199 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T12:29:50.390901Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:39:23.346973Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T22:39:23.501754Z

Reference resolution

34 of 34 outbound references displayed

verified exact0
verified fuzzy22
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bd485047-f31d-42f7-87ac-8b569c3506f4 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.734434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ff968e15-555f-49e1-bf39-f0f89b0eda94 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.724338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e26c8180-7872-4a09-90aa-8a4ce6762bba · outbound

This paper cites Alvarez-Gaum´ e, G.Moore and C.Vafa, Theta functions, modular invariance, and strings,Comm.

Minimizing Lattice Energy and Hexagonal Crystallization Alvarez-Gaum´ e, G.Moore and C.Vafa, Theta functions, modular invariance, and strings,Comm

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.714643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5af75959-4943-4a29-bfc6-f33dc804cca9 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T12:29:50.288413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb23513d-011e-41aa-857c-20bc1d2ed053 · outbound

This paper cites B´ etermin and P.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin and P

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.699353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0c5a984e-9a21-4d72-b591-eaa923bd1b04 · outbound

This paper cites B´ etermin, Two-dimensional theta functions and crystallization among Bravais lattices, SIAM Journal on Mathematical Analysis, 48(5) (2016), 3236-269.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin, Two-dimensional theta functions and crystallization among Bravais lattices, SIAM Journal on Mathematical Analysis, 48(5) (2016), 3236-269

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.688439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 77533799-b44a-4d9b-ad67-df8ea23e3df1 · outbound

This paper cites B´ etermin, Local variational study of 2d lattice energies and application to Lennard-Jones type interactions, Nonlinearity, 31(9) (2018), 973-4005.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin, Local variational study of 2d lattice energies and application to Lennard-Jones type interactions, Nonlinearity, 31(9) (2018), 973-4005

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.679075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c4ed8299-30e0-464a-a07f-36a852b06a70 · outbound

This paper cites B´ etermin, Minimizing lattice structures for Morse potential energy in two and three dimensions, Journal of Mathematical Physics, 60(10) (2019), 102901.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin, Minimizing lattice structures for Morse potential energy in two and three dimensions, Journal of Mathematical Physics, 60(10) (2019), 102901

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.669669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d9931c53-ea70-4cd6-98cd-94a24d08d84c · outbound

This paper cites B´ etermin and M.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin and M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.659900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 84bd18c1-2263-4b51-96fa-f2e714c55d55 · outbound

This paper cites B´ etermin, M.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin, M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.650515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1e225b81-ec13-4fc6-b34a-ecd7a8de4b77 · outbound

This paper cites B´ etermin and M.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin and M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.640787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e802b8fa-2971-4e75-b967-2202ed4436dd · outbound

This paper cites B´ etermin, On energy ground states among crystal lattice structures with prescribed bonds, Journal of Physics A, 54(24): 245202, 2021.

Minimizing Lattice Energy and Hexagonal Crystallization B´ etermin, On energy ground states among crystal lattice structures with prescribed bonds, Journal of Physics A, 54(24): 245202, 2021

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.631666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cc599f57-5bcd-4ddc-8e3a-c8a5a22a2f10 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.622322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 852a81c0-1949-4c49-ad0c-a6594456bae1 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.613182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b00444ce-fe26-4335-9ec8-b59859ec2f69 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.604489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 36831b70-5a72-4eaa-8594-ca1dfcf2659b · outbound

This paper cites Evans, A fundamental region for Hecke modular group, J.

Minimizing Lattice Energy and Hexagonal Crystallization Evans, A fundamental region for Hecke modular group, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.595668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f7d136b8-25d9-4014-a744-98eeab2e5efe · outbound

This paper cites Faulhuber, M.

Minimizing Lattice Energy and Hexagonal Crystallization Faulhuber, M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.586436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 580e691a-bb6b-47a4-a4cf-0ba27763ef56 · outbound

This paper cites Faulhuber, A short note on the frame set of odd functions, Bulletin of the Australian Mathematical Society, 2018, 98(3), 481-493.

Minimizing Lattice Energy and Hexagonal Crystallization Faulhuber, A short note on the frame set of odd functions, Bulletin of the Australian Mathematical Society, 2018, 98(3), 481-493

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.577029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 14dbed1e-7479-4169-a434-afc836ad90bc · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.567977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c23df606-d4ae-482e-a67f-16d9a6380a47 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.558810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b49336cc-4cf9-42f1-a541-d88f30d86d48 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.549486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6f67ddac-9baf-44ea-989a-7de944248000 · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.539925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 687f3f2a-becf-4e77-a0f0-514395c61f0d · outbound

This paper cites an unresolved cited work.

Minimizing Lattice Energy and Hexagonal Crystallization Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:29:50.530744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f748ebfa-2164-4d00-8333-aab4eb64304a · outbound

This paper cites Luo and J.

Minimizing Lattice Energy and Hexagonal Crystallization Luo and J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.520812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3685fa5a-c5d2-49c2-97b2-5152b764dc63 · outbound

This paper cites Luo and J.

Minimizing Lattice Energy and Hexagonal Crystallization Luo and J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.510946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ad648e1b-4286-4132-b2fe-f61a0ce71a41 · outbound

This paper cites On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials.

Minimizing Lattice Energy and Hexagonal Crystallization On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-12T12:29:50.363440Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e42ac5d2-6853-43c8-8764-eef2f2a3777b · outbound

This paper cites Luo and J.

Minimizing Lattice Energy and Hexagonal Crystallization Luo and J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.501332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2c044f95-a495-4fce-89ce-b126dadfeb98 · outbound

This paper cites Montgomery, Minimal theta functions, Glasgow Math.

Minimizing Lattice Energy and Hexagonal Crystallization Montgomery, Minimal theta functions, Glasgow Math

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.491522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f83f3f67-b3bc-4b45-8d09-9affbdb44d87 · outbound

This paper cites Sandier and S.

Minimizing Lattice Energy and Hexagonal Crystallization Sandier and S

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.480989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 54851a38-5896-4b40-87e7-10dd39883b14 · outbound

This paper cites Serfaty, Systems of points with Coulomb interactions, Proceedings of the International Congress of Mathe- maticians Rio de Janeiro 2018,Vol.

Minimizing Lattice Energy and Hexagonal Crystallization Serfaty, Systems of points with Coulomb interactions, Proceedings of the International Congress of Mathe- maticians Rio de Janeiro 2018,Vol

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.470702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 338c8db0-b72c-4e9c-8f25-092750190041 · outbound

This paper cites Simon, Fifteen problems in mathematical physics, Oberwolfach Anniversary Volume, 1984, 423-454.

Minimizing Lattice Energy and Hexagonal Crystallization Simon, Fifteen problems in mathematical physics, Oberwolfach Anniversary Volume, 1984, 423-454

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.459869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ba75d091-ec02-4e12-a9be-0f3d84a40706 · outbound

This paper cites Simon, Schr¨odinger Operators in the Twenty-First Century, Mathematical Physics 2000, Imperial College London, pp.

Minimizing Lattice Energy and Hexagonal Crystallization Simon, Schr¨odinger Operators in the Twenty-First Century, Mathematical Physics 2000, Imperial College London, pp

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.450298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fbefd34d-a16d-4b4a-96e8-4865746de70b · outbound

This paper cites Strohmer and S.

Minimizing Lattice Energy and Hexagonal Crystallization Strohmer and S

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.439910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9e350914-1684-47ae-9ca6-f41b6a6abec7 · outbound

This paper cites Uzunova, W.

Minimizing Lattice Energy and Hexagonal Crystallization Uzunova, W

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:29:50.430066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation a3156f94-b090-4b38-88e6-b60a5a4a36d6 · inbound

Signs of high order derivatives for the theta and Epstein zeta functions and application cites this paper.

Signs of high order derivatives for the theta and Epstein zeta functions and application Minimizing Lattice Energy and Hexagonal Crystallization

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T22:39:23.506344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.