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Paper Citation Record · LEDGER

A graph energy conjecture through the lenses of semidefinite programming

As of 21 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 2 inbound Pith citation observations for arXiv:2509.05814.

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

pith.paper-citation-record.v1
2509.05814 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:13:49.902006Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T19:05:43.242399Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-08T19:05:43.378178Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact2
  • verified fuzzy9
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0ecc82f1-52f2-4af2-b242-2db808b3edcf · outbound

This paper cites Abiad, W.

A graph energy conjecture through the lenses of semidefinite programming Abiad, W

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.507618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.157703Z digest=sha256:3644b22f53dc3f7202b8d849143ea477b1adb4273444afc545e633b4b9c8ebed

Observation 82ef8aff-68fd-450d-92b0-6222cb889e3f · outbound

This paper cites Hoffman colorability of (strongly) regular graphs.

A graph energy conjecture through the lenses of semidefinite programming Hoffman colorability of (strongly) regular graphs

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-05T05:13:50.278778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 65252154-6f25-4605-a8b8-a9c6a6dca97e · outbound

This paper cites Akbari, M.

A graph energy conjecture through the lenses of semidefinite programming Akbari, M

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.499275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.295282Z digest=sha256:0b95e87bbc534424b938fdc3245261eabbf4a49013e669295180df57c75ce0d2

Observation 07ea30a5-0c5f-4cf9-8813-c0b85f101fec · outbound

This paper cites Andrade, M.

A graph energy conjecture through the lenses of semidefinite programming Andrade, M

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.490864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.358307Z digest=sha256:f770f7a80e98a01d2d77ee09318fc80a49d6e86c9355aca6db8e9269a489e34b

Observation 3629ba8a-6fb1-485b-b2bc-2648a73e3429 · outbound

This paper cites Aouchiche and P.

A graph energy conjecture through the lenses of semidefinite programming Aouchiche and P

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.482080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 68b0a8e0-3244-430c-a9bd-7d7f34d205d4 · outbound

This paper cites Conic programming to understand sums of squares of eigenvalues of graphs.

A graph energy conjecture through the lenses of semidefinite programming Conic programming to understand sums of squares of eigenvalues of graphs

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-05T05:13:48.516481Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T05:13:48.516481Z digest=sha256:aad967ce0e407e57f40d459ac52008d37b4a1ceb8478695ba8842bf3ca7086b2

Observation 22459954-e756-4a2d-a4c3-e4ae5932b7d6 · outbound

This paper cites Day and W.

A graph energy conjecture through the lenses of semidefinite programming Day and W

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.474012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.630423Z digest=sha256:94f644ce0c98dd1f59d58b2c539059c682f774ed29a7388ef50f566f0832527d

Observation baab5b8e-c685-4589-8a6f-323169c10063 · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:51.465799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.746843Z digest=sha256:4afe754702a85935eb02a4aa3e7539e54d765d37c07ef15fdc51dee93c81f2f3

Observation 9a96182b-c14b-4686-8459-35a9259c75db · outbound

This paper cites A Spectral Lower Bound on Chromatic Numbers using $p$-Energy.

A graph energy conjecture through the lenses of semidefinite programming A Spectral Lower Bound on Chromatic Numbers using $p$-Energy

Reference 9

Resolution
verified exact
local_arxiv, observed 2026-08-05T05:13:50.069623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:48.875779Z digest=sha256:ffe2815cf6812619dabf5ee0b5a4e76f3ae02e44465d9dff322249196c1ae2ff

Observation 25c908fb-74aa-4b91-9ff4-6943ba675cca · outbound

This paper cites Erd˝ os and A.

A graph energy conjecture through the lenses of semidefinite programming Erd˝ os and A

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.457111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation e58f6bc3-8824-40dd-8f86-ba1f64c13bce · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:51.447296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.077509Z digest=sha256:ac636220fa4d929b545d9bc5dc1bf7eb70ba8a2b840e59600f6436a538d60bef

Observation 1a2062d3-cf18-4312-857e-6ec72ef790c2 · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:51.437971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.137728Z digest=sha256:3a23944b98ddfe2e639c6364c2d795a3c2a9c7679abc554485b170e7125e76ec

Observation d4759657-1a7f-4779-8182-f54c1ec5b43f · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:51.428809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6d2c8fd0-8ce0-44e0-89ec-c7b68c154f8e · outbound

This paper cites Laurent, S.

A graph energy conjecture through the lenses of semidefinite programming Laurent, S

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.269050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.372043Z digest=sha256:3f842a4683d0c1221156c23eb0ad330c979491fef6a094ef973fdc1c64293baf

Observation 6f5003c1-e744-4361-9451-4f5d2771e625 · outbound

This paper cites Liu and B.

A graph energy conjecture through the lenses of semidefinite programming Liu and B

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:51.054221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ce8ef138-58d9-46f1-80c8-f8db78bb4f15 · outbound

This paper cites Lov´ asz.

A graph energy conjecture through the lenses of semidefinite programming Lov´ asz

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-05T05:13:49.480281Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T05:13:49.480281Z digest=sha256:eab54230317e7d4cc13e8e68499dcc750f89521bd70198b050ed0b69fe80e65c

Observation 9fccc9a3-1d8d-4988-b429-b6580200f36c · outbound

This paper cites Nikiforov.

A graph energy conjecture through the lenses of semidefinite programming Nikiforov

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:13:50.887788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.603456Z digest=sha256:48f76cd34df4cf7b77c3e1f2217ab85d5e73936421616d8e2ad1b8502a79f44e

Observation 5d40ccff-0945-48ce-87da-4a0c89e78fd5 · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:50.723990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.682472Z digest=sha256:48cf5d68288ebb3c89967045dea47e5415f116b6c8052a35927d971dbece00e4

Observation 08444992-3fd1-40bc-841f-95875517b909 · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:50.542552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation fa77cb32-2fdc-4445-9b58-4ed4e66a2836 · outbound

This paper cites an unresolved cited work.

A graph energy conjecture through the lenses of semidefinite programming Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:13:50.450341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T05:13:49.860553Z digest=sha256:8e73b5a0486933fde1e7be7cd1ba437a5f0bfc9621bfd67a9f459f92d5d06716

Observation 2ff493f4-e5c8-408c-880e-69dfad0626b5 · outbound

This paper cites Extremal values for the square energies of graphs.

A graph energy conjecture through the lenses of semidefinite programming Extremal values for the square energies of graphs

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-05T05:13:49.902006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T05:13:49.902006Z digest=sha256:462f2c5f4b13252e5db57600bd7cdd7ac004df245845b692910beea17cc08f92

Pith citing papers

Observation 1d35fcdd-6005-4429-bf25-fe2d070ba43e · inbound

Energy and independence number cites this paper.

Energy and independence number A graph energy conjecture through the lenses of semidefinite programming

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-01T11:42:47.552323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T11:42:47.552323Z digest=sha256:a2d3c764645f7f19fc0d6c4435be364385e4a8beee6c753f531243b2cedf3334

Observation f1705c4e-2c60-46b2-b495-8e20be0fad9c · inbound

Extremal Graphs for the Energy-Independence Number Inequality cites this paper.

Extremal Graphs for the Energy-Independence Number Inequality A graph energy conjecture through the lenses of semidefinite programming

Reference 1

Resolution
verified exact
local_arxiv, observed 2026-08-08T19:05:43.383058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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