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Paper Citation Record · LEDGER

A graph energy conjecture through the lenses of semidefinite programming

As of 8 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation 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 22 of 22 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T11:42:47.552323Z

measured 0 of 1 external citation measurements

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

Source: cited_works

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.157703Z digest=sha256:fea81fbe5f7998377339b34127f4f92586f9775e55a0f4ecc917f7458833628e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.246010Z digest=sha256:96caf2afd59dda10829ef901f5acf76d02f079afdfa71cab4e180e53ccf84260

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.295282Z digest=sha256:6cdc0e02e97645061e39846b55fe5805e96f62e7fdb844ae1414c677be66a9a7

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.358307Z digest=sha256:0129121ca125f2bf7bf98ee4251b4c42cb75b61ccfcd33ae25a369c2e31b2d48

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.483595Z digest=sha256:11ef2102dd8443e18254422c99f4a84282aef936e1170a09ff539d189e6fcc63

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:b005b5b0c650c2906f3c494abfde9ef208f364d3d2b76d03d60c3c7c0f2c53d2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.630423Z digest=sha256:88fb8eff8e9f1bdb179669268b374f2edb1c804a970ff4811a912929f5b1567a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.746843Z digest=sha256:2f0e36d628cf871d1b0d1d04211c9a1e7b4f8b6a97570a514c77f69dcb2e819b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.875779Z digest=sha256:6a3a3bb0ef4119ef69870adf487e7d505029078a73ac9c883eab78db4dc5a7e1

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:48.946717Z digest=sha256:01f12f0b862e4995a996e6aa217895eb8028096593357ddcab206ad08e094de0

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.077509Z digest=sha256:7abcab1152f033fb72f7950df32bb3335b075badd8ea6bf185ce8ea15bb9c8f6

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.137728Z digest=sha256:e26b9617bfd064767d4b90a3273a8d1f5e34dc4020788df2fa41af1917628910

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.196716Z digest=sha256:758b5d824d2f7f29af4e6e71b0ddab9c6e1c3cb6b7adc1b8d5287ba8bceb6e4b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.372043Z digest=sha256:b4ea23f3493933257c189d55321aca5ffd69ccf1a1c4e874a35879c54c883b1c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.438516Z digest=sha256:b9f09560e4abef951316d67753bdde6914b9ae129b5238c11ab6887c5f322cd4

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=sha256:99399c4af88362c7f6dbfee73776503e15d4a395ed3fb2a53dd3614be471b1c1

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.603456Z digest=sha256:e0a23e3fed67ae4d50f96030e69c4cac97e51314599b057d768503c1f7cef018

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.682472Z digest=sha256:6d58b141060654f061d2a8d433a70ff4f35f4c29265a4a8e43f5aa33ccfa0b41

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.774798Z digest=sha256:00aa3aeeee8b236e1aa333d47e347d67a0b20760d0859f2e0d0bff8a0dd27cab

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T05:13:49.860553Z digest=sha256:19668dadf533781c7d890a5cc140396bf1a8ee26b17f78ad6c925540f88e7421

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:e3b5b1d934ddad1eb35c6261d3094298544de136441b975110813db07ab49cca

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:c293b234db1d12d5de8402ab714893a404aaeb350f5e52d02653a1bdd3300515