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Paper Citation Record · LEDGER

A graph energy conjecture through the lenses of semidefinite programming

As of 16 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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.

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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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.295282Z digest=sha256:ea855e6208ae5da1dad4b3eebb975ecdeca15b3fd1ead1c7bda65f11de47a6e8

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.358307Z digest=sha256:58fc71cfbd39940e078afd1a54469b3eb1573457403de609336fd26305874c1d

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.483595Z digest=sha256:32e1e8c92d223ed0fcb101ae01829a309730cc7f2d51b1574079fe7f05fd53da

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=sha256:89a058257e4ecea26bcb119b6a559153ee8a52e7f3a8700c9b2f5fdf1b7c652b

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.630423Z digest=sha256:30d2040831565c935ac4d37201f9ed3f42609a07953e8516714de028b63647a6

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.746843Z digest=sha256:377b28cc844ff91feb3dc28a99a5dbe74e0b372d26399e5a3b69561c119364bb

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.875779Z digest=sha256:1e0e33d67a2dda2464b9b5b89d1093ca4204401d1cd83e3be2452c1b3f90158b

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:48.946717Z digest=sha256:9277eda118a43d591f59c82f7c289a58163d25f8c212c33656e1d03d24fdcb1c

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.077509Z digest=sha256:e898da094b4b1c7d708b8f76a1a6d9e12d25e9e721f6755c910a0f6f4b982332

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.137728Z digest=sha256:6a9b8c90a6856e87ac520a95fe64a5b2ffd33df54514ecb5503526b93141bd85

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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.372043Z digest=sha256:631c6685244fc27239536c1555a53407a21530f0b39f6d8175da380d5d55a301

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.438516Z digest=sha256:af9dd94c91815fa27c187e24440385bc9ea42b0f9e7d7503f991ac6fdc1dfd38

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.603456Z digest=sha256:3d9ab7372bbcc22bdd883917c6d1a92595936efd9df056d2890623146fab9723

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.682472Z digest=sha256:ad8bb6d6820caa1a5dde9c83728237464943fd210f43c86a6eb8b7056e8a90dc

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.774798Z digest=sha256:0d102c71ba50daa1dfa667e6216fc00701d461ec4920e8b9777a3ef9faea7d73

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-05T05:13:49.860553Z digest=sha256:7d26615d48fb527575570b44b901777db33eb0e3d79e6049a542c34fb20eb032

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=sha256:486dd6eb4d1392074bead81b416f5d1a0182b19d4714f506531cd85bef7b3b2c

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-08T19:05:43.242399Z digest=sha256:d2d31ab8c77e16358ed357497ff670dd83825ab95a4f5aa66d712f623de9a9f5