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Paper Citation Record · LEDGER

Softly $\pi g\hat{D}$-Normal Spaces

As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2506.08431.

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

pith.paper-citation-record.v1
2506.08431 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:20:14.553508Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

28 of 28 outbound references displayed

  • verified exact0
  • verified fuzzy17
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7a928985-2afc-498a-a822-a580917ed69c · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.404548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:12.594246Z digest=sha256:4cc572cf20b5371bd6d9c3971c952c5be75f8899c0d6a4c719c25b274adbd731

Observation 26b3925a-8a49-4845-9973-808f9498f191 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.391420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:12.675410Z digest=sha256:cbd875eacdc8f6d81b3c67d872e0ca0355245917895e20a19b3f8a8b83f333f1

Observation 6e8e30cd-208a-4284-95b1-8f6e084c2667 · outbound

This paper cites V., Real functions and near normal spaces , Sibirskii Mat.

Softly $\pi g\hat{D}$-Normal Spaces V., Real functions and near normal spaces , Sibirskii Mat

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.378004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:12.756013Z digest=sha256:d328804a8c40616a2cbe4bea1c885e19c790d07b30dbedfaf4d0d1e48c0dcdad

Observation 59936204-7ece-4bac-9ccd-4ea42c9f143d · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.363781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:12.839395Z digest=sha256:051876ee1ca66350c2d2404e0252bd215264d12aeafd2c0bd47626432e74d01a

Observation 3cc09131-f863-4618-9441-77f99f36876a · outbound

This paper cites and Rahman, M.

Softly $\pi g\hat{D}$-Normal Spaces and Rahman, M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.349979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:12.925606Z digest=sha256:08d08e948037b8e05c4e10817951f916939bbbfa6710e82d86b3ff666acc8479

Observation c8104926-5ecc-4f1e-a0a9-9666605d3dc1 · outbound

This paper cites N., π-normal toplogical spaces , Filomat, 22 (1), 173-181 (2008).

Softly $\pi g\hat{D}$-Normal Spaces N., π-normal toplogical spaces , Filomat, 22 (1), 173-181 (2008)

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.336638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.011836Z digest=sha256:a8538b1a090d8f62ced7be8f556f91ea399dff23d3ecaebfafb8a8e1d128ef21

Observation da0a8f02-fc5f-4e61-ac85-5f944d1e87e5 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.322601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.116224Z digest=sha256:66be430bf02c11fa41a0de95b04e4e57c3a4c4152e5187581d28268b2a1ec5d1

Observation b193d8ed-a5e9-4250-bd48-f57496d075f0 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.308396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.219653Z digest=sha256:4e66ff16e7e4d7a8ce2d00ef84f63714ccac3fb79cd3e40ca622a292fa441e3d

Observation 5e3ca026-d175-4028-9d2a-4905492686e4 · outbound

This paper cites G., Benchalli, S.

Softly $\pi g\hat{D}$-Normal Spaces G., Benchalli, S

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.294408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.281459Z digest=sha256:fa7b5aa36ef6e60f784ee55cff6a804ccba6492e5c8d02362ee452d3b91ad336

Observation 7519725d-ce93-4e66-bced-e7ea167a1344 · outbound

This paper cites and Rajpal, R., πgβ -normal spaces in topological spaces, International J.

Softly $\pi g\hat{D}$-Normal Spaces and Rajpal, R., πgβ -normal spaces in topological spaces, International J

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.281547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.349368Z digest=sha256:e63c230cb4ab78b60801da2522c7515ccae83e9ae17ba5812a13f889731157d1

Observation 776ce133-ae65-4472-9417-2a83e30bd8ca · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.268151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.432848Z digest=sha256:6916ade43c83a298756651df3f88e41d38a693f8f3fc7ae3571f9c2c4391176f

Observation baf647f4-761a-4ae6-95f0-5aed1f27221b · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.254588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.531632Z digest=sha256:ba314eaf6b3deed5081d79f69b5d3207526cb38a8c6c789aa52afb38f69fcb39

Observation adf9ac6d-6656-4a47-abee-f097bf7d8682 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.240847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.588876Z digest=sha256:d739cc9c0a4da28d445f0c2d2a1546f21aca10353f1f3d8b4c1f547585cbc6d8

Observation e981a30d-2bea-452c-8a01-e1aba43000ce · outbound

This paper cites Levine, Semi-open sets and semi-continuity in topological spaces , Amer.

Softly $\pi g\hat{D}$-Normal Spaces Levine, Semi-open sets and semi-continuity in topological spaces , Amer

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.227749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.661076Z digest=sha256:4592da3bc22a66d9dd99d1473e4199f723cdf3dce29585ef226245648465b9ba

Observation 273b3a86-bc87-428f-b09c-4eb7c626e1c4 · outbound

This paper cites On Some Class of Nearly Open Sets,.

Softly $\pi g\hat{D}$-Normal Spaces On Some Class of Nearly Open Sets,

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.213481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.719177Z digest=sha256:b622d3839ce3d54ef2ca2ff8780bad8957cb8c7f982ed9b42bf02070565f5234

Observation a5b497b2-08f9-48df-8807-3dd855245bc4 · outbound

This paper cites Andrijevie, Semi- preopen sets , Math.

Softly $\pi g\hat{D}$-Normal Spaces Andrijevie, Semi- preopen sets , Math

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.199787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.786114Z digest=sha256:43c73982a9b56a671a8d8bd548f55377d9dd0a43e2148351e220f6d71cb122c4

Observation 151c6c08-86fc-404b-9f54-aebabe283dae · outbound

This paper cites Levine, generalized closed sets in topology , Rend.

Softly $\pi g\hat{D}$-Normal Spaces Levine, generalized closed sets in topology , Rend

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.186373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.863301Z digest=sha256:41e6fa2eaa7bd8638bbd4ea91c80527bd34f6176b8396772cda14644a1925447

Observation 46e5b4cb-ba84-4536-aee5-069fc7a3caeb · outbound

This paper cites Quasi Normal Spaces and πg -closed sets.

Softly $\pi g\hat{D}$-Normal Spaces Quasi Normal Spaces and πg -closed sets

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.172750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.938267Z digest=sha256:0b7f268be336f19678c464d3fe4c92512effa86261c4c28bcdbac230a1342375

Observation b7cec582-9981-4a3d-80ba-f815e01652fd · outbound

This paper cites Maki, R, Deviand K.

Softly $\pi g\hat{D}$-Normal Spaces Maki, R, Deviand K

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.157958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:13.995127Z digest=sha256:60a35cb00e28a889fbd2babd52c48b4f4859b965fcf015e5a9958cb8ce7b1d1f

Observation 678d9684-8941-43e2-903d-1140ec681cb2 · outbound

This paper cites Studies on πgα -closed sets in Topology.

Softly $\pi g\hat{D}$-Normal Spaces Studies on πgα -closed sets in Topology

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.144315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.054539Z digest=sha256:5c3fc918b52e93799aa8a9e2316df72f03bb5fdb803928b9c7779fdd26648ec3

Observation 0736fe1e-f0f9-4564-a136-d3cfa308fb95 · outbound

This paper cites Dontchev, On generalized semi-pre open sets , Mem.

Softly $\pi g\hat{D}$-Normal Spaces Dontchev, On generalized semi-pre open sets , Mem

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.129933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.120601Z digest=sha256:80d23ef80a555b4453c2f857c2c4275e94cf522819c9b061f2db078a29787ee5

Observation 5aa83aec-8f50-4d4b-b04a-3f8312ff094f · outbound

This paper cites Palaniappan and K.

Softly $\pi g\hat{D}$-Normal Spaces Palaniappan and K

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.116556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.198760Z digest=sha256:39894bcd0a9665b87de2415dee8202120a55bd0b774736176e4a7ca28ce3fe7c

Observation 3b4da3f5-b324-41c8-819f-5901e5a99661 · outbound

This paper cites Gnanambal, On generalized pre-regular closed sets in topological spac es, Indian J.

Softly $\pi g\hat{D}$-Normal Spaces Gnanambal, On generalized pre-regular closed sets in topological spac es, Indian J

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:15.101805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.255646Z digest=sha256:41e0b31a4833cd810677c19bc06427f7b47c3fba18a265e8c4cb820f1997e399

Observation 27ddbe33-747b-4798-9e39-f04ab50842f3 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.085547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.322784Z digest=sha256:8d4459e30290b52d8200acc499f524558f2135db341d71acbba54b8e6d7a3cee

Observation 7b47145d-def7-4b66-b155-29869b4a06de · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.071720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.378932Z digest=sha256:bbee8a75510c2e3e4be7809151f5fa5d0508a60adffc5fb40f5c3341357e7301

Observation c99532c7-fe82-4c56-b326-a5f2313474e6 · outbound

This paper cites an unresolved cited work.

Softly $\pi g\hat{D}$-Normal Spaces Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:20:15.023783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.436813Z digest=sha256:dacbf5365d23bbb2b5381151dab16d73d7b554f150b83d72dc0af9ab07ed8e6e

Observation 57e01097-a555-4634-b0b3-899ed531eb1c · outbound

This paper cites Dass and G.

Softly $\pi g\hat{D}$-Normal Spaces Dass and G

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:14.895280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.492595Z digest=sha256:ea681114e71003e0301b3542ff03a857b2a03a32d62604ad075ae8f805893787

Observation e00ceddb-9f0c-47aa-8d87-da5472c04bb4 · outbound

This paper cites Noiri, Mildly - normal spaces and some functions.

Softly $\pi g\hat{D}$-Normal Spaces Noiri, Mildly - normal spaces and some functions

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:20:14.746419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T05:20:14.553508Z digest=sha256:a3f16d894e20ae5cc1acb5ba1a45c066e535683b8442af36668af4d3d7ca9a4c

Pith citing papers

No inbound Pith citation observations are available.