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Paper Citation Record · LEDGER

Law of large numbers for the discriminant of random polynomials

As of 14 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2506.12206.

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

pith.paper-citation-record.v1
2506.12206 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T01:09:56.189099Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

22 of 22 outbound references displayed

  • verified exact2
  • verified fuzzy12
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5e8fe0d0-6831-4e7f-a6b0-bca66176c929 · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.535803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.091857Z digest=sha256:f07fca567157fd4de57973c56a30704120895d65771d33e4bf627548c4502bea

Observation 8da1485f-79a7-469c-b541-1ffb02f14af7 · outbound

This paper cites Aza ¨ ıs and M.

Law of large numbers for the discriminant of random polynomials Aza ¨ ıs and M

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.522897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.097005Z digest=sha256:93cdd95842c733616374a5f6673f5170d8ead54f808f027ec4a47ec3c9e207eb

Observation 8eda345b-ecd5-4ead-ad56-bbe9cdc1cb11 · outbound

This paper cites Bary-Soroker, O.

Law of large numbers for the discriminant of random polynomials Bary-Soroker, O

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.509318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.102053Z digest=sha256:1974cded6b9b4101795cf90fd6bac7e0ff85f0e0cd973f640e81bd54d7094d7a

Observation 6dbeac25-3e2a-4c0f-925d-3bd033fd8ab0 · outbound

This paper cites Bary-Soroker and N.

Law of large numbers for the discriminant of random polynomials Bary-Soroker and N

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.495660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.107109Z digest=sha256:d095d0d30a49bee5a9b4917f8956bf0a3f7247bd054a1f2dd6c4b868e18df16c

Observation c4e28114-2ef5-4498-bc67-2a797d01654c · outbound

This paper cites Bary-Soroker and G.

Law of large numbers for the discriminant of random polynomials Bary-Soroker and G

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.483217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.112493Z digest=sha256:4b9db3de63355de3f464eafbdddf7aba6cd51e4764fff260586e05244ba3acbf

Observation e23a4aa7-0476-477c-aeeb-8c61a3e077d9 · outbound

This paper cites Bhargava.

Law of large numbers for the discriminant of random polynomials Bhargava

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.470337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.117109Z digest=sha256:070b966b582a81af4f22988f13e02ec61bc2899ef1e6ba8c7bd859197e0a486c

Observation fcdacd0f-3784-4216-ac64-7f11a0415c84 · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.455881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.122023Z digest=sha256:c81cc786837cc0dd5a3ca64dced5d6e71ab1be1fb44458955411012fba1b4b64

Observation ef4f9acd-233d-42f4-ad26-c417c0e37233 · outbound

This paper cites Breuillard and P.

Law of large numbers for the discriminant of random polynomials Breuillard and P

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.441523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.126181Z digest=sha256:527f0c914d099357244e1998cac72b92ebc17936cc5a1f0f37fb515e5dbe8443

Observation b88feb00-dc59-407c-ab7b-c196978894e0 · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.427795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.130135Z digest=sha256:9dcfee91eec6e35f128b8269375d501785ea7fd4de165754c97e029704ad69b2

Observation ac45faf8-9dfa-44f6-bcb1-cc8897fd891c · outbound

This paper cites Erd˝ os and P.

Law of large numbers for the discriminant of random polynomials Erd˝ os and P

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.414317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.134838Z digest=sha256:b72fc4d284941447dd6290f351495dd57fa80197d23e512be9a418bb6a3708d1

Observation 30af4207-b6af-4fc6-84fc-7407a5c20ae8 · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.401073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.139477Z digest=sha256:22f6bf4ba227a319ae4930fbc9fa0e44a4ae26f8812755efe497c941a03acc2e

Observation 7fa7a073-912f-4b23-ae8f-c6b465de8459 · outbound

This paper cites G¨ otze and D.

Law of large numbers for the discriminant of random polynomials G¨ otze and D

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.387204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.143725Z digest=sha256:59fa412afb710a4f6a60916a1a891b1630476db7ce49cc79e8673c3714341bb6

Observation a3171f46-3301-4c27-a87b-b2096a4400a2 · outbound

This paper cites Counting (skew-)reciprocal Littlewood polynomials with square discriminant.

Law of large numbers for the discriminant of random polynomials Counting (skew-)reciprocal Littlewood polynomials with square discriminant

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-08-07T01:09:56.252493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.148275Z digest=sha256:10e40eb7d299339277b1b1f491d44d29953da744f97dcf16ac64ddd4e4858582

Observation 72290684-2249-4a0e-a76b-1631415df07e · outbound

This paper cites Ibragimov and O.

Law of large numbers for the discriminant of random polynomials Ibragimov and O

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.373330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.152967Z digest=sha256:7a8f775da363a5c6643018a1820a3be8d9977cb55851d02ca132fe10c80cdc46

Observation 935b132b-6a80-4b35-8216-11c7eee39c36 · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.358671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.157760Z digest=sha256:7a396c7edc1dae25ffc0990a3f1957391b52f84e496783fbd8ebcd30a2b239fd

Observation d8296ac7-e4f8-4b95-b178-dda1b86cf61c · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.344153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.162438Z digest=sha256:440ee1be26371c9d94b3ed19bc40dfb07005c8dcc63ad65d04ec204ac3ae2ed8

Observation f224c46b-2e58-40da-9b97-33b39a85edf3 · outbound

This paper cites McKee and C.

Law of large numbers for the discriminant of random polynomials McKee and C

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.328433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.166408Z digest=sha256:b44a3e3a69d56017aaee05516add454d3196f407f8bf594ae6412416a4deeb41

Observation e892cd50-b69f-4138-ada3-d54769e7de46 · outbound

This paper cites Michelen and O.

Law of large numbers for the discriminant of random polynomials Michelen and O

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.312336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.170644Z digest=sha256:b82497da0be1771ef4d34530a65263a5dff345aba618cbb3f55debdba66a9643

Observation 74727b6d-7718-4e60-8723-1e8d759dc135 · outbound

This paper cites Limit law for root separation in random polynomials.

Law of large numbers for the discriminant of random polynomials Limit law for root separation in random polynomials

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-07T01:09:56.230657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.175085Z digest=sha256:15a36be620e80c11be8a78d5380dba99b92a51c26d54e7fc5baab0c3448e595d

Observation 69c817e8-a023-4ac5-9b12-ae7b0a5a3f4c · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.296521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.179939Z digest=sha256:87c2eed95751c093d1a9d35ed42b133fe09b7dbac5cea36aba3489556b0e1124

Observation 5355f662-25aa-4017-a95a-76546d5b0add · outbound

This paper cites an unresolved cited work.

Law of large numbers for the discriminant of random polynomials Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-07T01:09:56.281205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.184548Z digest=sha256:88bb48c34beeddef1bcab772bfdfe25316ec362a2560b53889690201440a446d

Observation 9be127f8-b87d-40a5-b664-0527969e1531 · outbound

This paper cites Yakir and O.

Law of large numbers for the discriminant of random polynomials Yakir and O

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T01:09:56.267016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T01:09:56.189099Z digest=sha256:965fea5e7f752c2a8c56017ef2ddbea2b3910d07978fa6b5ec7c21373a13b26e

Pith citing papers

No inbound Pith citation observations are available.