Paper Citation Record · LEDGER

Algebraic identities to prove that a neat finite free algebra is tracically \'etale

As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2506.03851.

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

pith.paper-citation-record.v1
2506.03851 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:05:34.998991Z

measured 13 of 13 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 2026-08-07T05:53:03.831569Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T05:53:03.870394Z

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy7
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 60f27b4f-deb1-4bd5-bfd5-18142f0ae3c6 · outbound

This paper cites an unresolved cited work.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:05:37.702725Z

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.

Observation 480d49b7-80d2-48b5-ba74-94ed1d71a23e · outbound

This paper cites AlorsDisc(B/A)est inversible.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale AlorsDisc(B/A)est inversible

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:37.540971Z

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.

Observation eb161a75-8080-41e6-b55a-a747f4c52ea7 · outbound

This paper cites an unresolved cited work.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:05:37.274850Z

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.

Observation 18a6dd41-e866-4f65-b3b1-8b9e9d78d65b · outbound

This paper cites En conséquence,Disc(B/A)diviseN B/A(b)pour toutb∈µ(Ann(J)).

Algebraic identities to prove that a neat finite free algebra is tracically \'etale En conséquence,Disc(B/A)diviseN B/A(b)pour toutb∈µ(Ann(J))

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:37.000191Z

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.

Observation c8c1a4ab-78c1-4818-a4ad-4e27c251115c · outbound

This paper cites De plus pourδ∈Ann(J)etβ∈B⊗ A Bon a µ(β)δ=δµ(β) =βδ.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale De plus pourδ∈Ann(J)etβ∈B⊗ A Bon a µ(β)δ=δµ(β) =βδ

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:36.726860Z

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.

Observation 3012a67d-2e92-49a5-9b01-792300a70548 · outbound

This paper cites Démonstration.1.Pourb∈B, il faut vérifier que(b⊗1)δ= (1⊗b)δ, ce qui est immédiat carb⊗1−1⊗b∈J.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Démonstration.1.Pourb∈B, il faut vérifier que(b⊗1)δ= (1⊗b)δ, ce qui est immédiat carb⊗1−1⊗b∈J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:36.423656Z

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.

Observation 397b1c44-c8b7-4626-85d3-f94407dc4314 · outbound

This paper cites Alors pourβ= ∑ ixi⊗y i∈B⊗ A Bon obtient Tr(B⊗AB)/B(β) = ∑ ixi TrB/A(yi).

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Alors pourβ= ∑ ixi⊗y i∈B⊗ A Bon obtient Tr(B⊗AB)/B(β) = ∑ ixi TrB/A(yi)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:36.200474Z

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.

Observation cbc4b792-06fa-40e7-bf76-4d4c3637c0bf · outbound

This paper cites Démonstration.1.Il suffit de le vérifier pourβ=x⊗y.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Démonstration.1.Il suffit de le vérifier pourβ=x⊗y

Reference 8

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T11:05:35.980776Z

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.

Observation 7a509c29-7483-436f-b4a9-a54fac922a58 · outbound

This paper cites an unresolved cited work.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:05:35.725552Z

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.

Observation 2a623284-1b0b-4718-ac44-15193fd8c870 · outbound

This paper cites C’est l’idéal engendré parf ′(x), oùf(T)est le polynôme caractéristique de (la multiplication par)xdans leA-module projectif de type finiB.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale C’est l’idéal engendré parf ′(x), oùf(T)est le polynôme caractéristique de (la multiplication par)xdans leA-module projectif de type finiB

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:35.471314Z

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.

Observation 77cb5793-3630-40be-881d-ef944dc73678 · outbound

This paper cites De la même manière, soitB=A[x 1,...,x n]l’algèbre définie par les relations x2 1 =···=x 2 n etx ixj = 0pouri < j.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale De la même manière, soitB=A[x 1,...,x n]l’algèbre définie par les relations x2 1 =···=x 2 n etx ixj = 0pouri < j

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:35.252907Z

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.

Observation b00cbb0b-cdc6-44eb-89e1-820bdf8f082b · outbound

This paper cites Commutative algebra: Constructive methods. Finite projective modules.

Algebraic identities to prove that a neat finite free algebra is tracically \'etale Commutative algebra: Constructive methods. Finite projective modules

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T11:05:34.998991Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation bc0077cf-e995-4a10-ae47-b1d2ca65ee25 · inbound

A decisive Theorem (Un th\'eor\`eme d\'ecisif) cites this paper.

A decisive Theorem (Un th\'eor\`eme d\'ecisif) Algebraic identities to prove that a neat finite free algebra is tracically \'etale

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:53:03.878538Z

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.