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Paper Citation Record · LEDGER

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case

As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2506.17813.

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

pith.paper-citation-record.v1
2506.17813 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:08:34.452406Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T13:13:24.478141Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T00:56:24.343378Z

Reference resolution

28 of 28 outbound references displayed

  • verified exact2
  • verified fuzzy16
  • unresolved10
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 687a9812-d2f7-4d5f-b70a-5c75f5d93961 · outbound

This paper cites J Almgren, Almgren’s big regularity paper: Q-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to codimension 2 , Vol.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case J Almgren, Almgren’s big regularity paper: Q-valued functions minimizing Dirichlet’s integral and the regularity of area-minimizing rectifiable currents up to codimension 2 , Vol

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.549598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.512904Z digest=sha256:51c512c3cf81c1fc9dcb0f1ec97704d865b89bd6668f77db88d98efe18457213

Observation 3aa47cad-528c-44cd-b73f-6c05570e4e7e · outbound

This paper cites De Lellis, J.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case De Lellis, J

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:33.602145Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:33.602145Z digest=sha256:f29284c0701ae9e733f22738174c6b03b29f530ff5954374ae34ad14180b639f

Observation 656edb41-4ef3-45a9-91fe-bb277a6c1a30 · outbound

This paper cites Fine structure of the singular set of area minimizing hypersurfaces modulo $p$.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Fine structure of the singular set of area minimizing hypersurfaces modulo $p$

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:33.642806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:33.642806Z digest=sha256:210235fc696e0963fb93ff930038b853d9b8d1dc424e13d1a8af2740b063c27d

Observation 3a859a77-7bfc-47b3-8d05-72108b75734d · outbound

This paper cites 247 (2024), Paper No.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case 247 (2024), Paper No

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.468724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.652186Z digest=sha256:0aed35cdead6bf80bec72bacd1e2ae212c27db5dcbd81b8a93c910cdb0b36a7c

Observation ac2e5a24-23c2-4a6e-bb1e-36078c7ecf70 · outbound

This paper cites De Lellis, J.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case De Lellis, J

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.458786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.657072Z digest=sha256:2e491a50eeb44e7643436be44c50768b5f971e8d36eba054bdf4edcf6b30788a

Observation d666be11-8164-4d9c-8998-494d9a7fd3e3 · outbound

This paper cites Pure Appl.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Pure Appl

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.447514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.746529Z digest=sha256:c846a918c7488f7a21605319478107cf83ec6a28d7e06560ab33ea6abb757087

Observation 1aebadcb-3282-48da-8336-6a0756362458 · outbound

This paper cites Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:33.836878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:33.836878Z digest=sha256:a112c6c8238c7c64a954bd79b2f66da68732367cf05ccddccf20071419ed84eb

Observation 99824014-bea1-45cb-ac37-74599107bb2a · outbound

This paper cites The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:33.855251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:33.855251Z digest=sha256:2aa7cc868abe7a9ab7816f6bf2e62c7d838d0a341d2df8933a9f619d60104ccf

Observation 607c7f75-8d48-43ef-a9bc-3f7df4c9c39e · outbound

This paper cites The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case The fine structure of the singular set of area-minimizing integral currents II: rectifiability of flat singular points with singularity degree larger than $1$

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:33.859004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:33.859004Z digest=sha256:5129696766e3ade8a273aa056baf79df51f7ab41f149809eded06409a82c94b8

Observation 9498106e-8f14-4a7f-b19c-d15a2b6b2854 · outbound

This paper cites De Lellis and E.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case De Lellis and E

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.404755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.864261Z digest=sha256:7bb9c1401a4d2011a2ddfe219e4cba29235bdae6ebb2a6df712ef0c33160e3c7

Observation f865acf7-e37d-4f33-8e31-4722dcc07919 · outbound

This paper cites of Math.(2) (2016), 499–575.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case of Math.(2) (2016), 499–575

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.333945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.868146Z digest=sha256:03a0728ef58d907d7a1f786ed89d64a167d1f5c7b4c7b5d918dd5d286cffa9ad

Observation d07ef6a9-e4fa-4aec-9fbc-9808285cd79c · outbound

This paper cites of Math.(2) (2016), 577–617.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case of Math.(2) (2016), 577–617

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.323512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.872223Z digest=sha256:701f79b86827215a5eee72775231a33d07460eaa3ceee9dbb5af89df72a85c17

Observation 79f98660-7f13-4a3d-860d-55f880926bfa · outbound

This paper cites De Lellis, E.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case De Lellis, E

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.302744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.875882Z digest=sha256:a4bb5a0245101dd0b10ebe84a0e974c22623753461eb05209107a0307e31ba86

Observation 55b57c96-51ea-4dcb-b1df-1e8aac07e90d · outbound

This paper cites an unresolved cited work.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:08:35.260870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:33.954042Z digest=sha256:3b129147e9d495582e75dc103a6ab289f3368ab2fc215c98734726520cee0b81

Observation e382730e-a845-4788-91c1-d868b02d6bb4 · outbound

This paper cites Differential Geom.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Differential Geom

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.251340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.032630Z digest=sha256:823b8a9b7df2c54bb9200116bab802b1cecdd360690ef3a6c39439ccc0ddaf68

Observation 69242ac8-a44b-43b9-8957-103f422a0be1 · outbound

This paper cites Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area mini- mizing flat chains modulo two with arbitrary codimension , Bull.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area mini- mizing flat chains modulo two with arbitrary codimension , Bull

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.217909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.063972Z digest=sha256:a365c5086dbfd610a99392af0be02440fabc6445c143494bedf79a71eb250df9

Observation 4dc66f5a-166b-41db-9bc4-f722d75bb2e9 · outbound

This paper cites Hirsch, A.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Hirsch, A

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.111398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.068194Z digest=sha256:1494185e23a017715024d27427dba8e117c596a7a03b19612111f3b951a7f8ca

Observation 73d27290-f301-4d08-8eb3-1692e77b32a3 · outbound

This paper cites Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Fine properties of branch point singularities: stationary two-valued graphs and stable minimal hypersurfaces near points of density $< 3$

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-15T19:08:34.071655Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:08:34.071655Z digest=sha256:feafd0628197a6a1c1f250d8fdd1de98fbeb67412c2e494e4ded52fb5e558a27

Observation cc520712-b599-4b52-a314-e47b1e7102fe · outbound

This paper cites Homologically area-minimizing surfaces mod $v$ have at worst codimension 2 singular sets asymptotically.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Homologically area-minimizing surfaces mod $v$ have at worst codimension 2 singular sets asymptotically

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-15T19:08:34.588843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.075172Z digest=sha256:2c2c73e544c51f75a2de174fdfb671f5056ee25b21aa8fe29fa3b18ad2dbee8f

Observation b52f823c-06f9-452a-ac2d-144256c2d5b6 · outbound

This paper cites Minter, The structure of stable codimension one integral varifolds near classical cones of density Q+ 1/2 , Calc.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Minter, The structure of stable codimension one integral varifolds near classical cones of density Q+ 1/2 , Calc

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.101166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.079211Z digest=sha256:8c116ee4013b77933bdf9ebf51aff104aecdb6ae58df3b9437d48078012471aa

Observation 4b29c5b0-1bfe-427d-b8bc-5ec0577432f5 · outbound

This paper cites Minter and N.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Minter and N

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:35.063263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.149738Z digest=sha256:104af69bac6eca7865867afd0a86714d5312698ccded207a6c2bcea1624877b8

Observation 6264cb20-aba8-456a-8691-82a2cb1ef582 · outbound

This paper cites Simon, Cylindrical tangent cones and the singular set of minimal submanifolds , J.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Simon, Cylindrical tangent cones and the singular set of minimal submanifolds , J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:34.992051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.241175Z digest=sha256:408e2763eeec0c8e462ce350be3a918263470c824e01e753a3235e7f61e3a4dc

Observation f942cb24-6b9c-4f32-a07b-562ba6b27c78 · outbound

This paper cites An upper Minkowski bound for the interior singular set of area minimizing currents.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case An upper Minkowski bound for the interior singular set of area minimizing currents

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-08-15T19:08:34.488544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.258068Z digest=sha256:6baaeb5c94e2e5d01f25519660626cb3f5d096944588238f1f0b4e7709f49dd0

Observation db2a24de-2d8e-4948-aa4c-bd04c0d911fc · outbound

This paper cites an unresolved cited work.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:08:34.978763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.264110Z digest=sha256:39031b49b2ad4627cd30bf15f4e6a0297ffed3bf1311cb6f0a1e3f55f54bddd8

Observation 528a0bd7-c696-4a0d-bfc1-2a1d99835c45 · outbound

This paper cites an unresolved cited work.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:08:34.940685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.267556Z digest=sha256:4e0fdc6d64dcea346dec205f226bc8384c8d2a202da217b0031d95ecab18ca37

Observation 1231e09a-825f-4ead-9b94-fac06718d1d3 · outbound

This paper cites White, The structure of minimizing hypersurfaces mod 4, Invent.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case White, The structure of minimizing hypersurfaces mod 4, Invent

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:34.819341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.345450Z digest=sha256:ade95533ad009d3790c286ba8933a9db972b3940838abe5214f772d274aea660

Observation f3a3bae7-a457-470a-8c8d-ea44d9227c42 · outbound

This paper cites an unresolved cited work.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:08:34.807962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.448171Z digest=sha256:80d198764cc61b7195ccb0bcf74ad042fdd04eb002c73533ac957cf169d5354e

Observation 3a0e18d6-0458-468e-b54d-1b2bfe1c7a1e · outbound

This paper cites Wickramasekera, A general regularity theory for stable codimension 1 integral varifolds , Ann.

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case Wickramasekera, A general regularity theory for stable codimension 1 integral varifolds , Ann

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:08:34.795773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-15T19:08:34.452406Z digest=sha256:d5b4602af55251e110c08f867198eb3488ce6f4f511f57543ba8605a5fd7b51b

Pith citing papers

Observation 4a0ab678-8621-45d9-8421-499c64ab8f84 · inbound

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity cites this paper.

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case

Reference 16

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.345522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-06-28T13:13:24.478141Z digest=sha256:b5faad76f45e418c1a9ade892ea0a39af7ab0bf7cf2f5bc747a46dc91ed196b0