Paper Citation Record · LEDGER

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs

As of 17 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2501.07551.

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

pith.paper-citation-record.v1
2501.07551 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:47:38.663710Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T15:02:34.585098Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T03:37:35.832165Z

Reference resolution

43 of 43 outbound references displayed

verified exact4
verified fuzzy15
unresolved24
parse uncertain0
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External citation measurements

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Outbound references

Observation dc254032-8d03-48e1-a51d-4940c9dea424 · outbound

This paper cites Abramovich, A.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Abramovich, A

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:40.194748Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d69a7a42-4534-4362-93d0-95badb729a89 · outbound

This paper cites Abramovich, F.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Abramovich, F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:40.134766Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1a45c4f2-88fd-4370-9129-62ae4d76215c · outbound

This paper cites Birkar, Singularities on Fano fibrations and beyond, arXiv:2305.18770.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Singularities on Fano fibrations and beyond, arXiv:2305.18770

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.392683Z

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Unavailable: canonical work link unavailable.

Observation 5576dec0-ac2e-4691-af81-259032094df3 · outbound

This paper cites Birkar, Generalised pairs in birational geometry, EMS Surv.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Generalised pairs in birational geometry, EMS Surv

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:40.079690Z

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Observation cca17fd9-4a2a-4b4f-8db8-ed005b335563 · outbound

This paper cites Birkar, Singularities of linear systems and boundedness of Fano varieties, Ann.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Singularities of linear systems and boundedness of Fano varieties, Ann

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:40.058341Z

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Observation 8432eed3-a572-44f4-8a5e-fb66464677a4 · outbound

This paper cites Birkar, Anti–pluricanonical systems on Fano varieties.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Anti–pluricanonical systems on Fano varieties

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.417834Z

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Observation 1b436ca8-72bf-4d31-8032-f1347969cf26 · outbound

This paper cites Birkar, Existence of log canonical flips and a special LMMP, Publ.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Existence of log canonical flips and a special LMMP, Publ

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.423243Z

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Observation a0c80329-fbad-43f3-a9c1-ceb1cfcba0ed · outbound

This paper cites Birkar, P.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, P

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.428420Z

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Observation c48cad89-1f2a-47b4-ad4b-fff5fa697b96 · outbound

This paper cites Birkar, Z.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, Z

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.432846Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f989f1e6-1049-4759-b41b-aa8820aa1b4c · outbound

This paper cites Birkar, D.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Birkar, D

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.437579Z

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Observation 8da4ada4-fa18-4f85-80f9-aa460b0dd13f · outbound

This paper cites Minimal model program for algebraically integrable foliations and generalized pairs.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Minimal model program for algebraically integrable foliations and generalized pairs

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.442284Z

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Observation abc59b58-2804-44d4-ba10-62fca99fdf33 · outbound

This paper cites Vanishing theorems for generalized pairs.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Vanishing theorems for generalized pairs

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-10T20:47:39.052970Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1c8372d0-ec89-4c50-a0da-ebdcfac2538b · outbound

This paper cites Anticanonical divisor with good asymptotic base loci.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Anticanonical divisor with good asymptotic base loci

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.459510Z

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Observation 98c499d5-bb4a-41ae-8314-5f3807e2f128 · outbound

This paper cites Choi and J.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Choi and J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.893019Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7d388729-ccfb-4e0e-9570-0a62680ddc35 · outbound

This paper cites On the Minimal Model Program for K\"ahler 3-folds.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs On the Minimal Model Program for K\"ahler 3-folds

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.471053Z

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Unavailable: canonical work link unavailable.

Observation bfd23e9d-f241-462d-bce1-b192d9291dab · outbound

This paper cites Transcendental Minimal Model Program for Projective Varieties.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Transcendental Minimal Model Program for Projective Varieties

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.476064Z

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Unavailable: canonical work link unavailable.

Observation 65d7cfcc-4806-4e48-92a9-f470f247ea7e · outbound

This paper cites MMP for Generalized Pairs on K\"ahler 3-folds.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs MMP for Generalized Pairs on K\"ahler 3-folds

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.481881Z

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Observation 8806ee86-47e5-4ae1-a5b8-4e5dc590b55b · outbound

This paper cites Demailly, C.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Demailly, C

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.490255Z

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Observation e00cc920-78f0-4a30-91fb-a43d803563a9 · outbound

This paper cites On subadditivity of the logarithmic Kodaira dimension.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs On subadditivity of the logarithmic Kodaira dimension

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.838909Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c3a596e2-ab55-4818-8ffd-0e9f1ab57c04 · outbound

This paper cites Fujino; Special termination and reduction to pl flips.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Fujino; Special termination and reduction to pl flips

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.780465Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1b9ee549-8e47-4a91-9725-fb55fcc01dce · outbound

This paper cites Anticanonical minimal models and Zariski decomposition.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Anticanonical minimal models and Zariski decomposition

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.505902Z

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Unavailable: canonical work link unavailable.

Observation bf01bbfe-5d9b-4e56-b917-0759f9405ea2 · outbound

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$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:47:39.722339Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f14edc2d-70f8-465a-9b02-2ef8422b1949 · outbound

This paper cites an unresolved cited work.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:47:39.706009Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b19ffc9a-9563-43d1-8dfc-3baf4511f766 · outbound

This paper cites an unresolved cited work.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:47:39.684039Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0398cf52-675c-49ed-8307-077c63ce6637 · outbound

This paper cites On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.529188Z

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Observation 9c8bd821-3c5e-413f-981b-a2f64bce5284 · outbound

This paper cites an unresolved cited work.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 26

Resolution: verified exact; doi, observed 2026-08-10T20:47:38.799798Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7a74eda1-1710-47a3-94df-fb9e3290eaf3 · outbound

This paper cites an unresolved cited work.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:47:39.618876Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation da814bbb-5569-47a7-9377-8f510a20064a · outbound

This paper cites Hartshorne, Algebraic geometry , Graduate Texts in Mathematics, No.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Hartshorne, Algebraic geometry , Graduate Texts in Mathematics, No

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.548181Z

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Observation 0697eb0e-f91c-4a4f-b1bd-d770697e05e5 · outbound

This paper cites Hashizume, Non-vanishing theorem for generalized log canonical pairs with a polarization, Selecta Mathematica 28 (4) (2022), 77.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Hashizume, Non-vanishing theorem for generalized log canonical pairs with a polarization, Selecta Mathematica 28 (4) (2022), 77

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.584183Z

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Observation 4f917e16-9713-47e4-931f-5bba5e7f3c15 · outbound

This paper cites Hashizume, Z.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Hashizume, Z

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.568579Z

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Observation 4524b89c-9a7d-43f0-910e-2bbf5f448142 · outbound

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$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Unresolved cited work

Reference 31

Resolution: verified exact; doi, observed 2026-08-10T20:47:38.749317Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d39a546f-8ef6-4971-91c6-a96c8e5a7de2 · outbound

This paper cites An abundance theorem for generalised pairs.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs An abundance theorem for generalised pairs

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.577680Z

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Observation 09ae31f1-4028-4ad3-9e9f-4ff9deb05118 · outbound

This paper cites Log abundance of the moduli b-divisors of lc-trivial fibrations.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Log abundance of the moduli b-divisors of lc-trivial fibrations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.585808Z

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Observation 87f4f52a-35b0-40c0-9c7f-7e82252d62c9 · outbound

This paper cites Log canonical pairs with boundaries containing ample divisors.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Log canonical pairs with boundaries containing ample divisors

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.595290Z

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Observation bcf8b8ce-6f10-4f8d-90cc-71e098bed056 · outbound

This paper cites Koll\'ar, S.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Koll\'ar, S

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.488690Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4def6104-ea47-4e9a-9fca-23aaedae0ab7 · outbound

This paper cites Lazarsfeld, Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series , (2004).

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Lazarsfeld, Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series , (2004)

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T20:47:38.607968Z

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Observation 7d00d904-35fa-43c5-87e5-cc302391bd4e · outbound

This paper cites Liu and L.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Liu and L

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.440667Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c9af3f14-18b8-40a6-af29-4b33157c8457 · outbound

This paper cites Liu and L.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Liu and L

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.392960Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 966e794a-4099-47ad-99cc-dbd89776a7c4 · outbound

This paper cites Nakayama, Zariski-decomposition and abundance , MSJ Mem., 14 , Mathematical Society of Japan, Tokyo, (2004).

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Nakayama, Zariski-decomposition and abundance , MSJ Mem., 14 , Mathematical Society of Japan, Tokyo, (2004)

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.366337Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1f3378d8-3fa2-4793-9ddd-01705127406a · outbound

This paper cites Shokurov, 3-fold log flips , With an appendix by Yujiro Kawamata, Russian Acad.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Shokurov, 3-fold log flips , With an appendix by Yujiro Kawamata, Russian Acad

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.333306Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0d03b922-fb12-4e84-a9b7-b34ab3eb09c9 · outbound

This paper cites Tsakanikas, L.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Tsakanikas, L

Reference 41

Resolution: verified exact; doi, observed 2026-08-10T20:47:38.711061Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0681a4ad-0320-4c5d-ad1e-fba7bb654188 · outbound

This paper cites van Dobben de Bruyn, Infinitely small intersections with nef -Cartier divisors.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs van Dobben de Bruyn, Infinitely small intersections with nef -Cartier divisors

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.273065Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8e2e1c39-4661-417f-a4b6-4b1ac64a1e70 · outbound

This paper cites Xie, Contraction theorem for generalized pairs, Algebraic Geometry and Physics 1 (2024), no.

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs Xie, Contraction theorem for generalized pairs, Algebraic Geometry and Physics 1 (2024), no

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:47:39.244790Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation fce92757-7dca-48d3-8edb-2261a9994f1a · inbound

A numerical generalized canonical bundle formula cites this paper.

A numerical generalized canonical bundle formula $P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:37:35.833759Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.