Paper Citation Record · LEDGER

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

As of 11 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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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

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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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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 2026-08-11T06:34:44.6726+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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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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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

This paper cites an unresolved cited work.

$P$-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 2026-08-11T06:34:44.6726+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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Unavailable: canonical work link unavailable.

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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+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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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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

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

On the minimal model theory for generalized pairs of relative log numerical dimension zero cites this paper.

On the minimal model theory for generalized pairs of relative log numerical dimension zero $P$-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 2026-08-11T06:34:44.6726+00:00.