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Paper Citation Record · LEDGER

BPS polynomials and Welschinger invariants

As of 15 August 2026, this Paper Citation Record lists 92 of 92 outbound references and 1 inbound Pith citation observation for arXiv:2506.02770.

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pith.paper-citation-record.v1
2506.02770 v1

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measured 92 of 92 reference resolution

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measured 93 of 93 standing notices

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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Source: arxiv_reference, observed 2026-05-15T14:40:04.334007Z

Reference resolution

92 of 92 outbound references displayed

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  • verified fuzzy55
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Outbound references

Observation e453eb81-31d2-4c01-8648-5b1f6d28b882 · outbound

This paper cites The formula 12 = 10 + 2 × 1 and its generalizations: counting rational curves on F2.

BPS polynomials and Welschinger invariants The formula 12 = 10 + 2 × 1 and its generalizations: counting rational curves on F2

Reference 1

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Observation 5f28199c-4f4a-4b9b-b4d2-2d29b9ce2abf · outbound

This paper cites Stable logarithmic maps to Deligne-Faltings pairs II.

BPS polynomials and Welschinger invariants Stable logarithmic maps to Deligne-Faltings pairs II

Reference 2

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Observation 07858531-4343-4dfc-8f96-3609c188753a · outbound

This paper cites Decomposition of degenerate Gromov- Witten invariants.

BPS polynomials and Welschinger invariants Decomposition of degenerate Gromov- Witten invariants

Reference 3

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Observation 47c2f767-938e-4441-b32f-8935d74144cf · outbound

This paper cites Refinements of Kool-Thomas Invariants via Equivariant $K$-theoretic invariants.

BPS polynomials and Welschinger invariants Refinements of Kool-Thomas Invariants via Equivariant $K$-theoretic invariants

Reference 4

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Observation c0f96f03-cefc-4a02-8150-e80ed6cc0d2b · outbound

This paper cites Real loci in (log) Calabi-Yau manifolds via Kato-Nakayama spaces of toric degenerations.

BPS polynomials and Welschinger invariants Real loci in (log) Calabi-Yau manifolds via Kato-Nakayama spaces of toric degenerations

Reference 5

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Observation 34af108e-379c-42b2-a744-824697c821a1 · outbound

This paper cites Recursive formulas for Welschinger in- variants of the projective plane.

BPS polynomials and Welschinger invariants Recursive formulas for Welschinger in- variants of the projective plane

Reference 6

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Observation 81a120cc-3aeb-4ffc-ad99-fe3ddaa82280 · outbound

This paper cites Gromov-Witten invariants in algebraic geometry.

BPS polynomials and Welschinger invariants Gromov-Witten invariants in algebraic geometry

Reference 7

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Observation 87789940-f9d8-4bd5-b345-2a6ea49f9990 · outbound

This paper cites The product formula for Gromov-Witten invariants.

BPS polynomials and Welschinger invariants The product formula for Gromov-Witten invariants

Reference 8

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Observation f2fe1e29-c4e7-40f9-8138-0a4073955149 · outbound

This paper cites Refined curve counting with tropical geometry.

BPS polynomials and Welschinger invariants Refined curve counting with tropical geometry

Reference 9

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Observation 99173631-5b8c-424a-ab7c-1e4a0f39ef6e · outbound

This paper cites Refined count of oriented real rational curves.

BPS polynomials and Welschinger invariants Refined count of oriented real rational curves

Reference 10

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Observation 90f18029-871f-4685-b97e-08e44174a966 · outbound

This paper cites Tropical refined curve counting from higher genera and lambda classes.

BPS polynomials and Welschinger invariants Tropical refined curve counting from higher genera and lambda classes

Reference 11

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Observation 4c467a83-a1b8-4993-9517-cd11dad49326 · outbound

This paper cites Tropical refined from higher genera and lambda classes.

BPS polynomials and Welschinger invariants Tropical refined from higher genera and lambda classes

Reference 12

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Observation cb98608a-c33c-422a-9529-54aadd1269fa · outbound

This paper cites Refined floor diagrams from higher genera and lambda classes.

BPS polynomials and Welschinger invariants Refined floor diagrams from higher genera and lambda classes

Reference 13

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Observation 79edfed5-e2e6-449f-b07c-5e652283d10b · outbound

This paper cites A proof of N.

BPS polynomials and Welschinger invariants A proof of N

Reference 14

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Observation e8d0e2bd-4339-4425-87fe-261cc3f95c30 · outbound

This paper cites Stable maps to Looijenga pairs.

BPS polynomials and Welschinger invariants Stable maps to Looijenga pairs

Reference 15

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source=pdf_text observed=2026-08-07T11:22:40.037011Z digest=sha256:be54b0393e2308e7fbab85c919a303e3a1e54e072a7335baca1d2eab9a295ed7

Observation f82a394b-f50e-4403-bcba-ac1bc258e121 · outbound

This paper cites All-genus WDVV recursion, quivers, and BPS invariants.

BPS polynomials and Welschinger invariants All-genus WDVV recursion, quivers, and BPS invariants

Reference 16

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source=pdf_text observed=2026-08-07T11:22:40.041012Z digest=sha256:206792ad8eb5fe88872bfba85c2c2f5d6265ffc8ba9d64661468aaef724bd6da

Observation 105b8f54-fa65-4db2-85f5-8758e1943ee9 · outbound

This paper cites Refined Gromov-Witten invariants.

BPS polynomials and Welschinger invariants Refined Gromov-Witten invariants

Reference 17

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Observation 6f6564b2-ef12-47b2-ae87-e31f53b7e96f · outbound

This paper cites Floor diagrams relative to a conic, and GW-W invariants of del Pezzo surfaces.

BPS polynomials and Welschinger invariants Floor diagrams relative to a conic, and GW-W invariants of del Pezzo surfaces

Reference 18

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Observation b0ada2ea-5d50-4434-a313-8669aba7ea38 · outbound

This paper cites On the invariance of Welschinger invariants.

BPS polynomials and Welschinger invariants On the invariance of Welschinger invariants

Reference 19

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Observation a6c70df7-79cd-4092-99a4-81f5ed97f57d · outbound

This paper cites Enumeration of curves via floor diagrams.

BPS polynomials and Welschinger invariants Enumeration of curves via floor diagrams

Reference 20

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Observation 885a35a6-544d-41f9-a09c-edb72a99d009 · outbound

This paper cites Floor decompositions of tropical curves: the planar case.

BPS polynomials and Welschinger invariants Floor decompositions of tropical curves: the planar case

Reference 21

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source=pdf_text observed=2026-08-07T11:22:40.062807Z digest=sha256:8692a45abcdc4db62c2a1bb0834f267c73f93ed4c79cfa85c67326c86f511b91

Observation dd5e75dc-b651-4e1b-b7ba-60f4a636bea5 · outbound

This paper cites Behavior of Welschinger invariants under Morse simplifications.

BPS polynomials and Welschinger invariants Behavior of Welschinger invariants under Morse simplifications

Reference 22

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source=pdf_text observed=2026-08-07T11:22:40.066434Z digest=sha256:25733e53c705b196b378db5aa0df351f3b073875da58d8c0df1c97b6c4f4c336

Observation 0af80919-6150-496c-ae2d-58a195cf55cc · outbound

This paper cites On Welschinger invariants of symplectic 4-manifolds.

BPS polynomials and Welschinger invariants On Welschinger invariants of symplectic 4-manifolds

Reference 23

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source=pdf_text observed=2026-08-07T11:22:40.070396Z digest=sha256:ff1b9d103ad5dce3fd4a3ffe42b9c4913840188ee3381c7cbe292937ac4d0a3d

Observation 63f45a38-31e0-4762-953c-0796fab17dea · outbound

This paper cites The local Gromov-Witten theory of curves.

BPS polynomials and Welschinger invariants The local Gromov-Witten theory of curves

Reference 24

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Observation 9e78a913-6ece-49bb-a452-7a6bb970ecb0 · outbound

This paper cites Counting curves on Hirze- bruch surfaces: tropical geometry and the Fock space.

BPS polynomials and Welschinger invariants Counting curves on Hirze- bruch surfaces: tropical geometry and the Fock space

Reference 25

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source=pdf_text observed=2026-08-07T11:22:40.078211Z digest=sha256:c88d44393022085902822cf0f67cbcc5d8ca5a331c9f54ce929c9b5dbcc36a0b

Observation 93886f8d-6e96-422c-a1bd-6ba7a343da07 · outbound

This paper cites Tropical and logarithmic methods in enu- merative geometry, volume 52 of Oberwolfach Seminars.

BPS polynomials and Welschinger invariants Tropical and logarithmic methods in enu- merative geometry, volume 52 of Oberwolfach Seminars

Reference 26

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Observation f013f887-45ff-4399-a042-d19e46a209e3 · outbound

This paper cites Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invari- ants.

BPS polynomials and Welschinger invariants Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invari- ants

Reference 27

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Observation e17f4093-7530-4af7-a66e-516cdf55148a · outbound

This paper cites WDVV-type relations for Welschinger invariants: applications.

BPS polynomials and Welschinger invariants WDVV-type relations for Welschinger invariants: applications

Reference 28

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Observation a39bcd7d-23e0-4439-83d3-9c255a48dccf · outbound

This paper cites Counting real J-holomorphic discs and spheres in dimension four and six.

BPS polynomials and Welschinger invariants Counting real J-holomorphic discs and spheres in dimension four and six

Reference 29

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Observation 1ac271a9-e579-499c-835e-03cea69e5bd6 · outbound

This paper cites Real Enriques surfaces , volume 1746 of Lecture Notes in Mathematics.

BPS polynomials and Welschinger invariants Real Enriques surfaces , volume 1746 of Lecture Notes in Mathematics

Reference 30

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Observation 0eaaa98b-6f8c-4908-9f03-6a207081d78a · outbound

This paper cites The Gopakumar-Vafa finiteness conjec- ture.

BPS polynomials and Welschinger invariants The Gopakumar-Vafa finiteness conjec- ture

Reference 31

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Observation 4d09a2b5-8d10-4a6f-9b26-d32b83f4db19 · outbound

This paper cites Counting embedded curves in symplectic 6-manifolds.

BPS polynomials and Welschinger invariants Counting embedded curves in symplectic 6-manifolds

Reference 32

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Observation 1ba390fb-fa4a-4fa5-a3c9-e1195708c9f0 · outbound

This paper cites Notes on stable maps and quantum cohomology.

BPS polynomials and Welschinger invariants Notes on stable maps and quantum cohomology

Reference 33

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Observation f8e62c8e-d02b-4d29-bcdb-a5478f8e4d95 · outbound

This paper cites Open Gromov-Witten disk invariants in the presence of an anti-symplectic involution.

BPS polynomials and Welschinger invariants Open Gromov-Witten disk invariants in the presence of an anti-symplectic involution

Reference 34

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source=pdf_text observed=2026-08-07T11:22:40.114742Z digest=sha256:41f9b913a7a5b84af4ff1b6e23fea0fea4543e6fba0face4bb3ecf4ae5016790

Observation 10a17f19-0996-484a-8b1c-3d29e70d2137 · outbound

This paper cites M-Theory and Topological Strings–I.

BPS polynomials and Welschinger invariants M-Theory and Topological Strings–I

Reference 35

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source=pdf_text observed=2026-08-07T11:22:40.119238Z digest=sha256:7d661d3df46ace345e359cd0bcd5326bfeb9c41ea1c0fe5e40dc55d64acbb54a

Observation 66cadae0-dce2-4b53-bc66-b8d91c735cd0 · outbound

This paper cites M-theory and topological strings–II.

BPS polynomials and Welschinger invariants M-theory and topological strings–II

Reference 36

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source=pdf_text observed=2026-08-07T11:22:40.123033Z digest=sha256:db2c788950700fc29ac52325ecd9c172a65ee65b5b0a3aeda206ae3b40092a62

Observation 3751fc22-e760-4854-824c-e5980fd4488b · outbound

This paper cites The quantum cohomology of blow-ups ofP2 and enumera- tive geometry.

BPS polynomials and Welschinger invariants The quantum cohomology of blow-ups ofP2 and enumera- tive geometry

Reference 37

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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=2026-08-07T11:22:40.127356Z digest=sha256:8881a9e37e213e3ac09fd0072a942d4fa1fe9618ec461af76e59320dac1bac87

Observation d95b87d0-b7c4-407e-be4a-555674d427f0 · outbound

This paper cites Refined curve counting on complex surfaces.

BPS polynomials and Welschinger invariants Refined curve counting on complex surfaces

Reference 38

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raw_fallback, observed 2026-08-07T11:22:49.003577Z

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=2026-08-07T11:22:40.131598Z digest=sha256:6d772b9035fa8b398077cd5977f848c842d941712a6308ddd56f9c85a11cb222

Observation b102adb1-ecbb-47cd-9080-b29ad0bac4f3 · outbound

This paper cites Localization of virtual classes.

BPS polynomials and Welschinger invariants Localization of virtual classes

Reference 39

Resolution
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raw_fallback, observed 2026-08-07T11:22:48.835456Z

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=2026-08-07T11:22:40.135933Z digest=sha256:01ac398f3ec04cee1661861282ab203362982a8691ce9c56eec84ca11903d698

Observation e4ddc81a-6d93-45c6-9282-422a7b533f90 · outbound

This paper cites The tropical vertex.

BPS polynomials and Welschinger invariants The tropical vertex

Reference 40

Resolution
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raw_fallback, observed 2026-08-07T11:22:48.619528Z

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=2026-08-07T11:22:40.140408Z digest=sha256:b4b7e4485ea32bb2c01b53588f26fd46f2218a236437a0a2031274b84ad0ca49

Observation 2a415aa6-d25e-4be5-9724-4e51468692f4 · outbound

This paper cites Logarithmic Gromov-Witten invariants.

BPS polynomials and Welschinger invariants Logarithmic Gromov-Witten invariants

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:48.446448Z

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=2026-08-07T11:22:40.144584Z digest=sha256:b9363af9aba2ed8e896f758f6684e79ee7e99aa15dec80713ba72d05cbb77131

Observation f0598293-3864-4ee3-b43f-62630d2634e1 · outbound

This paper cites Poincar\'e polynomials of moduli spaces of one-dimensional sheaves on the projective plane.

BPS polynomials and Welschinger invariants Poincar\'e polynomials of moduli spaces of one-dimensional sheaves on the projective plane

Reference 42

Resolution
verified exact
local_arxiv, observed 2026-08-07T11:22:40.573117Z

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=2026-08-07T11:22:40.149159Z digest=sha256:af3a09df3e75758b1d6614298a021b62dcaf45a0946930e5b20cb0f836c0539a

Observation ae81d6df-f0bb-4081-826b-faf503d5b4b4 · outbound

This paper cites The open Gromov-Witten-Welschinger theory of blowups of the projective plane.

BPS polynomials and Welschinger invariants The open Gromov-Witten-Welschinger theory of blowups of the projective plane

Reference 43

Resolution
verified exact
local_arxiv, observed 2026-08-07T11:22:40.552902Z

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=2026-08-07T11:22:40.154562Z digest=sha256:46fa6b4daf9466a8896b8d08264ca4f72dc0526cc09b5309086aa5e697667095

Observation 0ead4511-b4c4-4880-a530-899f5f9485ab · outbound

This paper cites Gromov-Witten invariants of blow-ups along points and curves.

BPS polynomials and Welschinger invariants Gromov-Witten invariants of blow-ups along points and curves

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:48.284723Z

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=2026-08-07T11:22:40.159256Z digest=sha256:d6fee60a004f9d85f1865a013f55940586c02715c80b01b10697c0df184ba21d

Observation ad98b510-e967-4f11-a0f9-2c7c22fe4d7f · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:48.115358Z

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=2026-08-07T11:22:40.163278Z digest=sha256:26f5283d0f2ad6921dd0b649fbca6b257caba1b23ffcace104aab573c60afb0e

Observation 046b946c-0ca2-4a7c-85d4-b9b2ea508a86 · outbound

This paper cites Appendix to "Welschinger invariant and enumeration of real rational curves".

BPS polynomials and Welschinger invariants Appendix to "Welschinger invariant and enumeration of real rational curves"

Reference 46

Resolution
verified exact
local_arxiv, observed 2026-08-07T11:22:40.532017Z

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=2026-08-07T11:22:40.167683Z digest=sha256:48af7b06993f00ffb326741309281d9b8dd7c4e8b2ebb20c8109a9062d7c9948

Observation 6a99b284-7695-4349-baa2-fdf6b30433a4 · outbound

This paper cites A Caporaso-Harris type formula for Welschinger invariants of real toric del Pezzo surfaces.

BPS polynomials and Welschinger invariants A Caporaso-Harris type formula for Welschinger invariants of real toric del Pezzo surfaces

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:47.973829Z

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=2026-08-07T11:22:40.172358Z digest=sha256:0b09ea787fe2837d5795cba2e8744807f77732456a8c6e778145c275da0e1b8e

Observation 241fb19f-1592-457e-93a1-de88bfa3d255 · outbound

This paper cites Welschinger invariants of real del Pezzo surfaces of degree ≥ 3.

BPS polynomials and Welschinger invariants Welschinger invariants of real del Pezzo surfaces of degree ≥ 3

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:47.714947Z

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=2026-08-07T11:22:40.176916Z digest=sha256:ff6143ee069001f57a4bd5038d75237973385b9845c4bbb2c95c7cb9395d5780

Observation ae8d0684-1284-474c-9cc1-48cb52e4d15d · outbound

This paper cites Welschinger invariants of small non-toric Del Pezzo surfaces.

BPS polynomials and Welschinger invariants Welschinger invariants of small non-toric Del Pezzo surfaces

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:47.414915Z

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=2026-08-07T11:22:40.181996Z digest=sha256:b43eb4553862e29ac909f2b346f0421d708a786d58bb194da8e3eb7c4afde84b

Observation 1cbae8fa-dcff-4666-bce3-6d4615b72553 · outbound

This paper cites Welschinger invariants of real del Pezzo surfaces of degree ≥ 2.

BPS polynomials and Welschinger invariants Welschinger invariants of real del Pezzo surfaces of degree ≥ 2

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:47.160931Z

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=2026-08-07T11:22:40.187269Z digest=sha256:136401cccc23e404b60438a99ec20d111deb07ef4bd614416074e23be05fe944

Observation fd6b09d8-86c7-4e33-b34c-a7aa6301f67e · outbound

This paper cites Welschinger invariants revisited.

BPS polynomials and Welschinger invariants Welschinger invariants revisited

Reference 51

Resolution
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raw_fallback, observed 2026-08-07T11:22:46.894574Z

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=2026-08-07T11:22:40.191852Z digest=sha256:e98e2bf57429001511813979e9c4668c652535181d989d5fd7c85269df471fb0

Observation f7136a90-77ae-4c7e-9af4-9c22be2e6441 · outbound

This paper cites On Block-G¨ ottsche multiplicities for planar tropical curves.

BPS polynomials and Welschinger invariants On Block-G¨ ottsche multiplicities for planar tropical curves

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:46.669191Z

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=2026-08-07T11:22:40.196218Z digest=sha256:43968ce4b2438504f26cfbba7ddee0c226a655bb4618b91e959b9e7ae753d61c

Observation be661b0f-7c56-4792-b5d6-d46c9bbdbdc8 · outbound

This paper cites Real enumerative invariants relative to the anti-canonical divisor and their refinement.

BPS polynomials and Welschinger invariants Real enumerative invariants relative to the anti-canonical divisor and their refinement

Reference 53

Resolution
verified exact
local_arxiv, observed 2026-08-07T11:22:40.509271Z

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=2026-08-07T11:22:40.200560Z digest=sha256:b55efc1b39b644b09c99fb692499db3000edef78c20b89a1c7d1d6f8a8b3d7f7

Observation 3423ae9b-a082-4a82-8cdb-e244e38c99bf · outbound

This paper cites Real enumerative invariants relative to the toric boundary and their refinement.

BPS polynomials and Welschinger invariants Real enumerative invariants relative to the toric boundary and their refinement

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.205399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.205399Z digest=sha256:73cdbe295e5254acaa236af8bf04e2dc4894317036d0883ec89343a3e3ddf701

Observation 5dba2549-a143-4cfa-9e17-3f26e99e5772 · outbound

This paper cites M-theory, topological strings and spinning black holes.

BPS polynomials and Welschinger invariants M-theory, topological strings and spinning black holes

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:46.384768Z

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=2026-08-07T11:22:40.210348Z digest=sha256:585e8160f38fe776a78dc192e0a81a4592d5dd9a0bfdce37bd98a9b5bed2bb56

Observation bbdc90d6-4f49-4e56-88e4-c2ed677141a4 · outbound

This paper cites Tropical refined curve counting with descendants.

BPS polynomials and Welschinger invariants Tropical refined curve counting with descendants

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:46.100199Z

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=2026-08-07T11:22:40.215205Z digest=sha256:852885d76c11b6b374637030def416800405bbd5d7d8df9d4eec8c46479cf8c7

Observation cc887086-76e7-4749-90f0-053286459634 · outbound

This paper cites Counting real rational curves on K3 surfaces.

BPS polynomials and Welschinger invariants Counting real rational curves on K3 surfaces

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:45.786280Z

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=2026-08-07T11:22:40.220469Z digest=sha256:bf515f6794527e136321e36e1540f6bbc68025b0df131a37293601c5bbf0c846

Observation d8a49724-908b-4025-8705-acf15b6fc3aa · outbound

This paper cites A compactification of the space of maps from curves.

BPS polynomials and Welschinger invariants A compactification of the space of maps from curves

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:45.478031Z

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=2026-08-07T11:22:40.224586Z digest=sha256:8aa9b63d8e36b4febe7784dfa490e9ae426adaffc2ff2a81d670637c2e2871e8

Observation 81b2430f-5819-4fbf-bc44-95683ab7a635 · outbound

This paper cites A degeneration formula of GW-invariants.

BPS polynomials and Welschinger invariants A degeneration formula of GW-invariants

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:45.344663Z

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=2026-08-07T11:22:40.230394Z digest=sha256:41d2064a2ddfae80e5803000d2ec551ab1a26e641ed367102b5e1765f1cd6771

Observation cd73b676-fde5-45aa-af98-8fff8c756904 · outbound

This paper cites Comparison of algebraic and symplectic Gromov-Witten invariants.

BPS polynomials and Welschinger invariants Comparison of algebraic and symplectic Gromov-Witten invariants

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:45.208541Z

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=2026-08-07T11:22:40.235087Z digest=sha256:5db4d90bf6d7810de3b2be7cf46dea99b06754d353098625a89788e21df6ff67

Observation 1787c0a3-1228-4af9-936c-1cd52949a4dc · outbound

This paper cites Gromov–Witten invariants of blow-ups of P2 using logarithmic geometry.

BPS polynomials and Welschinger invariants Gromov–Witten invariants of blow-ups of P2 using logarithmic geometry

Reference 61

Resolution
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raw_fallback, observed 2026-08-07T11:22:45.072168Z

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=2026-08-07T11:22:40.239554Z digest=sha256:c102f7ffc373922161d073583d49770562a6f208493f98356bdef8f8936131c9

Observation ea038838-f2e8-4100-9433-21dbcb4dd105 · outbound

This paper cites Framed knots at large N.

BPS polynomials and Welschinger invariants Framed knots at large N

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:44.893749Z

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=2026-08-07T11:22:40.243670Z digest=sha256:2339cb05f2a755ed5f89dfb6f7790b7f7977bca14290d9d152bf5ea4d2aaed47

Observation eb2fc6cf-fa20-4b5c-9ef7-030a1613c110 · outbound

This paper cites Gromov-Witten theory and Donaldson-Thomas theory.

BPS polynomials and Welschinger invariants Gromov-Witten theory and Donaldson-Thomas theory

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:44.733012Z

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=2026-08-07T11:22:40.247801Z digest=sha256:50bbda03a20b4c8428e31e228919392e6d9bf763de647ea8194608b668faeec4

Observation 6e61e9f1-b1aa-4da7-a5f2-9e428fae8805 · outbound

This paper cites Gromov-Witten theory and Donaldson-Thomas theory.

BPS polynomials and Welschinger invariants Gromov-Witten theory and Donaldson-Thomas theory

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:44.600575Z

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=2026-08-07T11:22:40.251915Z digest=sha256:8d432a247083ed9af3918bac9a707240efb480fd413ce945195132822c286683

Observation 5cff4776-39b0-4501-8c66-da790f5afee9 · outbound

This paper cites Gromov- Witten/Donaldson-Thomas correspondence for toric 3-folds.

BPS polynomials and Welschinger invariants Gromov- Witten/Donaldson-Thomas correspondence for toric 3-folds

Reference 65

Resolution
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raw_fallback, observed 2026-08-07T11:22:44.451569Z

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=2026-08-07T11:22:40.256144Z digest=sha256:ea36a964990f70e68d84fb42ce5eb49c34f0ab83b219554513c48ad3cb4ac7a7

Observation 01848e94-486e-460b-9ad6-dc6fc29a128e · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 66

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:44.270718Z

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=2026-08-07T11:22:40.260402Z digest=sha256:bd0740a2215b8ecbf8a15e9d232e3ef0e7b2c7b4d8403d035ce4612cdbf64724

Observation 826d7bb7-2362-4012-9d91-8101a53dd4f6 · outbound

This paper cites Enumerative tropical algebraic geometry in R2.

BPS polynomials and Welschinger invariants Enumerative tropical algebraic geometry in R2

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:44.051232Z

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=2026-08-07T11:22:40.264966Z digest=sha256:bc982e185835cd369384d81b8675116526abb1bd1b67f7961feacd8e3fc3af48

Observation a17be381-5e6a-4a08-96be-54978bd54b00 · outbound

This paper cites Quantum indices and refined enumeration of real plane curves.

BPS polynomials and Welschinger invariants Quantum indices and refined enumeration of real plane curves

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:43.944453Z

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=2026-08-07T11:22:40.269052Z digest=sha256:f275190fef0d03cf0756a0a296f468228ebf477b63b2623b8680125594f94fbc

Observation 4e84a66e-576d-4b1a-b18d-00e6cdc963b3 · outbound

This paper cites Towards an enumerative geometry of the moduli space of curves.

BPS polynomials and Welschinger invariants Towards an enumerative geometry of the moduli space of curves

Reference 69

Resolution
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raw_fallback, observed 2026-08-07T11:22:43.800428Z

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=2026-08-07T11:22:40.273980Z digest=sha256:a2abb05c46c2367ee36a76e0c2102ddc76f96e563c40b4480aca4d6e5272ba0c

Observation 49ec72da-e436-4843-83fb-95ffd61b3e0b · outbound

This paper cites Membranes and sheaves.

BPS polynomials and Welschinger invariants Membranes and sheaves

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:43.599621Z

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=2026-08-07T11:22:40.278490Z digest=sha256:c6aa23e0087da47cece72486a4b6c5931393811af607e38ae9f0628dc025a679

Observation 5c9b6aa7-fa3d-40ad-8398-15f345291c12 · outbound

This paper cites Unramified Gromov-Witten and Gopakumar-Vafa invariants.

BPS polynomials and Welschinger invariants Unramified Gromov-Witten and Gopakumar-Vafa invariants

Reference 71

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.283130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.283130Z digest=sha256:bee1f759b0edc867f93a7fc138242e1345a71afe07a849a1e6936f759dc2db0d

Observation 7b368256-d386-4d7c-a2ae-c3643c333efd · outbound

This paper cites Toric degenerations of toric varieties and tropical curves.

BPS polynomials and Welschinger invariants Toric degenerations of toric varieties and tropical curves

Reference 72

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.288327Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.288327Z digest=sha256:9cf641752b8e3f28ec8e655038523a812f5fbe88b895e5b2a4b1b4b3e7050ffc

Observation d62b7339-b272-4978-85df-51f89901b4d5 · outbound

This paper cites Hodge integrals and degenerate contributions.

BPS polynomials and Welschinger invariants Hodge integrals and degenerate contributions

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:43.484345Z

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=2026-08-07T11:22:40.293547Z digest=sha256:7a19c50f0469845bfd8b3d5ebc59acdffdb1f4b6dc1adbb178115961232ecea5

Observation 734c4cfe-3415-426f-a593-38cfba7c57ef · outbound

This paper cites Three questions in Gromov-Witten theory.

BPS polynomials and Welschinger invariants Three questions in Gromov-Witten theory

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:43.361595Z

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=2026-08-07T11:22:40.298430Z digest=sha256:d67d14776cbafaaa6e30966f93043b329e9a6b5495ab1b410ef46f29d4fe82df

Observation ee1a608f-d033-40ba-ba27-4f125ef565ab · outbound

This paper cites Gromov-Witten/Pairs correspondence for the quintic 3-fold.

BPS polynomials and Welschinger invariants Gromov-Witten/Pairs correspondence for the quintic 3-fold

Reference 75

Resolution
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raw_fallback, observed 2026-08-07T11:22:43.209577Z

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=2026-08-07T11:22:40.303401Z digest=sha256:c3cbf0c34ff137e6eed8688114bdcf8cfadd0a24029212c798ac7fedd56acfe0

Observation b99f3d5d-cf88-46e2-97c8-0f722db1fd24 · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 76

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:43.119577Z

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=2026-08-07T11:22:40.308177Z digest=sha256:71ea12c4961328afc29aad1b92ec5611266ca4c7f021de206e751591c72cc2d6

Observation 27615d0d-632a-480a-ba09-ebfeebf6af6d · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 77

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:42.941937Z

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=2026-08-07T11:22:40.313944Z digest=sha256:bb81548f2dfa3be3fa7d38f9505e67cd675cb8b3b190023adff3eb921a285840

Observation 71fe9238-dcf1-4faa-983f-298ba487e554 · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 78

Resolution
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raw_fallback, observed 2026-08-07T11:22:42.807007Z

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=2026-08-07T11:22:40.318595Z digest=sha256:4fd5723ac4cbfdb6354f4ff987efdfebb3a6db798872b20e560f311fb0aadfd2

Observation d3033dd4-9a22-4061-892d-0c18d0e52493 · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 79

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:42.682595Z

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=2026-08-07T11:22:40.323265Z digest=sha256:5b05ef864f9cda24829073668d90bf43449cc343f3c01445fd808c9b03892502

Observation d8212652-4d2a-4b31-b33a-b62492bf53b9 · outbound

This paper cites Universally counting curves in Calabi--Yau threefolds.

BPS polynomials and Welschinger invariants Universally counting curves in Calabi--Yau threefolds

Reference 80

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.327755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.327755Z digest=sha256:cc121dfa576be2a71b8f3b8f0900b1f43e65d288805ee397b3892dd8ce20ae96

Observation 044464f4-2f4f-42b8-84a8-89b3bb4d8f56 · outbound

This paper cites Tropical enumeration of curves in blowups of CP 2.

BPS polynomials and Welschinger invariants Tropical enumeration of curves in blowups of CP 2

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:42.551274Z

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=2026-08-07T11:22:40.332434Z digest=sha256:8a32a254f9ac48d8617a5dbc94e2f8bf0e4dcccfc6d7e881ed07a5fe3756a6d7

Observation 273cb43d-459b-4045-8a23-b756ec3cb7c0 · outbound

This paper cites On Gromov-Witten invariants of del Pezzo surfaces.

BPS polynomials and Welschinger invariants On Gromov-Witten invariants of del Pezzo surfaces

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:42.423828Z

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=2026-08-07T11:22:40.336788Z digest=sha256:d1f81cab908523011fa2215849ec51e7227bfceced731204fed990016d5dc066

Observation 5ecd094b-f16f-457f-9581-697a8646d362 · outbound

This paper cites Algebraic and symplectic Gromov-Witten invariants coincide.

BPS polynomials and Welschinger invariants Algebraic and symplectic Gromov-Witten invariants coincide

Reference 83

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:42.254465Z

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=2026-08-07T11:22:40.341557Z digest=sha256:58d059f9073ede4fb078d13b3e6dfda8c1729ad72fc6ff2c122dfedb972fe869

Observation efcd6e86-610b-43f7-93e6-d54c7fd21023 · outbound

This paper cites Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions.

BPS polynomials and Welschinger invariants Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

Reference 84

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.346162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.346162Z digest=sha256:75596d6aa00f359385608e741a3537cc84a599d81ce4abbdd3dc665dc7975be1

Observation 7e3487f4-9dce-46d4-b8e2-4515736b5732 · outbound

This paper cites Solomon and Sara B.

BPS polynomials and Welschinger invariants Solomon and Sara B

Reference 85

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:42.086141Z

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=2026-08-07T11:22:40.351455Z digest=sha256:351f2c41b93506eefd7d1272e84153d320379aaa8afb72094b05dbf270ccb244

Observation 929a0236-acad-4b04-9d4f-0274aa9c6d01 · outbound

This paper cites an unresolved cited work.

BPS polynomials and Welschinger invariants Unresolved cited work

Reference 86

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:22:41.939274Z

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=2026-08-07T11:22:40.356194Z digest=sha256:e1edac75e865ce84ccdcc184d952b6401db756b51528a3adfaf8a89d7396dd1a

Observation f0c8a9e9-edd8-43e7-aec8-147573fcffca · outbound

This paper cites Refined sheaf counting on local K3 surfaces.

BPS polynomials and Welschinger invariants Refined sheaf counting on local K3 surfaces

Reference 87

Resolution
unresolved
no resolver link, observed 2026-08-07T11:22:40.360591Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:22:40.360591Z digest=sha256:ae18a9eebbf614bfee68e5f181fa5884f256ea013401a4df1dc5c4b22af5c61f

Observation 24965f87-9451-481e-8a2e-34e196ee83df · outbound

This paper cites Counting curves on rational surfaces.

BPS polynomials and Welschinger invariants Counting curves on rational surfaces

Reference 88

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:41.802952Z

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=2026-08-07T11:22:40.365288Z digest=sha256:89d3afcb820ea6eceac56c7751df8ae7aeb97d27749ed2f9227141d3f779351e

Observation 70340800-88fd-4f56-b252-e2339b46dade · outbound

This paper cites Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry.

BPS polynomials and Welschinger invariants Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry

Reference 89

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:41.647291Z

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=2026-08-07T11:22:40.369706Z digest=sha256:33477b9695c206c8b547f455cbd64b155d201067bc4aba30ca6255ff5c099f22

Observation d7204fdf-9ea0-4315-949e-f12f3c7ad40e · outbound

This paper cites Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry.

BPS polynomials and Welschinger invariants Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

Reference 90

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:41.516410Z

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=2026-08-07T11:22:40.374136Z digest=sha256:2dee2a3f13495b4fcce5323b4d6fed59a14a6896398adef5f449e05b84416138

Observation 677feb26-4bd6-4099-a46b-ade165f19cc2 · outbound

This paper cites Open/closed BPS correspondence and integrality.

BPS polynomials and Welschinger invariants Open/closed BPS correspondence and integrality

Reference 91

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:41.379871Z

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=2026-08-07T11:22:40.378953Z digest=sha256:c8cb8044383a81fa90937b755779bc35af27dfd5ccf1c8479531c759b464279d

Observation 51d14708-7870-41ac-be46-e8f9a626a8f4 · outbound

This paper cites A comparison theorem for Gromov-Witten invariants in the symplectic category.

BPS polynomials and Welschinger invariants A comparison theorem for Gromov-Witten invariants in the symplectic category

Reference 92

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:22:41.216842Z

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=2026-08-07T11:22:40.385252Z digest=sha256:d8b99283655e1eaf686be783c22be817180b32ee2d4cd637cedd72bea72a7909

Pith citing papers

Observation ea0cf605-5887-414c-b0f3-696f7f5a4619 · inbound

The GW/PT conjectures for toric pairs cites this paper.

The GW/PT conjectures for toric pairs BPS polynomials and Welschinger invariants

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-05-15T14:40:04.336331Z

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=2026-05-15T14:38:09.721519Z digest=sha256:619f4781fce0d07dea50dcba39894f090c225a83da127124a56fad2562c6191e