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Paper Citation Record · LEDGER

BPS polynomials and Welschinger invariants

As of 8 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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source=pdf_text observed=2026-08-07T11:22:39.977418Z digest=sha256:24479a495fba5930954f83f023885c49515ca889177bb6e4e0e9d562cd5379c8

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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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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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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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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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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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:b12afce9b8aebe9d5e170d29000001bb157505ae93bc65781f62bb8d39873756

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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source=pdf_text observed=2026-08-07T11:22:40.086119Z digest=sha256:9090274cf641e9dbd695757d0b7f9415c496a39f49e0e61c7838c8b82c2f0b07

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=sha256:2a0e98a2bf5b98b29c420b13a4dbca75aee0f0dd9c70475102ed9b2d7045b828

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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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=sha256:2b0869b43ff759ad3329bc7b95ad357bb91d574cea4dfeb54817e61860182f55

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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raw_fallback, observed 2026-08-07T11:22:49.172639Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.127356Z digest=sha256:0b21df37121afbfe42c228f9a9f271cf9d17814d0a4ec30b8aee83c9d18b730e

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

Resolution
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.131598Z digest=sha256:cf3000854b5ca19a9d8b193eb3e99570b11035b67a1e4c74a47a38b9516524cc

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
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.135933Z digest=sha256:8c4d2e0fca0363544d457014649adf6887d62b0191b4e4b567af86f362af0737

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

This paper cites The tropical vertex.

BPS polynomials and Welschinger invariants The tropical vertex

Reference 40

Resolution
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.140408Z digest=sha256:b542c9e0175e84f8a60802046ec6227170f530110a6805a60cc60683db68aa20

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.144584Z digest=sha256:266be6fab36a9fa23a8c2c108d6fd258e6750bc60157f57cc7f70e181c8ef859

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.149159Z digest=sha256:99d26a235fc62f4e764a1fe09302bfca4997d2b1a3073212792274f86946c84c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.154562Z digest=sha256:0541f8ffda67b2e6098b0d4c4c68766d67fbc2113bacc8c7025def1157e1ffdd

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.159256Z digest=sha256:1896755e5472216dbe8d70f3bd3491dd570a67ea2b6cbd614254a4cfc3c5ba34

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.163278Z digest=sha256:bf0dcb8d1549fddc5b750c1561f41e99b33c599076380d1deedc6b35396d9228

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.167683Z digest=sha256:3173f120d8de8a8858887d1f8effcdef5a4c38755d88b9f68c7d64f664414232

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.172358Z digest=sha256:0ff391c2208af56ea704a3eb12f2375c71eec787c56d55c126270844504060c5

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.176916Z digest=sha256:60146eedcc497757b87f4114617c4c00c5b78ac30b08824754b9c4bd80925790

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.181996Z digest=sha256:c54ade16dbf15131a3eae23dd087d0352805aa90d6772a4a95fc96baa8cf44b3

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.187269Z digest=sha256:452d6cbc548cb43e6a32fc362cbfce84893bd2572bded4a5a8f75bdc901378a6

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

This paper cites Welschinger invariants revisited.

BPS polynomials and Welschinger invariants Welschinger invariants revisited

Reference 51

Resolution
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.191852Z digest=sha256:e9759b032333c56bb418d1a9acbb50230a7b0a3b2fb7c9a1d3e2ddc440592d8f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.196218Z digest=sha256:08d29ca5e7168a74c5cbcb0143157e1d336ba5c849e3ab6e8a630e89f280eefe

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.200560Z digest=sha256:8ecfde00df17e4bb630369c0d5e1073e6c878ce67ecb8763439b6a328ac8216a

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:ae3a564509ed14781ff76e10b10249bbcf42e2d46a5782e9f5140f12cca931c2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.210348Z digest=sha256:0cdc30f0ecd0fa904698e47aefe3188dc5e62095d8fc0a716a433cf0014dbc1b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.215205Z digest=sha256:788bc84b493d5eb65b7e889a39afe25c6e757ee95f9c74961f5ab2db2d315423

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.220469Z digest=sha256:342ed149d288cd88a729d866feecb4980bcd772f16cb4c6d9ea9857725907c8c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.224586Z digest=sha256:0bf86cdb40fd48941cbbd85a321fad3b62bb6cd539528d50ebd5f411398f4f52

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.230394Z digest=sha256:d67a3fd2d80b8acaef456a073f15a0d540fc0ac6f52b2ea71398b48340cf449f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.235087Z digest=sha256:e19267d5c1bcada1c3c73a0816cc1d3a6f5329ff76c04b1832cdfcfee759da03

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
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.239554Z digest=sha256:18c223c433350b27178cb42d16fd59dbe05d5cb40ff3d60cd20fb076d49d7029

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.243670Z digest=sha256:f5610fdc922cfde531b4e05e2f8faf2e5606114ae9b3719c6e9d3883adb7f914

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.247801Z digest=sha256:3ab7c24c820f3fb9164f9061c439aa20d4f95353ae15c9d30c03a6ecc2c4fc38

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.251915Z digest=sha256:d6b395dda461695e54bc8c2002bcf51137f62142a1e7e459ea2e2d0e71e3d774

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
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.256144Z digest=sha256:ea1fc2e1332b5928a1f0a566021c5129e2acf6fa83edd5930fb43268347edd4e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.260402Z digest=sha256:d3e2382e669f049a1ca26a3f53bf1b52b79925399ab636fe77b326ce1139fb98

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.264966Z digest=sha256:d01e162ffb7336d55821ccf7dd7e4358c5165df218dc9ed762e4dd7e92449134

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.269052Z digest=sha256:b85b1b824e935d5fd12858785c5e74f7dbebd070105d1c5da7f64d0e9fec6d57

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
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.273980Z digest=sha256:3b331e6ae147209d2c3b51aac1a2b3d8d4af0257eaf7cfb3dc8cc22473ef684b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.278490Z digest=sha256:77ebf49df7f115dee93e7c437b179a4dcf3e0032ab6c61e76d8e5971c9b53b84

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=sha256:14f5b2dad74346883be16e7ce878fb45667f11e85d171fe7f7437616ccedb8ef

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=sha256:93c2a299fc21261daa00d0cda8c5bc43a8ae6372c9d68873a60a6bd5191b1e03

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.293547Z digest=sha256:f753233a977d94ba0d6d399363211a65c1ded7dd96d78c101d432979bea14c75

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.298430Z digest=sha256:7f51c323490e8cde9b576cfc459164857c908677afdbf4d7bd5fd3df14d3b352

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
verified fuzzy
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.303401Z digest=sha256:e5b2f1054637a51ba5b984160c17795be6a0430f01af2d170253734beeb03ee6

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.308177Z digest=sha256:baf227f32d9f3559a6c3051b78887c2196f0cde7be1c14840f624d2c275e22ad

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.313944Z digest=sha256:1ceb8f8873d43f470839ad2ad69f64ac99005177c4434b11bb6bdb701057a178

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
unresolved
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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.318595Z digest=sha256:08b3798c9268cbe5dafacda390e3d1f19f97a5fbf6c80a30f57ffd9e6df46802

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.323265Z digest=sha256:c8fdb55bd2f5194bc060d437312738b86a7bbf5395219975b172552c2bf581ec

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=sha256:20e31b7a5015dc93a00d7e3dc63f6528cd1ea80db703118c032b0368b01b586a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.332434Z digest=sha256:93a7f7ad40895bbd57843d332a89fb7934f28aea8ae31b625437aea23b1007b2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.336788Z digest=sha256:98fd77d793b6140d79c932fd054ee550156de140d6dfe65c85ba60d4dce13f10

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.341557Z digest=sha256:88522e02ff996680296e6f06705591069f59dc3d8fafd8a47427e76adafde40e

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=sha256:3b98f2468f1899940d35ea53d4753e05e4d26397006e23c7bc7ed58574458e91

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.351455Z digest=sha256:2a7c87f8f0dc58f69a09b03fa1c7dfdf90cdcd131f841f8cf9fa8cdb62d8d3b2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.356194Z digest=sha256:09b2da74f475b9fedee2c8a6fd9e39214b46e887e3bc5e51d7ff457b94c3242c

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:abcc12f003b236b75d8459c904822cbac2a47e25c4be3d3e2ab0b8cb7ab3604d

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.365288Z digest=sha256:047ced12284ae2b3105a4a73209e557a1cd937bbd94a7b516a2b9011f177b95e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.369706Z digest=sha256:1a99f46a34cf826192c3211fd5e26db5bddc244c1925d26f1da394249c51ea3b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.374136Z digest=sha256:fc6253599298299c9e079e3b1766834a09cb4b51ca5b225c64e2ace76b81fda1

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.378953Z digest=sha256:643666bec003a7534a8a6c7e73997a3c86467137fabcacb2aeec8542c81dae6d

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:22:40.385252Z digest=sha256:3ab9726824ef28e618f7586243cbb51459d2de673f4efc63d9d783742b8356aa

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-05-15T14:38:09.721519Z digest=sha256:9db4047fec19ec9a2a86acb7ac021346a695aa03f9ef7359e7f4064952d06005