Paper Citation Record · LEDGER

Conditional GMC within the stochastic heat flow

As of 9 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 7 inbound Pith citation observations for arXiv:2507.16056.

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

pith.paper-citation-record.v1
2507.16056 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:32:13.058791Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:43:23.410140Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T02:19:22.981783Z

Reference resolution

25 of 25 outbound references displayed

verified exact2
verified fuzzy17
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0071e3aa-418e-41d1-ad92-727b6cbe850e · outbound

This paper cites The intermediate disorder regime for directed polymers in dimension 1+1.

Conditional GMC within the stochastic heat flow The intermediate disorder regime for directed polymers in dimension 1+1

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.284723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a3195326-f8b5-4ea3-8246-a7f52c9d3789 · outbound

This paper cites Handbook of mathematical functions: with formulas, graphs, and mathematical tables , volume 55.

Conditional GMC within the stochastic heat flow Handbook of mathematical functions: with formulas, graphs, and mathematical tables , volume 55

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.004279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15dd8ea0-74be-4395-a8bc-f5245f794f1a · outbound

This paper cites Bogachev.

Conditional GMC within the stochastic heat flow Bogachev

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.275051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 64338b8c-06cf-4da8-808c-1e04b04b8fc9 · outbound

This paper cites Continuum models of directed polymers on disordered diamond fractals in the critical case.

Conditional GMC within the stochastic heat flow Continuum models of directed polymers on disordered diamond fractals in the critical case

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.269402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ebcd7b5e-3555-486d-87b9-5ae7a21e3745 · outbound

This paper cites The conditional G aussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractal.

Conditional GMC within the stochastic heat flow The conditional G aussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractal

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.263206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f7cd5f4f-6daf-4b92-9c7e-b57177b88c7e · outbound

This paper cites On planar Brownian motion singularly tilted through a point potential.

Conditional GMC within the stochastic heat flow On planar Brownian motion singularly tilted through a point potential

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:32:13.177074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 936f8282-375b-40b9-822a-fccd96885499 · outbound

This paper cites Continuum polymer measures corresponding to the critical 2d stochastic heat flow.

Conditional GMC within the stochastic heat flow Continuum polymer measures corresponding to the critical 2d stochastic heat flow

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.016730Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aae1da84-e0d6-4eee-bb7e-22cd82d87d62 · outbound

This paper cites The critical 2d stochastic heat flow.

Conditional GMC within the stochastic heat flow The critical 2d stochastic heat flow

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.257094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7f47daf0-0e14-4031-bcbf-70d2b91b654a · outbound

This paper cites The critical 2d stochastic heat flow is not a gaussian multiplicative chaos.

Conditional GMC within the stochastic heat flow The critical 2d stochastic heat flow is not a gaussian multiplicative chaos

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.251452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation efe8f63c-91e6-4bde-8d5f-bb962a740121 · outbound

This paper cites The Critical 2d Stochastic Heat Flow and Related Models.

Conditional GMC within the stochastic heat flow The Critical 2d Stochastic Heat Flow and Related Models

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.023610Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a28e66f-13ac-4402-9618-b635cd3dd28e · outbound

This paper cites Singularity and regularity of the critical 2D Stochastic Heat Flow.

Conditional GMC within the stochastic heat flow Singularity and regularity of the critical 2D Stochastic Heat Flow

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.026289Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1643b5d-dee1-4a71-844e-c312904fd816 · outbound

This paper cites H amiltonians for systems of N particles interacting through point interactions.

Conditional GMC within the stochastic heat flow H amiltonians for systems of N particles interacting through point interactions

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.245969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 836b2ab6-208b-40c9-9e62-7d355f69be00 · outbound

This paper cites Multi-particle S chr \"o dinger operators with point interactions in the plane.

Conditional GMC within the stochastic heat flow Multi-particle S chr \"o dinger operators with point interactions in the plane

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.240046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 02f4c2d9-26ac-4f61-8eea-08eea75bc9b4 · outbound

This paper cites Moments of the 2d SHE at criticality.

Conditional GMC within the stochastic heat flow Moments of the 2d SHE at criticality

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.233747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a99564b6-4a97-4266-9779-0d62cb972fd4 · outbound

This paper cites Sur le chaos multiplicatif.

Conditional GMC within the stochastic heat flow Sur le chaos multiplicatif

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.227902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 21aca7fc-0335-47d8-bd9b-dde7951f0e6b · outbound

This paper cites Foundations of modern probability , volume 99 of Probability Theory and Stochastic Modelling.

Conditional GMC within the stochastic heat flow Foundations of modern probability , volume 99 of Probability Theory and Stochastic Modelling

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.222105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2ed7c553-05a6-4255-8b39-0cbe4f359e99 · outbound

This paper cites Moreno Flores.

Conditional GMC within the stochastic heat flow Moreno Flores

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.216232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 80858083-4922-433d-93b9-f4793ae8e5b9 · outbound

This paper cites On the support of solutions to the heat equation with noise.

Conditional GMC within the stochastic heat flow On the support of solutions to the heat equation with noise

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.209970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1f950b51-98d0-48f5-8643-573b690cea37 · outbound

This paper cites KPZ fluctuations in the planar stochastic heat equation.

Conditional GMC within the stochastic heat flow KPZ fluctuations in the planar stochastic heat equation

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:32:13.151513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8485a794-1308-491b-aad4-9b53fa7483a3 · outbound

This paper cites A Condensation of Interacting Bosons in Two Dimensional Space.

Conditional GMC within the stochastic heat flow A Condensation of Interacting Bosons in Two Dimensional Space

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.047596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 270c0003-1629-4881-a3bc-a4adefbbc3aa · outbound

This paper cites Methods of modern mathematical physics.

Conditional GMC within the stochastic heat flow Methods of modern mathematical physics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.203967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 997d98b3-6c31-48bc-a1c6-4256f9ca4ee3 · outbound

This paper cites Gaussian multiplicative chaos and applications: a review.

Conditional GMC within the stochastic heat flow Gaussian multiplicative chaos and applications: a review

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.197552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dd6368ed-3062-4719-8964-5df8f1ba049c · outbound

This paper cites On G aussian multiplicative chaos.

Conditional GMC within the stochastic heat flow On G aussian multiplicative chaos

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.190803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 97c94b1a-b1e9-4fff-bfa3-8c7121342a3e · outbound

This paper cites Two dimensional delta- B ose gas in a weighted space.

Conditional GMC within the stochastic heat flow Two dimensional delta- B ose gas in a weighted space

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:32:13.183895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7f7e924d-8391-4b35-9a2a-cdc43a7e53e8 · outbound

This paper cites Stochastic heat flow by moments.

Conditional GMC within the stochastic heat flow Stochastic heat flow by moments

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T15:32:13.058791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation a39be014-4faf-46b7-ab3b-3fd5aea9c8d4 · inbound

Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow cites this paper.

Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow Conditional GMC within the stochastic heat flow

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T17:43:23.410140Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f9c3b4a-e5b3-4f87-ab71-a5ccc2bb1cf5 · inbound

An upper bound of the lower tail of the mass of balls under the critical $2d$ stochastic heat flow cites this paper.

An upper bound of the lower tail of the mass of balls under the critical $2d$ stochastic heat flow Conditional GMC within the stochastic heat flow

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-19T03:27:01.134474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a0735195-b8dc-468e-95c2-a38b04dd7d8d · inbound

Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow cites this paper.

Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow Conditional GMC within the stochastic heat flow

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T12:18:53.797484Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0b47156-3f17-476a-801d-1ad942506743 · inbound

Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers cites this paper.

Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers Conditional GMC within the stochastic heat flow

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-19T01:06:57.241585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0db1c7fb-808a-4228-997f-fb61758ec54a · inbound

McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data cites this paper.

McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data Conditional GMC within the stochastic heat flow

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T23:59:13.350794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53d5c8f8-856d-4a8c-9a25-9e07733c1af6 · inbound

Extrema of cooling branching Brownian motion and related Gaussian fields cites this paper.

Extrema of cooling branching Brownian motion and related Gaussian fields Conditional GMC within the stochastic heat flow

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T02:19:22.983697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3816aba3-cc14-4dc6-b43d-55fea4dcd6dd · inbound

Extrema of cooling branching Brownian motion and related Gaussian fields cites this paper.

Extrema of cooling branching Brownian motion and related Gaussian fields Conditional GMC within the stochastic heat flow

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T11:06:54.471726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.