Paper Citation Record · LEDGER

Breaking coexistence: Zealotry vs. nonlinear social impact

As of 8 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2505.21407.

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

pith.paper-citation-record.v1
2505.21407 v2

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:44:21.032843Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T11:55:53.395391Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

33 of 33 outbound references displayed

verified exact1
verified fuzzy29
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c022b1d6-c528-4683-8081-e6b96d80bf1d · outbound

This paper cites (6)] with one-sided zealots as follows, dx dt = (1 − x − z) f (x + z) − x f(1 − x − z), (29) where f (x) is the social impact function.

Breaking coexistence: Zealotry vs. nonlinear social impact (6)] with one-sided zealots as follows, dx dt = (1 − x − z) f (x + z) − x f(1 − x − z), (29) where f (x) is the social impact function

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:28.296458Z

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.

Observation ceb3b21e-6bc2-4ef3-bd73-c2fee13f132a · outbound

This paper cites Thus, for any q < 1 we find f ′(x) → +∞ for x ↓ 0.

Breaking coexistence: Zealotry vs. nonlinear social impact Thus, for any q < 1 we find f ′(x) → +∞ for x ↓ 0

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:28.090086Z

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.

Observation 24744c71-613f-4df2-a461-acc0910d9b16 · outbound

This paper cites (13)] can be generalised as follows, to account for a social impact function f , dx dt = (1 − x − z) f (x + z)π+(x, z) −x f(1 − x − z)π−(x, z).

Breaking coexistence: Zealotry vs. nonlinear social impact (13)] can be generalised as follows, to account for a social impact function f , dx dt = (1 − x − z) f (x + z)π+(x, z) −x f(1 − x − z)π−(x, z)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:27.922273Z

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.

Observation fe19a8f0-92c4-44eb-88a7-3f50e4b78268 · outbound

This paper cites (33) For α > 1/2 this condition is always fulfilled (for all z) as (1 − α)/α is then smaller than one.

Breaking coexistence: Zealotry vs. nonlinear social impact (33) For α > 1/2 this condition is always fulfilled (for all z) as (1 − α)/α is then smaller than one

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:27.630897Z

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.

Observation 24758465-ebe2-4aff-9342-4da67b5b23da · outbound

This paper cites We focus again on f (x) =xq, noting that q-deformed evolutionary dynamics without zealots were pre- viously studied in Ref.

Breaking coexistence: Zealotry vs. nonlinear social impact We focus again on f (x) =xq, noting that q-deformed evolutionary dynamics without zealots were pre- viously studied in Ref

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:27.377606Z

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.

Observation 09dd3852-372b-43b8-b9d4-59c116a4a510 · outbound

This paper cites Allowing for a general social impact 11 function, Eqs.

Breaking coexistence: Zealotry vs. nonlinear social impact Allowing for a general social impact 11 function, Eqs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:27.165156Z

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.

Observation 10cda3b9-2c84-4527-8eee-3be3b667c807 · outbound

This paper cites an unresolved cited work.

Breaking coexistence: Zealotry vs. nonlinear social impact Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:44:26.883598Z

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.

Observation 2cf7f996-8f50-4f16-bfb5-950d9d7b35bb · outbound

This paper cites This is restricted to the nonlinear voter model and evolu- tionary games.

Breaking coexistence: Zealotry vs. nonlinear social impact This is restricted to the nonlinear voter model and evolu- tionary games

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:26.621748Z

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.

Observation a58e500e-4b67-428a-b9da-56ea53bf11cf · outbound

This paper cites (5) T + n = N S − n N n + Z N − 1 q , T − n = N n N N − Z − n N − 1 q.

Breaking coexistence: Zealotry vs. nonlinear social impact (5) T + n = N S − n N n + Z N − 1 q , T − n = N n N N − Z − n N − 1 q

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:26.306527Z

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.

Observation 3b1f3161-514a-4036-9753-85f619f2a854 · outbound

This paper cites an unresolved cited work.

Breaking coexistence: Zealotry vs. nonlinear social impact Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:44:26.093941Z

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.

Observation e552aba9-086c-4e0b-98d3-a5381d324c41 · outbound

This paper cites We report simulation results in Fig.

Breaking coexistence: Zealotry vs. nonlinear social impact We report simulation results in Fig

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:25.858109Z

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.

Observation b610c149-d2f2-42d4-be12-63f9cfb4fb6e · outbound

This paper cites For example in Fig.

Breaking coexistence: Zealotry vs. nonlinear social impact For example in Fig

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:25.634101Z

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.

Observation 24c422e6-318b-4d68-8083-347516aa80e5 · outbound

This paper cites 6 we plot the quasi-stationary distribution for the nonlinear voter model with varying numbers of zealots.

Breaking coexistence: Zealotry vs. nonlinear social impact 6 we plot the quasi-stationary distribution for the nonlinear voter model with varying numbers of zealots

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:25.355381Z

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.

Observation e8a79048-2b11-46cd-ac36-0ff610f24d1e · outbound

This paper cites For fixed model parameters (e.g.

Breaking coexistence: Zealotry vs. nonlinear social impact For fixed model parameters (e.g

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:18.995108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f33dbe8e-60af-499e-b3b6-b480ead72679 · outbound

This paper cites (6) becomes dx dt = (1 − x − z) x + z 2 q − x 1 − x − z 2 q.

Breaking coexistence: Zealotry vs. nonlinear social impact (6) becomes dx dt = (1 − x − z) x + z 2 q − x 1 − x − z 2 q

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:25.226258Z

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.

Observation 1a3db1ee-e78d-4eb2-b1f1-a11b87f0c9d3 · outbound

This paper cites (6) becomes dx dt = (1 − x − z)(x + z)q − x(1 − x − z)q.

Breaking coexistence: Zealotry vs. nonlinear social impact (6) becomes dx dt = (1 − x − z)(x + z)q − x(1 − x − z)q

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:25.063021Z

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.

Observation 4699fdd5-6087-43de-8763-e36a8d47d9fa · outbound

This paper cites (A6) has two additional fixed points x∗ a and x∗ b where x∗ a < x∗ b < x∗ c.

Breaking coexistence: Zealotry vs. nonlinear social impact (A6) has two additional fixed points x∗ a and x∗ b where x∗ a < x∗ b < x∗ c

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:24.824791Z

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.

Observation 7b5ad04f-84a2-441f-85d6-ad47519c4239 · outbound

This paper cites (A6) has one additional fixed point x∗ a < x∗ c that is stable from the left and unstable from the right.

Breaking coexistence: Zealotry vs. nonlinear social impact (A6) has one additional fixed point x∗ a < x∗ c that is stable from the left and unstable from the right

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:24.648866Z

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.

Observation e95cf359-c29c-4bbc-896a-48ed3765f9c4 · outbound

This paper cites (A6) has no additional fixed points.

Breaking coexistence: Zealotry vs. nonlinear social impact (A6) has no additional fixed points

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:24.465258Z

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.

Observation 358f4570-ef17-4880-ab40-a18baf7837d1 · outbound

This paper cites (6)] becomes ˙x = (1 − x − z) x + 1 2 (1 + δ )z q − x 1 − x − 1 2 (1 + δ )z q.

Breaking coexistence: Zealotry vs. nonlinear social impact (6)] becomes ˙x = (1 − x − z) x + 1 2 (1 + δ )z q − x 1 − x − 1 2 (1 + δ )z q

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:24.296020Z

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.

Observation e4f1263a-47d0-4a87-95e3-96a468c7a5c6 · outbound

This paper cites (A13) Here we derive a closed form approximation to Eq.

Breaking coexistence: Zealotry vs. nonlinear social impact (A13) Here we derive a closed form approximation to Eq

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:24.160180Z

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.

Observation 60cd5867-b427-40dc-8f91-d9807b5f0877 · outbound

This paper cites α x + z 2 + (1 − α) 1 − x − z 2 # − x 1 − x − z 2 ×.

Breaking coexistence: Zealotry vs. nonlinear social impact α x + z 2 + (1 − α) 1 − x − z 2 # − x 1 − x − z 2 ×

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:23.893660Z

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.

Observation 1e29e15e-a7ef-4c88-b7b9-af70bb04e56c · outbound

This paper cites (B3) The stabilities of the various fixed points can be deduced by looking an interactive plot of Eq.

Breaking coexistence: Zealotry vs. nonlinear social impact (B3) The stabilities of the various fixed points can be deduced by looking an interactive plot of Eq

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:23.530935Z

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.

Observation 17680ffd-1d76-442c-8cbe-66424e3ba3b5 · outbound

This paper cites (13) becomes dx dt = (1 − x − z)(x + z) × α(x + z) + (1 − α)(1 − x − z) − x(1 − x − z) × (1 − α)(x + z) +α(1 − x − z).

Breaking coexistence: Zealotry vs. nonlinear social impact (13) becomes dx dt = (1 − x − z)(x + z) × α(x + z) + (1 − α)(1 − x − z) − x(1 − x − z) × (1 − α)(x + z) +α(1 − x − z)

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:23.259462Z

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.

Observation 477f380d-d8f9-4bec-8097-8dfc4b03581b · outbound

This paper cites α x + 1 + δ 2 z + (1 − α) 1 − x − 1 + δ 2 z # − x 1 − x − 1 + δ 2 z ×.

Breaking coexistence: Zealotry vs. nonlinear social impact α x + 1 + δ 2 z + (1 − α) 1 − x − 1 + δ 2 z # − x 1 − x − 1 + δ 2 z ×

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:23.045880Z

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.

Observation ead4ce14-b268-4070-a525-d043eceae7b8 · outbound

This paper cites (B4) except with a nonlinear social impact function xq, dx dt = (1 − x − z)(x + z)q × α(x + z) + (1 − α)(1 − x − z) − x(1 − x − z)q × (1 − α)(x + z) +α(1 − x − z).

Breaking coexistence: Zealotry vs. nonlinear social impact (B4) except with a nonlinear social impact function xq, dx dt = (1 − x − z)(x + z)q × α(x + z) + (1 − α)(1 − x − z) − x(1 − x − z)q × (1 − α)(x + z) +α(1 − x − z)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:22.734190Z

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.

Observation 23cccefc-7d3f-4e8e-8334-f381090e6ab5 · outbound

This paper cites (21) become Σ − (1 − z) ≤∆ ≤ −Σ + (1 − z), −Σ ≤∆ ≤ Σ.

Breaking coexistence: Zealotry vs. nonlinear social impact (21) become Σ − (1 − z) ≤∆ ≤ −Σ + (1 − z), −Σ ≤∆ ≤ Σ

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:22.523154Z

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.

Observation c7da69ae-3d34-42bd-b3eb-b33ac6ecaba7 · outbound

This paper cites (21)] are identical to the conditions for balanced zealots [Eqs.

Breaking coexistence: Zealotry vs. nonlinear social impact (21)] are identical to the conditions for balanced zealots [Eqs

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:22.328078Z

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.

Observation 0a65ddd8-13dd-4933-ae0f-c6cb9c294e9d · outbound

This paper cites (21) are again the same as in the balanced and one-sided zealots cases, i.e.

Breaking coexistence: Zealotry vs. nonlinear social impact (21) are again the same as in the balanced and one-sided zealots cases, i.e

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:22.150013Z

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.

Observation 0dbe97c3-a512-4eda-9dec-73541b19617f · outbound

This paper cites (35) we form the Jacobian matrix evaluated at C+ [Eq.

Breaking coexistence: Zealotry vs. nonlinear social impact (35) we form the Jacobian matrix evaluated at C+ [Eq

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:21.927095Z

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.

Observation 82bc1cd9-279c-4dbb-9d63-e535fbd3d894 · outbound

This paper cites (37) that the consensus fixed point C+ is stable when q < 1 and unstable when q > 1.

Breaking coexistence: Zealotry vs. nonlinear social impact (37) that the consensus fixed point C+ is stable when q < 1 and unstable when q > 1

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:21.723445Z

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.

Observation 7dcea340-2bb5-4553-93f3-b04ea17808c4 · outbound

This paper cites (39) We broadly follow the steps in Ref.

Breaking coexistence: Zealotry vs. nonlinear social impact (39) We broadly follow the steps in Ref

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:21.530190Z

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.

Observation e6fb6500-25ea-475d-bde3-dbeff26aa3e0 · outbound

This paper cites Stochastic evolutionary game dynamics,.

Breaking coexistence: Zealotry vs. nonlinear social impact Stochastic evolutionary game dynamics,

Reference 33

Resolution: verified exact; raw_fallback, observed 2026-08-07T13:44:21.356777Z

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.

Pith citing papers

Observation f0ee5455-bcf5-472a-9ac9-75b7289d64ab · inbound

Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs cites this paper.

Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs Breaking coexistence: Zealotry vs. nonlinear social impact

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T11:55:53.395391Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.