Pith Number

pith:I5YSCAHL

pith:2026:I5YSCAHLKGW3WVEISZPPI7RYZD

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Competitive Social Mobilization in Threshold Models of Collective Action

Bianca Y. S. Ishikawa, Jos\'e F. Fontanari

The stability of participation thresholds determines whether competing social movements end in one dominant consensus or complete fragmentation.

arxiv:2601.18682 v1 · 2026-01-26 · physics.soc-ph · nlin.AO

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Claims

C1strongest claim

the outcome of social competition depends critically on the stability of individual dispositions. In quenched environments where participation thresholds are fixed, increasing resistance initially allows a dominant movement to suppress its competitors; however, further resistance triggers a sudden collapse into total fragmentation... Conversely, in annealed environments where opinions are fluid, higher resistance paradoxically drives a winner-takes-all consensus.

C2weakest assumption

The model assumes movements are strictly mutually exclusive and that participation decisions follow simple threshold rules without overlapping interests or external influences, which may not hold in complex real-world settings.

C3one line summary

In competitive threshold models, fixed thresholds lead to fragmentation at high resistance while fluid thresholds produce winner-takes-all consensus, with discontinuous transitions in both cases.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Coleman, Introduction to Mathematical Sociology, Free Press Glen- coe, London, 1964 1964

[2] Gavrilets, Collective action problem in heterogeneous groups, Philos 2015 · doi:10.1098/rstb.2015.0016

[3] J.S. Coleman, J. James, The Equilibrium Size Distribu- tion of Freely-forming Groups, Sociometry 24 (1961) 36–45, https://doi.org/10.2307/2785927 1961 · doi:10.2307/2785927

[4] White, Chance Models of Systems of Casual Groups, Sociometry 25 (1962) 153–172, https://doi.org/10.2307/2785947 1962 · doi:10.2307/2785947

[5] Fontanari, Stochastic Simulations of Casual Groups, Mathematics 11 (2023) 2152, https://doi.org/10.3390/math11092152 2023 · doi:10.3390/math11092152

Receipt and verification

First computed	2026-05-18T02:45:05.866185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47712100eb51adbb5488965ef47e38c8ccd30b2a1885c7c786e1bcc7a0c8b76c

Aliases

arxiv: 2601.18682 · arxiv_version: 2601.18682v1 · doi: 10.48550/arxiv.2601.18682 · pith_short_12: I5YSCAHLKGW3 · pith_short_16: I5YSCAHLKGW3WVEI · pith_short_8: I5YSCAHL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I5YSCAHLKGW3WVEISZPPI7RYZD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 47712100eb51adbb5488965ef47e38c8ccd30b2a1885c7c786e1bcc7a0c8b76c

Canonical record JSON

{
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    "cross_cats_sorted": [
      "nlin.AO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2026-01-26T16:58:02Z",
    "title_canon_sha256": "e7a2d5261a9bf26915f5311468c5b33688fc574a133ff43214e6d67ec44c80e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.18682",
    "kind": "arxiv",
    "version": 1
  }
}