Forced Coincidence and Its Boundary in Finite Condition Structures
Abstract
Accounts of organizational dissolution explain survivor homogenization, temporally concentrated exit, and fragmentation into cohesive subgroups in different vocabularies. Their recurrence is the fact to be explained. A finite condition structure with a minimal dynamic extension generates all three, each in its own regime, with no actor responding to another; which conclusions survive when the restrictions defining those regimes are relaxed is then determined. With two requirement masks the union class is the only mediator between the pure types and the signature with the largest closed neighbourhood, and under positive endpoint loads it is also the unique maximizer of deficient load, so the independent derivations of fragmentation and homogenization both concern that class. With more than two masks the three roles need not coincide. Forced coincidence admits an exact characterization for every number of masks: it holds if and only if the requirement-derived join lies in the realized family and separates the endpoints. The proportion of family-pair instances meeting this condition vanishes under a uniform counting measure as the number of masks increases, and, at one actor per signature, an edge density above a stated bound excludes it. A common substrate does not make the mechanisms identical: selective attrition can hold while correlated collapse fails, and a change in exit dependence can change the population outcome while every actor's marginal lifetime law is unchanged.
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BibTeX
@misc{hirota2026forced,
title = {{Forced Coincidence and Its Boundary in Finite Condition Structures}},
author = {Daisuke Hirota},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15349},
eprint = {2609.15349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15349},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Forced Coincidence and Its Boundary in Finite Condition Structures
AU - Daisuke Hirota
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15349
UR - https://arxiv.org/abs/2609.15349
AB - Accounts of organizational dissolution explain survivor homogenization, temporally concentrated exit, and fragmentation into cohesive subgroups in different vocabularies. Their recurrence is the fact to be explained. A finite condition structure with a minimal dynamic extension generates all three, each in its own regime, with no actor responding to another; which conclusions survive when the restrictions defining those regimes are relaxed is then determined. With two requirement masks the union class is the only mediator between the pure types and the signature with the largest closed neighbourhood, and under positive endpoint loads it is also the unique maximizer of deficient load, so the independent derivations of fragmentation and homogenization both concern that class. With more than two masks the three roles need not coincide. Forced coincidence admits an exact characterization for every number of masks: it holds if and only if the requirement-derived join lies in the realized family and separates the endpoints. The proportion of family-pair instances meeting this condition vanishes under a uniform counting measure as the number of masks increases, and, at one actor per signature, an edge density above a stated bound excludes it. A common substrate does not make the mechanisms identical: selective attrition can hold while correlated collapse fails, and a change in exit dependence can change the population outcome while every actor's marginal lifetime law is unchanged.
ER -