Recognising Before Reacting: Temporal Signatures of Transactional Games

We formalise a source-verified corpus of seven transactional games - six classical Berne games from Games People Play plus one contemporary corpus scenario - as finite-trace LTL properties over Karpman-projected role traces. The paper introduces the antithesis window W = t_red - t_obs as the temporal invariant separating reactive (W>0), knife-edge (W=0), pre-committed (W<0), and unresolved (W=undefined) regimes, and instantiates each regime with a corpus witness. A catalogue of eight agent-property temporal formulae is classified in the Safety / Cosafety / Liveness / Coliveness intersection algebra of Bragetti-Italiano (Zenodo 10.5281/zenodo.21099448), together with the minimum verdict-alphabet cardinality required for prefix monitoring in each cell. An optional refinement-confirmation certification layer (Bragetti, Zenodo 10.5281/zenodo.22028019) is documented for the FG-persistence entries. Core results: prop:under (role-level under-determination), prop:karpman-noninj (Karpman non-injectivity), prop:sigma-insufficient (permutation classification refutation), prop:s3 (S_3 switch group), thm:t2 (architecture-side information loss). --- SCOPE AND STATUS. This is a preprint. It has not been peer reviewed and is not under journal acceptance.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-21
DOI
https://doi.org/10.5281/zenodo.22050701
Primary Topic
Logic, programming, and type systems
Type
preprint
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preprint

Recognising Before Reacting: Temporal Signatures of Transactional Games

Giuseppe Francesco Italiano, Davide Bragetti
Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
preprint

Recognising Before Reacting: Temporal Signatures of Transactional Games

Giuseppe Francesco Italiano, Davide Bragetti
preprint en

Abstract

We formalise a source-verified corpus of seven transactional games - six classical Berne games from Games People Play plus one contemporary corpus scenario - as finite-trace LTL properties over Karpman-projected role traces. The paper introduces the antithesis window W = t_red - t_obs as the temporal invariant separating reactive (W>0), knife-edge (W=0), pre-committed (W<0), and unresolved (W=undefined) regimes, and instantiates each regime with a corpus witness. A catalogue of eight agent-property temporal formulae is classified in the Safety / Cosafety / Liveness / Coliveness intersection algebra of Bragetti-Italiano (Zenodo 10.5281/zenodo.21099448), together with the minimum verdict-alphabet cardinality required for prefix monitoring in each cell. An optional refinement-confirmation certification layer (Bragetti, Zenodo 10.5281/zenodo.22028019) is documented for the FG-persistence entries. Core results: prop:under (role-level under-determination), prop:karpman-noninj (Karpman non-injectivity), prop:sigma-insufficient (permutation classification refutation), prop:s3 (S_3 switch group), thm:t2 (architecture-side information loss). --- SCOPE AND STATUS. This is a preprint. It has not been peer reviewed and is not under journal acceptance.

Zenodo (CERN European Organization for Nuclear Research)
Libera Università Internazionale degli Studi Sociali Guido Carli (IT)
Peace, Justice and strong institutions
Logic, programming, and type systems
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