Causal-Cone Saturation in Sequential Causal Growth: Independence, Clock Suppression, and Record Erasure

A causal order fixes a conformal class and hence a maximal local cone, but it does not by itself force a massless gauge field to propagate on that cone. We formulate the difference as a saturation problem, and show first that it is real: within the regular local constitutive class, the structural hypotheses admit a one-parameter family of strictly subcausal photon cones, so the availability of a causal cone does not imply saturation We then give dynamical mechanisms that remove the freedom. At the level of order, positive finite-support classical sequential growth exponentially suppresses persistent graded sectors whenever the highest coupling has order at least two; and transitive percolation, which lies outside that class, suppresses the wide layers a 3+1 clock requires at rate exp(−Θ(ε⁻⁶)). For quasi-gradings we isolate the regularity the argument needs, and show that without it the conclusion is false. At the level of the photon record, a one-branch phase leaves a single cone-mismatch scalar, and an explicit five-state refresh process erases it once the cumulative mixing depth diverges. The microscopic photon and causal couplings need not become equal: the differential cone disappears because their common source is erased, and the conclusion survives any smooth equivariant coarse-graining rule. A second, non-mixing closure makes the mismatch sector quantum-null under a single unitary boost, with no appeal to decoherence. At the level of the photon record, a one-branch phase leaves a single cone-mismatch scalar, and an explicit five-state refresh process erases it once the cumulative mixing depth diverges. The microscopic photon and causal couplings need not become equal: the differential cone disappears because their common source is erased, and the conclusion survives any smooth equivariant coarse-graining rule. A second, non-mixing closure makes the mismatch sector quantum-null under a single unitary boost, with no appeal to decoherence.

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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.22050888
Primary Topic
Quantum Information and Cryptography
Type
preprint
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preprint

Causal-Cone Saturation in Sequential Causal Growth: Independence, Clock Suppression, and Record Erasure

Simone Agnese
Zenodo (CERN European Organization for Nuclear Research)
Quantum Information and Cryptography
preprint

Causal-Cone Saturation in Sequential Causal Growth: Independence, Clock Suppression, and Record Erasure

Simone Agnese
preprint en

Abstract

A causal order fixes a conformal class and hence a maximal local cone, but it does not by itself force a massless gauge field to propagate on that cone. We formulate the difference as a saturation problem, and show first that it is real: within the regular local constitutive class, the structural hypotheses admit a one-parameter family of strictly subcausal photon cones, so the availability of a causal cone does not imply saturation We then give dynamical mechanisms that remove the freedom. At the level of order, positive finite-support classical sequential growth exponentially suppresses persistent graded sectors whenever the highest coupling has order at least two; and transitive percolation, which lies outside that class, suppresses the wide layers a 3+1 clock requires at rate exp(−Θ(ε⁻⁶)). For quasi-gradings we isolate the regularity the argument needs, and show that without it the conclusion is false. At the level of the photon record, a one-branch phase leaves a single cone-mismatch scalar, and an explicit five-state refresh process erases it once the cumulative mixing depth diverges. The microscopic photon and causal couplings need not become equal: the differential cone disappears because their common source is erased, and the conclusion survives any smooth equivariant coarse-graining rule. A second, non-mixing closure makes the mismatch sector quantum-null under a single unitary boost, with no appeal to decoherence. At the level of the photon record, a one-branch phase leaves a single cone-mismatch scalar, and an explicit five-state refresh process erases it once the cumulative mixing depth diverges. The microscopic photon and causal couplings need not become equal: the differential cone disappears because their common source is erased, and the conclusion survives any smooth equivariant coarse-graining rule. A second, non-mixing closure makes the mismatch sector quantum-null under a single unitary boost, with no appeal to decoherence.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Quantum Information and Cryptography
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