The Clock-Space Geometry: A Multitime Architecture for Multi-dimensional Time
Mathine: Clock-Space Governance Geometry Machine
Link: https://doi.org/10.5281/zenodo.18361878 [1]
Multitime treats time as a structural property: systems evolve through multiple transition families whose rates and irreversibility cannot be collapsed into one scalar clock without losing governance-relevant semantics. This paper adds a geometric control plane: it maps Temporal State Machine (TSM) traces into an embedded “clock-space” where heterogeneous clocks become comparable, gateable, and auditable. (Zenodo)
The core object is an enriched TSM state x(e,p) = (w,b,a,c,r), making admissibility a and receipts r first-class, and using commit depth c to represent managed irreversibility. From this, the paper formalizes clock vectors, matrices, and tensors over entities and horizons (including TTO-compatible horizons), and defines embeddings that preserve Unknown states, tribunal constraints, and reliability. [1], [2] (Zenodo)
A key operational payoff is geometry-native gating: operators like distance-to-corridor and strict_score implement admissibility corridors, vetoes, overrides, and reject options without reducing everything to a single “time” variable. This dovetails with contract-first evaluation: corridors and reject options become explicit regime objects rather than post-hoc interpretations. [1], [3]
Finally, the evaluation protocol emphasizes stability, abstention quality, replayable receipts, and robustness under latency, drift, and regime change—so multitime governance can be monitored and controlled as a portable, checkable system artifact, not a narrative. This fits naturally into layered governance stacks (field → overfield → metaoverfield) where comparability and escalation need explicit semantics and auditable transitions. [1], [4], [5]
References
[1] R. Figurelli, “The Clock-Space Geometry: A Multitime Architecture for Multi-dimensional Time”. Zenodo, Jan. 24, 2026. https://doi.org/10.5281/zenodo.18361878
[2] R. Figurelli, “TTOkay for Coding Assistants in Regulated Pipelines”. Zenodo, Feb. 19, 2026. https://doi.org/10.5281/zenodo.18688855
[3] R. Figurelli, “Benchmarks-as-Contracts: A ReceiptBench Spec Template for Regimes and Closure”. Zenodo, Feb. 17, 2026. https://doi.org/10.5281/zenodo.18675035
[4] R. Figurelli, “Layered Field Collapse: Executable Collapse Signatures from Benchmarks to Metaoverfields”. Zenodo, Feb. 17, 2026. https://doi.org/10.5281/zenodo.18675054
[5] R. Figurelli, “Fields as the Contract Layer for AI/AGI/ASI: From Physical Fields to Large Signals Fields (LSFs) and Large Language Fields (LLFs) — Architecture, Governance, and Receipt-Based Closure”. Zenodo, Feb. 18, 2026. https://doi.org/10.5281/zenodo.18684034
Mathine — Evidence In, Trust Out 