⏰ hexa-time — n=6 time substrate (HEXA family)

3-verb time substrate organized around the n=6 invariant lattice: HOROLOGY / CLOCKWORK / CALENDAR. Spec-first extraction from n6-architecture (commit c0f1f570) integrating escapement (τ=4 phase) canonics, bell-ratio harmonic canonics, and calendar 6-cycle / time- geography. Working .hexa simulators are TBD post-v1.0.

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Why

hexa-time is the n=6 time substrate. It composes three sister verbs into one coherent time module:

• escapement (τ=4 phase) — the divisor-count invariant τ(6)=4 of the n=6 lattice maps onto the four-phase escapement cycle that is the canonical oscillator regulator across mechanical, quartz, and atomic horology.
• bell ratio — bell-clockwork harmonic canonics encode the ratio family that drives both campanology and the gear-train transmission ratios used in striking clocks.
• calendar 6-cycle — calendar-time-geography composes the divisor lattice σ(6)=12, τ(6)=4, φ(6)=2, J₂(6)=24 into an atlas of calendar systems (12-month / 4-week-quarter / 2-equinox / 24-hour).

Together these three verbs form one time substrate where measurement (horology), transmission (clockwork), and indexing (calendar) compose under a single n=6 invariant.

Verbs

Verb	Status	n=6 lattice	Spec file
horology	SPEC v1.0.0	τ(6)=4 phase	horology/horology.md
clockwork	SPEC v1.0.0	bell ratio canonics	clockwork/bell-clockwork.md
calendar	SPEC v1.0.0	6-cycle geometry	calendar/calendar-time-geography.md

Verdict: SPEC_FIRST (0/3 verbs empirically wired; 3/3 specs imported verbatim from n6-architecture).

Status

3-verb 시간 substrate. spec-first (working .hexa CLI TBD). escapement (τ=4 phase) + bell ratio + calendar 6-cycle integration.

• v1.0.0 ships spec documents only. The CLI placeholder (cli/hexa-time.hexa) routes to status / selftest / per-verb spec-head printers; full empirical simulators (escapement ODE, bell-ratio audit, calendar generator) are deferred to post-v1.0 cycles.
• n=6 invariant lattice (σ(6)=12, τ(6)=4, φ(6)=2, J₂(6)=24) is inherited from n6-architecture@c0f1f570. Verb-specific empirical audits within hexa-time itself are deferred.
• No cross-link dependencies. This repo is self-sufficient — runs from any checkout root with HEXA_TIME_ROOT set or auto-inferred.

Install

Via hx (when registered)

hx install hexa-time          # global, pulls latest from registry
hexa-time --version           # → 1.0.0

Via git clone (works today)

git clone https://github.com/need-singularity/hexa-time.git ~/.hexa-time
export HEXA_TIME_ROOT=~/.hexa-time
export PATH="$HEXA_TIME_ROOT/cli:$PATH"

# Run any subcommand:
hexa run $HEXA_TIME_ROOT/cli/hexa-time.hexa selftest
hexa run $HEXA_TIME_ROOT/cli/hexa-time.hexa status
hexa run $HEXA_TIME_ROOT/cli/hexa-time.hexa horology

License

MIT — see LICENSE.

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Provenance: extracted from n6-architecture @ commit c0f1f570 on 2026-05-06.