⏰ hexa-time

HEXA-Time — n=6 time substrate · horology · clockwork · calendar · escapement (τ=4) · bell ratio · 6-cycle

temporal · escapement · oscillator · gear-train · campanology · calendar · 6-cycle · spec-first · MIT

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3-verb time substrate organized around the n=6 invariant lattice: HOROLOGY / CLOCKWORK / CALENDAR. Spec-first extraction from canon (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.

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.

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 canon@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

# 1. Install hexa-lang (gives you `hexa` + `hx` package manager)
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/dancinlab/hexa-lang/main/install.sh)"

# 2. Install hexa-time
hx install hexa-time

Run

hexa-time horology            # escapement / oscillator phase canonics (τ=4)  [SPEC]
hexa-time clockwork           # bell ratio / harmonic canonics                [SPEC]
hexa-time calendar            # calendar 6-cycle / time-geography             [SPEC]
hexa-time status              # 3-verb spec table + verdict + caveats
hexa-time selftest            # 3-verb spec sentinel sweep
hexa-time --version           # show version
hexa-time --help              # full usage

Verify

Spec-first closure (3/3) is attested by four .hexa verify scripts under verify/. Run the aggregate sweep:

hexa run verify/run_all.hexa     # exit 0 = all 4 scripts PASS

#	Script	What it checks
1	verify/spec_presence.hexa	3/3 verb spec docs (horology · clockwork · calendar) present at declared paths
2	verify/lattice_arithmetic.hexa	n=6 self-consistency (σ·φ = n·τ = J₂ = 24; 1/2 + 1/3 + 1/6 = 1) — aux only, per LATTICE_POLICY.md §1.3
3	verify/real_limits_anchor.hexa	LIMIT_BREAKTHROUGH.md anchors L1–L7 (c, atomic-clock stability, Heisenberg, SR/GR, leap-second, tropical year, Shannon) + NIST/BIPM/IERS/IAU sourcing
4	verify/closure_consistency.hexa	scoreboard cross-check (CLI SPEC_* decls = hexa.toml verbs_total = README badge = 3); standard artifacts present

• NIST (NIST-F2 caesium ~1e-16), BIPM (TAI/UTC), USNO, NPL, PTB, IERS use their own definitions (SI second via Cs-133 hyperfine, optical-lattice Yb/Sr ~1e-18, σ_y Allan-deviation). No hexa-time claim asserts these bodies fit n=6.
• Speed of light c (L1) and Heisenberg ΔE·Δt ≥ ℏ/2 (L3) are HARD walls — no verb output can exceed them. No FTL synchronisation claim allowed.
• Time travel is UNPROVEN. Closed timelike curves (CTCs) remain hypothetical (Gödel 1949, Tipler 1974, Thorne wormholes); no experimental evidence exists. Causality preservation is strict in this substrate.
• Planck time t_P ≈ 5.39 × 10⁻⁴⁴ s is the shortest physically meaningful interval; sub-Planck-time intervals carry no operational meaning.
• The 12-month / 24-hour / 4-quarter calendar is cultural-historical (Roman / Babylonian inheritance), NOT a physics derivation from n=6. Tropical year 365.2422 d (IAU 2015) is the actual physical anchor.

Repo layout

hexa-time/
├── README.md                          ← this file (public landing, 18-block format)
├── LICENSE                            ← MIT
├── AGENTS.tape                        ← governance + identity (.tape v1.2)
├── CLAUDE.md                          ← symlink → AGENTS.tape
├── CHANGELOG.md                       ← release notes per version
├── RELEASE_NOTES_v1.0.0.md            ← v1.0.0 release surface
├── CITATION.cff                       ← citation metadata
├── hexa.toml                          ← repo metadata (verbs_total, version)
├── install.hexa                       ← hx install entry point
├── BELL-CLOCKWORK.md                  ← clockwork verb deep-dive
├── HOROLOGY.md                        ← horology verb deep-dive
├── LATTICE_POLICY.md                  ← project-local lattice-as-tool standard
├── LIMIT_BREAKTHROUGH.md              ← L1–L7 real-physics anchors
├── IMPORTED_FROM_CANON.md             ← extraction provenance
├── TAPE-AUDIT.md                      ← .tape adoption audit ledger
├── cli/
│   └── hexa-time.hexa                 ← CLI dispatcher (spec-first placeholder)
├── horology/                          ← escapement / oscillator spec
├── clockwork/                         ← bell-ratio / gear-train spec
├── calendar/                          ← 6-cycle / time-geography spec
├── verify/                            ← 4 hexa verify scripts (run_all.hexa aggregator)
├── tests/                             ← regression scaffold
├── papers/                            ← supporting papers
├── state/                             ← runtime markers (gitignored)
└── docs/
    └── logo.svg                       ← README header glyph

License

MIT — see LICENSE file.

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