HEXA-Time — n=6 time substrate · horology · clockwork · calendar · escapement (τ=4) · bell ratio · 6-cycle
License DOI Version Verbs Closure Lattice Family
temporal · escapement · oscillator · gear-train · campanology · calendar · 6-cycle · spec-first · MIT
3-verb time substrate organized around the n=6 invariant lattice: HOROLOGY / CLOCKWORK / CALENDAR. Spec-first extraction from
canon(commitc0f1f570) integrating escapement (τ=4 phase) canonics, bell-ratio harmonic canonics, and calendar 6-cycle / time- geography. Working.hexasimulators are TBD post-v1.0.
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)=4of 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)=24into 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.
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 tostatus/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 fromcanon@c0f1f570. Verb-specific empirical audits withinhexa-timeitself are deferred. - No cross-link dependencies. This repo is self-sufficient — runs from
any checkout root with
HEXA_TIME_ROOTset or auto-inferred.
# 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
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
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-timeclaim 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 ×ばつ 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.
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
MIT — see LICENSE file.
Provenance: extracted from
canon
@ commit c0f1f570 on 2026年05月06日.