The Neap Calendar — NpS v3.0.a0

I — Date Converter

—

Gregorian → Neap

Day

Month

Year

Neap → Gregorian

Day

Month

Year

Calendar Rules — NpS v3.0.a0

Epoch anchor1 Jan 2001 NpS = 1 Jan 2001 GgS

Pre-2001 datesProleptic — rules extend unchanged into the past

Year zeroExists (ISO 8601 / astronomical convention)

Standard year366 days · all long months = 31

Early neap year363 days · (y − 2004) mod 8 = 0, not great neap · Jan, Mar, May = 30

Late neap year363 days · (y − 2008) mod 8 = 0, not great neap · Aug, Oct, Dec = 30

Great neap year360 days · (y − 2004) mod 384 = 0 · all long months = 30

Short monthsFeb, Apr, Jun, Jul, Sep, Nov — always 30 days

Month pattern (std)31 30 31 30 31 30 · 30 31 30 31 30 31 (palindrome)

Base cycle8 years: Std Std Std EarlyNeap Std Std Std LateNeap

Supercycle384 years (symmetric) · mean year = 365.242188 days · ~155× better than Gregorian

II — Structural Symmetry & Astronomical Accuracy

I — Annual Structure · Radial Month Map

30 days (short)

31 days — early long (Jan, Mar, May)

31 days — late long (Aug, Oct, Dec)

31 days — GgS long (irregular)

NpS v3.0a (left) shows perfect bilateral symmetry across the June–July axis.
Gregorian (right) shows the irregular historical accumulation with no geometric symmetry.

II — Base Cycle · 8-Year Rhythm (2001–2040)

Standard (366d)

Early neap (363d)

Late neap (363d)

Great neap (360d)

GgS leap (366d)

NpS alternates early and late neap years every 4 years with perfect regularity.
Gregorian leap years follow a 4-year rhythm interrupted at century years (not visible at this scale).

III — Month Length Heatmap · All Year Types

Each row shows month lengths for one year type. NpS lengths vary only in the six long months.
The palindromic structure is visible in standard years: the pattern reads identically forwards and backwards.

IV — Supercycle Timeline · 2001–2810

Early neap

Late neap

Great neap (supercycle correction)

GgS century skip

NpS neap events occur every 4 years with mechanical regularity. Great neap rule: (y − 2004) mod 384 = 0.
GgS century skips (2100, 2200, 2300...) shown above the axis.

V — NpS Error from Tropical Year (min/yr) · 1-Year Bins · 1993–2392

Great neap year (360d) — large negative spike (~−7549 min/yr)

Neap year (363d) — moderate negative spike (~−3229 min/yr)

Standard year (366d) — positive spike (~+1091 min/yr)

Each spike shows one year's error from the tropical year (365.24219 days) in minutes. Spikes rise from the zero baseline.
The repeating 8-year rhythm of neap corrections is clearly visible. The single great neap spike at 2004 (and 2388) provides the long-run supercycle correction.
Long-run mean across the 384-year supercycle: ~−0.003 min/yr.

VI — NpS / GgS Calendar Drift · Days Offset at 1 Jan · 1986–2026

NpS ahead of GgS (positive drift)

NpS behind GgS (negative drift)

Neap or great neap year — causes step in drift

Drift = how many days the NpS day-count leads (+) or lags (−) the GgS day-count at 1 January of each year.
Epoch anchor 2001 = 0 by definition. Before 2001 the sawtooth runs +1 → +3 → reset at each neap year. After 2004 (great neap) the pattern shifts to −3 → −1 → reset.

III — Solstices & Equinoxes — GMT

From To Times in GMT (UTC) · NpS dates shown in italic below each

Year	March Equinox	June Solstice	September Equinox	December Solstice

Current year

Neap year (363d)

Great neap year (360d)

Source: AstroPixels · astropixels.com/ephemeris/soleq2001.html

Data for 2001–2050 from AstroPixels (Fred Espenak). Data for 2000 and 2051–2100 extrapolated from the same source. Future dates (after March 2026) are predicted astronomical values.

IV — Formal Specification — NpS v3.0a

This specification covers NpS (Neap Style) and RNpS (Radical Neap Style). The canonical sub-variant is v3.0.a0. All rules apply to both variants unless explicitly overridden.

Part I — Shared Foundations

1.1 Epoch

The epoch of the Neap Calendar is defined as:

1 January 2001 NpS = 1 January 2001 GgS
A Monday. The two calendars are anchored on the same real day. Year numbers count identically from this anchor, though the calendars diverge in their accumulation of days thereafter.

2001 is a standard year in all v3.0a sub-variants.

1.2 Month Structure

The year contains twelve months bearing the same names and sequence as the Gregorian calendar. Months fall into three classes:

Class	Months	Days
Short months	February, April, June, July, September, November	Always 30
Early long months	January, March, May	31 in standard and late neap years; 30 in early neap and great neap years
Late long months	August, October, December	31 in standard and early neap years; 30 in late neap and great neap years

The standard year month pattern is a palindrome:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 31 30 31 30 31 30 30 31 30 31 30 31

The axis of symmetry falls between June and July. Ten of twelve months match Gregorian length in standard years; only February (30 vs 28/29) and July (30 vs 31) differ. The 31st of each long month, when observed, is designated a Neap Day.

1.3 Year Types and Intercalation

Four year types are defined, distinguished by which Neap Days are observed or omitted:

Type	Days	Jan Mar May	Aug Oct Dec	Rule
Standard	366	31	31	Default — all other years
Early neap	363	30	31	(y − 2004) mod 8 = 0, not great neap
Late neap	363	31	30	(y − 2008) mod 8 = 0, not great neap
Great neap	360	30	30	(y − 2004) mod 384 = 0

The base 8-year cycle has mean year (6×366 + 363 + 363) / 8 = 365.25 days, requiring downward supercycle correction.

1.4 Supercycle and Great Neap Year

The great neap year (360 days) replaces one neap year every 384 years. Three sub-variants differ only in which neap year type it replaces:

v3.0.a0 (canonical) — Great neap replaces an early neap year.
Rule: (y − 2004) mod 384 = 0
Sequence: … 852, 1236, 1620, 2004, 2388, 2772, …
Days removed (vs early neap): Aug 31, Oct 31, Dec 31 — maximally distant from the March equinox.

v3.0.a1 — Great neap replaces a late neap year. Rule: (y − 2008) mod 384 = 0.
Sequence: … 856, 1240, 1624, 2008, 2392, 2776, …

v3.0.a2 — Great neap alternates between early and late neap positions every 384 years.

Mean year verification (v3.0.a0, 384-year supercycle):

288 × 366 = 105,408 days 47 × 363 = 17,061 days 48 × 363 = 17,424 days 1 × 360 = 360 days ───────────────────────── 140,253 ÷ 384 = 365.242188 days

Error against the 1000-year mean tropical year (365.24219 days): ~0.000002 days/year — approximately 155× more accurate than the Gregorian calendar. This mean year holds symmetrically in both temporal directions from the great neap anchor year 2004.

1.5 Date Notation

Neap Calendar dates are suffixed NpS or RNpS. Gregorian dates are suffixed GgS (Gregorian Style). In cross-calendar contexts the suffix is mandatory. Example: 7 March 2026 GgS ≠ 7 March 2026 NpS.

1.6 Proleptic Extension

All NpS and RNpS rules apply for all integer year values including years before the epoch (2001) and year 0. The epoch anchor 1 January 2001 NpS = 1 January 2001 GgS is preserved exactly. Pre-2001 NpS dates are proleptic — they represent what the calendar would have assigned, not any historical usage.

Year zero exists (ISO 8601 / astronomical year numbering). Year 0 = 1 BC, year −1 = 2 BC, etc.

The offset D(y), defined as the number of days by which 1 January y NpS falls after 1 January y GgS, is computed as:

D(2001) = 0 (epoch anchor)
D(y) = D(y+1) + GgS_length(y) − NpS_length(y) for y < 2001

In the base cycle the drift follows a sawtooth pattern with period 4, resetting to zero at years satisfying (y − 2001) mod 4 = 0: … 1989, 1993, 1997, 2001, … Maximum drift between resets is 3 days — far smaller than the 13-day Julian/Gregorian discrepancy at 1582. The Gregorian century skips (1700, 1800, 1900, 2100…) shift the drift pattern by +1 day for all years prior to each skip, and must be accounted for in precise conversion outside 1901–2099.

Part II — Neap Style (NpS)

2.1 Week Structure

NpS retains the unmodified seven-day week with Sunday as the first day. The week is continuous and unbroken across the epoch boundary. Because no NpS year length (366, 363, or 360 days) is divisible by seven, the day-of-week on which any date falls varies from year to year. NpS is not a perpetual calendar.

2.2 Theological Compatibility

Retention of the seven-day week renders NpS fully compatible with Abrahamic religious observance. The Sabbath (Saturday in Judaism, Sunday in Christianity, Friday Jumu'ah in Islam) retains its established position within an unchanged weekly cycle. No modification to religious law or practice is required for NpS adoption.

Part III — Radical Neap Style (RNpS)

3.1 Week Structure

The RNpS week has six days: Tuesday · Wednesday · Thursday · Friday · Saturday · Sunday. Monday does not exist. The week runs Tuesday through Sunday continuously.

3.2 Neapday

In RNpS the 31st of each long month — when observed — is designated Neapday: an intercalary day belonging to no week, falling between the Sunday closing one week and the Tuesday opening the next. Standard years have six Neapdays; early and late neap years have three; great neap years have none.

3.3 The Perpetual Calendar Property

The combination of the six-day week and Neapdays makes RNpS perfectly perpetual. For every year type:

Standard year: 366 total − 6 Neapdays = 360 week-cycle days = 60 complete 6-day weeks ✓
Early neap year: 363 total − 3 Neapdays = 360 week-cycle days = 60 complete 6-day weeks ✓
Late neap year: 363 total − 3 Neapdays = 360 week-cycle days = 60 complete 6-day weeks ✓
Great neap year: 360 total − 0 Neapdays = 360 week-cycle days = 60 complete 6-day weeks ✓

Every year begins on the same weekday. Every calendar date falls on the same weekday in every year, without exception. The perpetual property holds in both temporal directions across the proleptic extension.

3.4 Theological Incompatibility

The abolition of Monday constitutes a fundamental departure from the seven-day week held sacred by Judaism, Christianity, and Islam. Historical precedent — including the French Revolutionary decimal calendar (1793) and Soviet five- and six-day weeks (1929–1940) — demonstrates that attempts to replace the seven-day week face profound and sustained popular resistance. RNpS should be understood as a system of theoretical and mathematical interest rather than a practical reform proposal.

Part IV — Comparative Summary

4.1 Property Comparison

Property	GgS (Gregorian)	NpS v3.0a	RNpS v3.0a
Epoch	1 Jan 1 AD	1 Jan 2001 (= GgS)	1 Jan 2001 (= GgS)
Base year	365 days	366 days	366 days
Correction year A	366 days (leap)	363 days (early neap)	363 days (early neap)
Correction year B	—	363 days (late neap)	363 days (late neap)
Supercycle correction	365 days (skip)	360 days (great neap)	360 days (great neap)
Supercycle	400 years	384 years (symmetric)	384 years (symmetric)
Mean year	365.2425 days	365.242188 days	365.242188 days
Week	7 days	7 days	6 days (no Monday)
Intercalary days	Feb 29	None	Neapday (0/3/6 per year)
Perpetual?	No	No	Yes — all year types
Abrahamic compatible?	Yes	Yes	No
Month pattern (std)	Irregular	Palindrome	Palindrome
Gregorian months matching	—	10 of 12	10 of 12

Part V — Glossary

Selected Terms

Term	Definition
GgS	Gregorian Style — dates in the proleptic Gregorian calendar.
NpS	Neap Style — the moderate variant retaining the seven-day week.
RNpS	Radical Neap Style — the reformed variant with a six-day week.
Standard year	366 days. All long months have 31 days. The default year type.
Early neap year	363 days. Every 8th year from 2004 (unless great neap). Jan, Mar, May = 30 days.
Late neap year	363 days. Every 8th year from 2008 (unless great neap). Aug, Oct, Dec = 30 days.
Great neap year	360 days. Every 384 years: … 1620, 2004, 2388, 2772 … All long months = 30.
Neap Day	The 31st of a long month when in effect. In RNpS becomes an intercalary Neapday.
Neapday (RNpS)	An intercalary day belonging to no week. Six per standard year; three per neap year; zero per great neap year.
Base cycle	8-year pattern: Std Std Std EarlyNeap Std Std Std LateNeap. Mean year 365.25 days.
Supercycle	384-year period anchored on 2004. Rule (y − 2004) mod 384 = 0 applies universally with no floors or ceilings.
Tropical year	~365.24219 days (1000-year mean). The astronomical accuracy target for both calendars.
Proleptic dates	Pre-2001 NpS dates derived by applying the rules backwards from the epoch anchor.

V — Version Index

v3.0a

Universal Proleptic Extension Current Great neap rule simplified to (y − 2004) mod 384 = 0 — universal, no floor, no ceiling. 2004 is the first great neap year. Calendar extends symmetrically into the past with mean year 365.242188 days in both temporal directions. Year 0 exists (ISO 8601).

v2.1a

384-Year Supercycle Recalibration Superseded Single change from v2.0: supercycle reduced from 400 to 384 years. Mean year 365.242188 days. Error ~0.000002 days/yr — ~155× more accurate than Gregorian. First great neap: 2388 (v2.1.a0).

v2.0

Alternating Neap Base Cycle & Great Neap Superseded Abolishes undifferentiated neap year. Introduces early neap (363d, every 8 yrs from 2004) and late neap (363d, every 8 yrs from 2008) as base cycle events. Introduces great neap (360d) as 400-year supercycle correction. Three sub-variants. Mean year 365.2425 days.

v1.2a

Palindromic Month Structure & Half-Neap Subtypes Superseded Retires even/odd month numbering. Introduces short / early-long / late-long month classification. Palindromic standard year. Short early and short late year subtypes alternating. 400-year supercycle.

v1.1a

Half-Neap 400-Year Supercycle Superseded Retires double neap. Introduces undifferentiated half-neap year (363 days). Feb, Jun, Oct retain 31 days in half-neap years. RNpS fully perpetual. 400-year supercycle.

v1.0

Initial Release Superseded Defines NpS and RNpS. Even/odd month structure. Standard (366d), neap (360d), double neap (354d). 800-year supercycle. RNpS has one perpetual exception per 800 years.

Version	Supercycle	Min. Year	Mean Year	Error (d/yr)	RNpS Perpetual
v1.0	800 years	354 days	365.2425	+0.00031	No (800yr exc.)
v1.1a	400 years	360 days	365.2425	+0.00031	Yes
v1.2a	400 years	360 days	365.2425	+0.00031	Yes
v2.0	400 years	360 days	365.2425	+0.00031	Yes
v2.1a	384 years	360 days	365.242188	~0.000002	Yes
v3.0a ★	384 yrs (±)	360 days	365.242188	~0.000002	Yes (both dirs)
GgS (ref)	400 years	365 days	365.2425	+0.00031	N/A

Error measured against 1000-year mean tropical year of 365.24219 days.