Executive Summary

Definitions (informal):

D(t) = lambda_Spica − lambda_AE(t), i.e., how many degrees east of the autumnal equinox the star Spica lies in year t.
Precession: D increases by about 1 deg every 71.6 years.
Delta (Δ) = Sun–Moon elongation at the first visible crescent that begins 1 Tishri (typical 11–14 deg).
delta (δ) = how many degrees (≈ days) after the autumnal equinox Rosh Hashanah falls in a given year.
Delta_N = days after the vernal equinox when 1 Nisan begins.

Geometry on 1 Tishri (“Spica window”):

Requirement: Sun west of Spica; crescent Moon east of Spica.
In degrees: D(t) − Delta ≤ δ < D(t).

Link between Nisan and Tishri:

Six lunations ≈ 177.18 d; VE→AE ≈ 186.39 d; therefore
delta ≈ Delta_N − 9.2 deg.

Spica‑anchored feasibility condition (with a lateness cap δ ≤ δ_max):

Hard‑stop inequality: D(t) ≤ Delta + δ_max.

Working constant today: D(2025) ≈ 24.2 deg (± about 1 deg).

Hard‑stop years (future), using the one‑line formula below:

Ancient/observational (allow 1 Nisan as late as one lunation after VE ⇒ δ_max ≈ 20.3 deg):
• If Delta = 12 deg: hard stop ≈ AD 2605.
• If Delta = 14 deg: hard stop ≈ AD 2748.
Modern fixed Hebrew calendar (today: 1 Nisan up to ~21–22 d after VE ⇒ δ_max ≈ 11.8–12.8 deg):
• If Delta = 12 deg: hard stop ≈ AD 1996–2068.
• If Delta = 14 deg: hard stop ≈ AD 2139–2211.

“Constellation‑only” outer bound (ignore Spica; require only “Sun in Virgo by RH”): mid‑4th to early‑5th millennium AD (the practical Spica limit ends things centuries earlier).

First‑failure (boundary) lens: the September equinox point enters Leo around AD 2439; this only affects very early RH dates in a given year and does not control the hard stop.

Plain-English takeaway (See Footnote)

When we say “Delta = 12 deg ⇒ hard stop ≈ AD 1996–2068”, we mean:

If you require a physically plausible first-sighting crescent (Delta ≈ 12 deg) and you use the modern fixed (Metonic) lateness available today (δ_max ≈ 11.8–12.8 deg), then the Spica-anchored Rev 12 configuration on Tishri 1 is already impossible if the true δ_max is on the tight side (1996), or it will remain barely possible for just a few more decades if δ_max is on the loose side (up to ~2068).

Footnotes:

Footnote 1:
“The Modern fixed Hebrew calendar”
The modern Hebrew calendar uses 235 lunations every 19 years (the Metonic arrangement) so months repeat on a 19-year pattern, and it applies postponement rules (dechiyot) that shift the start of months to avoid awkward weekday/festival placements. Those rules remove the direct, year-by-year dependence on actual crescent sightings.

Because of the 19-year locking and the postponement rules, Nisan 1 in the fixed calendar can empirically fall as late as about 21–22 days after the vernal equinox in the present era. That is the source of the δ_max ≈ 11.8…12.8 deg values used in the “Modern fixed (today)” lines (recall δ ≈ ΔN − 9.2 deg).

The fixed calendar drifts slowly relative to the tropical year (the 19-year average is slightly longer than the tropical year), so this lateness bound will grow slowly over centuries (roughly ~1 day per ~216 years). That produces the long-term shift we noted earlier (≈72 years per degree of D).

Footnote 2.
“If Delta = 12 deg ⇒ hard stop ≈ AD 1996–2068” means in the modern fixed (Metonic 19-year) calendar case.

What the line means (step by step)

Set-up.

We work with the fixed Hebrew calendar (19-year Metonic cycle + postponements).
In this system, the latest observed in the current era is Nisan 1 ≈ 21–22 days after the vernal equinox.
Using the identity delta ≈ Delta_N − 9.2 deg, this gives a lateness budget of
δ_max ≈ 11.8…12.8 deg (21–22 − 9.2).
We adopt Delta = 12 deg as a typical first-sighting crescent requirement for the Rev 12 geometry on Tishri 1.
Let D(2025) = 24.2 deg (Spica east of the autumnal equinox) and precession = 71.6 yr/deg.

Hard-stop condition.
Feasibility requires D(t) ≤ D* where D* = Delta + δ_max.
With Delta = 12 deg and δ_max = 11.8…12.8 deg, we get:

Lower end: D* = 12 + 11.8 = 23.8 deg
Latest year ≈ 2025 + (23.8 − 24.2) × 71.6 ≈ AD 1996.
Meaning: under the tighter (21-day) modern lateness, the window closed already (hard stop in the past).
Upper end: D* = 12 + 12.8 = 24.8 deg
Latest year ≈ 2025 + (24.8 − 24.2) × 71.6 ≈ AD 2068.
Meaning: under the looser (22-day) modern lateness, the window remains open until the early 2060s.

Therefore: with Delta fixed at 12 deg, the hard stop is a range because the modern lateness budget has a small empirical uncertainty (δ_max = 11.8–12.8 deg):
AD 1996 (tight end) to AD 2068 (loose end).

Why it’s a range (and what can shift it)

δ_max uncertainty (dominant here): whether you take 21 or 22 days for the latest Nisan 1 in the present era → δ_max = 11.8 vs 12.8 deg → a 0.9–1.0 deg swing, i.e., ~65–72 years.
D(2025) rounding: if you prefer D(2025) = 24.0 or 24.4 deg, the dates shift by ±~72 years.
Different Delta: choosing Delta = 11 or 13–14 deg moves the stop by ±1–2 deg × 71.6 yr/deg (see quick table below).

Quick sensitivity (modern fixed, δ_max = 11.8…12.8 deg)

Delta (deg)	D* (deg)	Hard stop (approx)
11	22.8…23.8	AD 1925–1996
12	23.8…24.8	AD 1996–2068
14	25.8…26.8	AD 2139–2211

(All with D(2025)=24.2 deg; 1 deg ≈ 71.6 yr.)

One more nuance (why drift won’t “save” it)

The fixed calendar drifts later against the tropical year by ~1 day per ~216 years, so δ_max will creep upward ~1 deg per ~216 years. But D(t) (Spica vs equinox) grows faster: 1 deg per 71.6 years. So over centuries, D(t) outruns any gain in δ_max—the window still closes.

End of Footnotes.

Why Spica Is the Right Anchor (Astronomy + Theology)

Astronomy:

Spica (alpha Virginis) is Virgo’s brightest star and lies about 2 deg from the ecliptic, so the Moon/planets pass it closely.
A bright, near‑ecliptic marker turns “Moon under the Woman’s feet; Sun clothing her” into a clean test: enforce “Moon east of Spica; Sun still west of Spica” at the first crescent. This yields the simple window D − Delta ≤ δ < D.

Theology:

“Seed” promise: Gen 3:15; the NT identifies the Seed as Christ (Gal 3:16).
“Grain of wheat”: John 12:24 (Christ’s death/resurrection fruitfulness).
“Under his feet”: Ps 8:6; Ps 110:1; 1 Cor 15:27; Heb 2:8; Rom 16:20; Luke 10:19.
Spica literally means “ear (spike) of wheat.” If Virgo figures Mary/Israel, the Seed borne is Christ; reading “moon under her feet” as “under the Seed (Spica)” aligns the sky‑geometry with the Bible’s under‑foot dominion motif. Using Spica as the boundary between “below” and “above” in Virgo is therefore both natural and testable.

**Rev 12 template on Rosh Hashanah, 3 BC.** The thin crescent Moon appears under Spica (α Virginis) in the figure of Virgo, while Jupiter lies adjacent to Regulus (α Leonis) in Leo. The alignment matches the traditional “woman clothed with the sun, moon under her feet” motif used for Rev. 12 studies; Regulus/Jupiter historically carry royal associations (Regulus = “little king”; Jupiter = planet of kings).

Definitions, Constants, and One‑Line Relations (plain text)

D(t) = lambda_Spica − lambda_AE(t).
Today: D(2025) ≈ 24.2 deg (± ~1 deg).
Precession: 1 deg ≈ 71.6 years (D grows into the future; decreases into the past).
Crescent elongation Delta (Δ): typical first‑visibility threshold ≈ 12 deg; generous allowance ≈ 14 deg (see “Why 12 and 14 deg?” below).
Nisan → Tishri offset: delta ≈ Delta_N − 9.2 deg
(since VE→AE ≈ 186.39 d and 6 lunations ≈ 177.18 d).
Spica window (must be non‑empty): D − Delta ≤ δ < D with 0 ≤ δ ≤ δ_max ⇒ feasibility iff D ≤ Delta + δ_max.

Hard‑stop year (future):
Hard_stop_year ≈ 2025 + ( (Delta + δ_max) − D(2025) ) * 71.6.

Earliest‑feasible year (past):
Earliest_year ≈ 2025 − ( D(2025) − δ_min ) * 71.6,
where δ_min = Delta_N,min − 9.2 deg (the earliest Tishri allowed by your Nisan rule).

Sensitivity: every ±1 deg in D(2025), or in δ_max/δ_min via calendar assumptions, shifts dates by about ±72 years.

Calendrical Regimes (how δ_max and δ_min are set)

Ancient / observational (Babylonian; Sanhedrin):

Working rule: 1 Nisan after the vernal equinox; if the equinox would be on/after 16 Nisan then intercalate. Agriculture (barley/fruit) can also force intercalation even if the equinox is earlier.
Latest 1 Nisan after VE: about one lunation ≈ 29.5 d ⇒ δ_max ≈ 29.5 − 9.2 = 20.3 deg.
Earliest 1 Nisan relative to VE:
• Strict Babylonian: 1 Nisan never before VE ⇒ Delta_N,min = 0 d ⇒ δ_min = −9.2 deg.
• Second‑Temple/Sanhedrin (Passover after VE): allow 1 Nisan up to about 14 d before VE so that 14 Nisan (evening) is after VE ⇒ Delta_N,min ≈ −14 d ⇒ δ_min ≈ −23.2 deg.

Modern fixed Hebrew calendar (today):

No annual equinox check; 19‑year cycle with postponements.
Observed maximum: 1 Nisan as late as ~21–22 d after VE ⇒ δ_max ≈ 11.8–12.8 deg.
Earliest (illustrative for sensitivity): today about 8–9 d before VE ⇒ δ_min ≈ −17.2 to −18.2 deg (not historically applicable to antiquity; shown only to gauge sensitivity).

Hard‑Stop Dates (future), Spica‑anchored

Assume D(2025) = 24.2 deg and precession 71.6 yr/deg.

Ancient / observational:
• Delta = 12 deg ⇒ D* = 12 + 20.3 = 32.3 deg ⇒ Hard stop ≈ AD 2605.
• Delta = 14 deg ⇒ D* = 14 + 20.3 = 34.3 deg ⇒ Hard stop ≈ AD 2748.
Modern fixed (today):
• Delta = 12 deg ⇒ D* = 12 + (11.8…12.8) = 23.8…24.8 deg ⇒ Hard stop ≈ AD 1996–2068.
• Delta = 14 deg ⇒ D* = 14 + (11.8…12.8) = 25.8…26.8 deg ⇒ Hard stop ≈ AD 2139–2211.

First‑failure (boundary only): September equinox enters Leo ≈ AD 2439 (affects only very early RH within a year).
Constellation‑only outer bound (ignore Spica): ≈ AD 3355 (modern δ_max) or ≈ AD 3893 (ancient δ_max).
In practice, Spica ends feasibility centuries earlier (see values above).

Earliest Feasible Epochs (past), Spica‑anchored

We now run the same constraints backward in time. Because D decreases into the past, the lower inequality controls feasibility: you need D(t) > δ_min.

Use: Earliest_year ≈ 2025 − ( D(2025) − δ_min ) * 71.6, with D(2025) = 24.2 deg.

Strict Babylonian (1 Nisan never before VE):
δ_min = −9.2 deg ⇒ Earliest ≈ 2025 − (24.2 − (−9.2)) * 71.6
= 2025 − (33.4 * 71.6) ≈ 2025 − 2392 ≈ 367 BC.
Second‑Temple/Sanhedrin (permit 1 Nisan ≈ 14 d before VE; Passover after VE):
δ_min = −23.2 deg ⇒ Earliest ≈ 2025 − (24.2 − (−23.2)) * 71.6
= 2025 − (47.4 * 71.6) ≈ 2025 − 3394 ≈ 1369 BC.
(If you take 13 d instead of 14 d, shift later by ~72 yrs; if 15 d, shift earlier by ~72 yrs.)
Modern fixed (illustrative, not historical):
δ_min ≈ −17.2…−18.2 deg ⇒ Earliest ≈ 1011…940 BC.

Sanity check (3 BC): D ≈ −4 deg. With Delta = 12 deg, the Spica window is (D − Delta, D) = (−16 deg, −4 deg).
Ancient allowance is [δ_min, δ_max] = [−9.2 deg, +20.3 deg]. The intersection is [−9.2 deg, −4 deg], which is non‑empty. This corresponds to 1 Nisan being roughly 0–5 days after the VE, fully consistent with the “after‑equinox” rule. The Sanhedrin regime (earlier‑permissive) also admits 3 BC.

Average Spans (See Tables and notes found at the end of the article.)

Sanhedrin (ancient, first‑sighting): total span ≈ 4,000 years (≈ 3,975–4,117 years; ±~72‑yr sensitivity).
Modern fixed (Metonic today): total span ≈ 3,100 years (≈ 2,936–3,222 years; depends on Δ and δ‑bounds).
A working horizon of ≈3,550 years is about one-seventh of the precessional (“Great-Year”) cycle, typically taken as ≈25,800–25,920 years; numerically this is within ≈2–3% of an exact 1/7.

Why Delta = 12 deg (typical) and 14 deg (generous)?

“Delta” here is the Sun–Moon elongation at the time of first naked‑eye visibility of the lunar crescent. Modern visibility work (Maunder; Bruin; Yallop; Doggett & Schaefer; Odeh; Sultan; plus USNO guidance) converges on:

Practical naked‑eye thresholds cluster near about 10–12 deg elongation, depending on geometry (Moon altitude at best time, arc of light, azimuth difference) and transparency.
The “easily visible” class in Yallop’s method typically has elongations around or above ~11–12 deg in mid‑latitude settings.
The Danjon physical limit is near ~7 deg; reported claims below ~8 deg are rare and very geometry‑dependent.
Using 12 deg as a typical threshold matches the “easily visible / normal conditions” regime.
Using 14 deg is a conservative allowance for less favorable geometry (lower Moon altitude at best time, larger azimuth separation, or marginal transparency).
Choosing 12 and 14 deg makes the future cut‑offs later rather than earlier (i.e., conservative). For the earliest epochs (past), Delta does not affect the bound (the lower‑bound inequality depends on δ_min, not Delta).

Error Audit and Final Checks

VE→AE − six lunations = ~9.2 d: confirmed (186.39 d − 177.18 d).
D(2025) ≈ 24.2 deg and precession 1 deg ≈ 71.6 yr: consistent.
Ancient δ_max ≈ 20.3 deg (one lunation after VE ⇒ 29.5 − 9.2).
Modern δ_max ≈ 11.8–12.8 deg (today’s 1 Nisan up to ~21–22 d after VE).
Lower‑bound δ_min values:
• Strict Babylonian: −9.2 deg (no early Nisan).
• Second‑Temple/Sanhedrin: about −23.2 deg (1 Nisan ≈ 14 d before VE; Passover still after VE).
Boundary (first‑failure) lens: September equinox into Leo ≈ AD 2439 (affects only very early RH; not a hard stop).
All forward hard‑stops and retrograde earliest dates recompute correctly with the one‑line formulas above.
Sensitivity remains: ±1 deg in any of D(2025), δ_max, δ_min shifts dates by ~±72 years.

One‑Line “Recipes” You Can Reuse

Hard‑stop year (future):
2025 + ( (Delta + δ_max) − D(2025) ) * 71.6

Earliest year (past):
2025 − ( D(2025) − δ_min ) * 71.6

Use degrees throughout; 1 day ≈ 1 deg here.

Selected References (short list)

Maimonides, Kiddush ha‑Chodesh 4:2–3 (tekufat Nisan rule; agricultural signs).
Josephus, Antiquities 3.248–249 (“Passover when the sun is in Aries”).
Yallop, B. D., “A Method for Predicting the First Sighting of the New Crescent Moon,” NAO Technical Note 69.
Doggett & Schaefer, “Young Moon Visibility,” (review of Danjon limit and observational thresholds).
Odeh, M., “New criterion for lunar crescent visibility,” Experimental Astronomy (2004).
Sultan, A. H., “First Visibility of the Lunar Crescent: Beyond Danjon’s Limit,” The Observatory (2006).
USNO, “Crescent Moon Visibility” (general guidance).
On precession rates and constellation boundaries: standard IAU values; September equinox enters Leo around AD 2439.

Bottom Line (with Gen 3:15 integrated)

Ancient/observational rules: if 1 Nisan can be as late as one lunation after the VE, the Spica‑anchored Rev 12 geometry on Rosh Hashanah disappears ~AD 2600–2750 (Delta = 12–14 deg).
Modern fixed rules: with today’s calendar, the same geometry ends between now and the early 22nd century (depending on Delta).
Earliest epochs: ~367 BC (strict Babylonian) or ~1369 BC (Second‑Temple/Sanhedrin, with Passover after VE).
The “moon under her feet” (Rev 12:1), read through Gen 3:15 and the NT’s “under‑foot” motif, is spatially realized by “Moon east of Spica” (under the Seed) while the Sun remains west of Spica (clothing the Woman), until precession and calendar rules render the configuration impossible.

Assumptions for all rows:

D(2025) = 24.2 deg, precession = 71.6 yr/deg
δ_min (present‑era empirical early bound) ≈ −18.2…−17.2 deg
δ_max (present‑era empirical late bound) ≈ +11.8…+12.8 deg
Hard‑stop formula (forward): Hard_stop ≈ 2025 + ( (Δ + δ_max) − 24.2 ) × 71.6
Earliest formula (retrograde): Earliest ≈ 2025 − ( 24.2 − δ_min ) × 71.6

Tables (1 & 2 = Metonic)

Parallel endpoints — Modern fixed (Metonic 19‑year), present‑era δ‑bounds

Table 1. Δ = 12 deg (typical first‑visibility crescent)

Endpoint	Parameter	Computation (deg → yr)	Result (approx)
Earliest‑min (BC)	δ_min = −18.2	2025 − (24.2 − (−18.2)) × 71.6 = 2025 − (42.4 × 71.6)	1011 BC
Earliest‑max (BC)	δ_min = −17.2	2025 − (24.2 − (−17.2)) × 71.6 = 2025 − (41.4 × 71.6)	940 BC
Latest‑min (AD)	δ_max = +11.8	D* = 12 + 11.8 = 23.8 ⇒ 2025 + (23.8 − 24.2) × 71.6	AD 1996
Latest‑max (AD)	δ_max = +12.8	D* = 12 + 12.8 = 24.8 ⇒ 2025 + (24.8 − 24.2) × 71.6	AD 2068

Table 2. Δ = 14 deg (generous first‑visibility crescent)

Endpoint	Parameter	Computation (deg → yr)	Result (approx)
Earliest‑min (BC)	δ_min = −18.2	2025 − (24.2 − (−18.2)) × 71.6 = 2025 − (42.4 × 71.6)	1011 BC
Earliest‑max (BC)	δ_min = −17.2	2025 − (24.2 − (−17.2)) × 71.6 = 2025 − (41.4 × 71.6)	940 BC
Latest‑min (AD)	δ_max = +11.8	D* = 14 + 11.8 = 25.8 ⇒ 2025 + (25.8 − 24.2) × 71.6	AD 2139
Latest‑max (AD)	δ_max = +12.8	D* = 14 + 12.8 = 26.8 ⇒ 2025 + (26.8 − 24.2) × 71.6	AD 2211

Tables (C & D = Comprehensive)

The earliest bound depends only on δ_min (how early Tishri 1 can fall relative to the equinox), not on Δ. The latest bound depends on Δ + δ_max. Hence:

BC side: fixed by δ_min ⇒ two endpoints (1011 BC and 940 BC).
AD side: depends on Δ and δ_max ⇒ four endpoints (1996, 2068, 2139, 2211).

Sensitivity note: ±1 deg in D(2025) or in your chosen δ_min / δ_max / Δ shifts any year by about ±72 years.

Table C — Earliest feasible epochs (retrograde), Spica‑anchored

Formula: Earliest_year ≈ 2025 − ( D(2025) − δ_min ) × 71.6
Assumptions: D(2025) = 24.2 deg, precession 1 deg ↔ 71.6 yr.

Regime / rule (Nisan vs VE)	ΔN_min (days)	δ_min (deg)	Computation (years)	Earliest year (approx)	Notes
Strict Babylonian — 1 Nisan never before VE	0	−9.2	2025 − (24.2 − (−9.2))×71.6 = 2025 − (33.4×71.6)	367 BC	Matches: 33.4×71.6 ≈ 2392 ⇒ 2025−2392 ≈ −366.44 (astronomical), i.e., 367 BC
Second‑Temple / Sanhedrin — allow 1 Nisan ≈ 14 d before VE (Pesach after VE)	−14	−23.2	2025 − (24.2 − (−23.2))×71.6 = 2025 − (47.4×71.6)	1369 BC	If 13 d instead: shift later ≈ +72 yr; if 15 d: earlier ≈ −72 yr
Modern fixed (illustrative, not historical)	≈ −8…−9	−17.2…−18.2	2025 − (24.2 − (−17.2…−18.2))×71.6	1011…940 BC	Range reflects present‑era minima; used only to gauge sensitivity

Sensitivity: ±1 deg in D(2025) (or in your δ_min choice) ⇒ ±≈ 72 yr on the date.

Table D — Future hard‑stop (forward), Spica‑anchored

Condition: D(t) ≤ D*, where D* = Δ + δ_max.
Formula: Hard_stop_year ≈ 2025 + ( D* − D(2025) ) × 71.6
Assumptions: D(2025) = 24.2 deg, precession 1 deg ↔ 71.6 yr.

Regime	Crescent elongation on 1 Tishri (Δ)	δ_max (deg)	D* = Δ + δ_max (deg)	Hard‑stop year (approx)	Notes
Ancient / observational (first‑sighting)	12	20.3	32.3	AD 2605	Δ=12 deg = typical first visibility; one‑lunation Nisan lateness gives δ_max≈20.3
	14	20.3	34.3	AD 2748	Δ=14 deg = generous first visibility
Modern fixed (today) (Metonic 19‑yr; postponements)	12	11.8…12.8	23.8…24.8	AD 1996–2068	Empirical present‑era: 1 Nisan up to ≈21–22 d after VE ⇒ δ_max≈11.8…12.8
	14	11.8…12.8	25.8…26.8	AD 2139–2211	Same δ_max range; Δ=14 deg gives later stop

Sensitivity:

The fixed calendar’s δ_max will creep up slowly (~1 day per ~216 yr), but precession increases D(t) faster (1 deg per 71.6 yr), so the window still closes.

±1 deg in D(2025) or in Δ/δ_max ⇒ ±≈ 72 yr on the date.

Average Spans

Sanhedrin (ancient, first‑sighting): total span ≈ 4,000 years (≈ 3,975–4,117 years; ±~72‑yr sensitivity).
Modern fixed (Metonic today): total span ≈ 3,100 years (≈ 2,936–3,222 years; depends on Δ and δ‑bounds).

How the spans are computed

Assumptions used everywhere:

D(2025) = 24.2 deg; precession = 1 deg ↔ 71.6 yr.
Day↔degree for lateness offsets: 1 day ≈ 1 deg.
Earliest (retrograde) uses δ_min (how early Tishri 1 can be); Latest (forward) uses Δ + δ_max.

A) Sanhedrin (ancient, first‑sighting)

Earliest (retrograde) with Sanhedrin rule (allow 1 Nisan ≈ 14 d before VE; Passover after VE):
δ_min = −23.2 deg ⇒ 1369 BC (±~72 yr if you take 13 or 15 d instead).
Latest (forward hard‑stop) with Δ (Sun–Moon elongation on 1 Tishri):
• Δ = 12 deg ⇒ AD 2605.
• Δ = 14 deg ⇒ AD 2748.

Total span (earliest to latest):

Using Δ = 12 deg: 1369 + 2605 = 3,974 years.
Using Δ = 14 deg: 1369 + 2748 = 4,117 years.

Round estimate: ≈ 4,000 years (practical band ~3,975–4,117; with ±1‑day early/late in the δ_min assumption, the envelope is ~3,902–4,189).

B) Modern fixed (Metonic 19‑year; postponements) — present‑era δ‑bounds

Earliest (retrograde) using present‑era early bound:
δ_min ≈ −18.2…−17.2 deg ⇒ 1011…940 BC.
Latest (forward hard‑stop) using present‑era late bound and two Δ choices:
Δ = 12 deg (typical first‑visibility crescent):
• δ_max = 11.8 deg ⇒ AD 1996; δ_max = 12.8 deg ⇒ AD 2068.
Δ = 14 deg (generous first‑visibility crescent):
• δ_max = 11.8 deg ⇒ AD 2139; δ_max = 12.8 deg ⇒ AD 2211.

Total spans (pairing earliest and latest endpoints):

Δ on 1 Tishri	Earliest (BC)	Latest (AD)	Total span (years)
12 deg (tightest pairing)	940	1996	2,936
12 deg (widest pairing)	1011	2068	3,079
14 deg (tightest pairing)	940	2139	3,079
14 deg (widest pairing)	1011	2211	3,222

Round estimate: ≈ 3,100 years overall (typical Δ = 12 deg gives ≈ 3,000 years; generous Δ = 14 deg gives ≈ 3,150–3,200 years).

Notes

Δ (Sun–Moon elongation): Δ ≈ 12–14 deg corresponds to first‑sighting crescents. Allowing delayed declarations (e.g., Δ ≈ 22–34 deg) would extend the latest AD endpoints by centuries, and the total span grows accordingly; we treat those as sensitivity cases, not primary results.
Sensitivity: Any ±1 deg change in D(2025), δ_min, δ_max, or Δ shifts the endpoints by ±≈72 years.
Why BC vs AD: Earliest limits are naturally BC (retrograde, using δ_min); latest limits are AD (forward, using Δ + δ_max).

Supplemental: Rev 12 on a 364‑Day (Enoch/Jubilees) Calendar — Earliest and Latest Windows with Spica Anchor

Scope. We apply the same Spica‑anchored geometry used for the lunar/observational cases to a 364‑day solar calendar (52 weeks; 91‑day quarters; months 30+30+31). In this system, by design, Nisan 1 is always a Wednesday (Day 4, the “luminaries” day of Gen 1), and because 6 months = 182 days = exactly 26 weeks, Tishri 1 is also always a Wednesday. Therefore, the “moon underfoot” on Tishri 1 must occur on a Wednesday evening, and this constraint is explicitly built into the analysis below.

We consider two start rules for the solar year:

Strict rule: Nisan 1 (Wednesday) is on or after the vernal equinox (VE).
Middle rule: Nisan 1 (Wednesday) may be up to one full week before the VE (i.e., the Wednesday immediately preceding the equinox week).

We keep the astronomical Rev 12 geometry and the Spica constraint unchanged:

On Tishri 1: Sun west of Spica and crescent Moon east of Spica (the “under‑her‑feet” scene).
Crescent visibility threshold Delta (Sun–Moon elongation): 12 deg (typical) and 14 deg (generous). These values come from modern crescent‑visibility studies: roughly 10–12 deg is the practical naked‑eye threshold under favorable geometry; 14 deg is a conservative allowance for less favorable conditions.

A) Fixed relations under a 364‑day year (all Wednesdays)

Quarter length = 91 days; six months = 182 days exactly (26 weeks).
VE to AE (spring to autumnal equinox) = about 186.39 days (use 186.4 days).
Let:
- D(t) = lambda_Spica minus lambda_AE(t), i.e., Spica’s longitude east of the autumnal equinox in year t (deg).
- Precession: D increases by about 1 deg every 71.6 years; use D(2025) = 24.2 deg (± about 1 deg).
- Delta (Δ) = Sun–Moon elongation at the evening crescent on Tishri 1 (deg): 12 (typical) or 14 (generous).
- Delta_N = how many days after the VE the solar Nisan 1 (Wednesday) begins (negative if before).
- delta (δ) = how many days/deg after the AE Tishri 1 falls in that year (negative if before).

Link (364‑day):
Because six solar months = 182 days while VE→AE ≈ 186.4 days, the Tishri offset is:

delta ≈ Delta_N − 4.4 deg.

Spica window (same geometric requirement, now on a Wednesday):

Feasibility on Tishri 1 requires: D(t) − Delta ≤ delta < D(t).

If the calendar restricts delta to a band [delta_min, delta_max], then existence is equivalent to:

delta_min < D(t) < Delta + delta_max.

Note that all dates in this section are Wednesdays by construction (both Nisan 1 and Tishri 1). The “moon underfoot” is therefore evaluated specifically on a Wednesday evening.

B) Allowed Delta_N (hence delta) with the Wednesday anchor

Because Nisan 1 must be a Wednesday, Delta_N is not continuous; it is discrete, depending on which weekday the VE falls:

Strict rule (Nisan 1 on or after VE):
Allowed Delta_N (days) = {0, 1, 2, 3, 4, 5, 6}.
Implied delta = {−4.4, −3.4, −2.4, −1.4, −0.4, +0.6, +1.6} deg.
Thus: delta_min = −4.4 deg; delta_max = +1.6 deg.
Middle rule (Nisan 1 up to one full week before VE):
Allowed Delta_N (days) = {−7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6}.
Implied delta = {−11.4, −10.4, …, +1.6} deg.
Thus: delta_min = −11.4 deg; delta_max = +1.6 deg.

These sets enforce the Wednesday condition for both Nisan 1 and Tishri 1 and therefore for the “moon underfoot” evening.

C) Earliest feasible epochs before Christ (Spica‑anchored, Wednesdays only)

Into the past, D(t) decreases. The earliest usable year is when the lower bound first holds:

Need D(t) > delta_min.

Use the one‑line retrograde formula:

earliest_year ≈ 2025 − ( D(2025) − delta_min ) * 71.6,
with D(2025) = 24.2 deg.

Results (all Wednesdays):

Strict rule: delta_min = −4.4 deg
earliest_year ≈ 2025 − (24.2 − (−4.4)) * 71.6
= 2025 − (28.6 * 71.6) ≈ 2025 − 2048 ≈ 23 BC.
Middle rule: delta_min = −11.4 deg
earliest_year ≈ 2025 − (24.2 − (−11.4)) * 71.6
= 2025 − (35.6 * 71.6) ≈ 2025 − 2549 ≈ 525 BC.

Uncertainty: ±1 deg in D(2025) shifts each date by about ±72 years. Because delta takes only the discrete Wednesday values listed above, feasible years occur in bands set by which weekday the equinox falls, but the boundaries above remain the correct first‑attainable epochs.

Sanity check (3 BC, a Wednesday case):
D ≈ −4 deg. With Delta = 12 deg, the Spica window is (D − Delta, D) = (−16 deg, −4 deg).
Under the Strict set, delta must equal one of {−4.4, −3.4, −2.4, −1.4, −0.4, +0.6, +1.6}. The intersection with (−16, −4) is {−4.4} only, i.e., the “first Wednesday after VE.” This confirms the Wednesday anchoring is active in the logic (and feasible). The Middle rule admits additional earlier Wednesday choices.

Note on the lunar‑phase filter. Because the 364‑day calendar is solar and not lunar‑started, the Moon’s actual elongation on a given Wednesday varies year to year. Our Delta = 12 or 14 deg values represent the visibility threshold. The Wednesday‑only feasible set above is therefore a necessary window; within it, actual years meeting Delta ≥ 12 deg on that Wednesday evening will be a subset. Over time, because the 364‑day year is not commensurate with the synodic month, the lunar age on Wednesday Tishri 1 drifts through all phases, so visible‑crescent Wednesdays do occur; the earliest boundary is therefore stable (it may “thin” interior years but does not shift the boundary by more than the ±72‑year sensitivity).

D) Latest (past‑tense) future feasibility under a 364‑day year (Wednesdays only)

Forward in time, the upper inequality controls feasibility:

Need D(t) < Delta + delta_max.

Here delta_max = +1.6 deg (same for both Strict and Middle, since the latest allowed Nisan 1 is the Wednesday six days after VE).

Thresholds and last years (Wednesdays):

Delta = 12 deg ⇒ threshold = 12 + 1.6 = 13.6 deg.
Last_year ≈ 2025 − ( 24.2 − 13.6 ) * 71.6 ≈ AD 1266.
Delta = 14 deg ⇒ threshold = 14 + 1.6 = 15.6 deg.
Last_year ≈ 2025 − ( 24.2 − 15.6 ) * 71.6 ≈ AD 1409.

Interpretation: on a pure 364‑day Wednesday‑anchored solar year, the Spica‑anchored Rev 12 scene on Tishri 1 ceased to be attainable centuries ago (AD 1266–1409), well before our modern era. This sharpening does not contradict the lunar‑anchored results; it reflects the much tighter lateness budget (delta_max only about +1.6 deg) when the year is fixed to Wednesdays.

E) Why Delta = 12 deg (typical) and 14 deg (generous)?

“Delta” is the Sun–Moon elongation on the Tishri‑1 Wednesday evening. Modern crescent‑visibility research (Yallop; Doggett & Schaefer; Odeh; Sultan; USNO summaries) shows:

Practical naked‑eye thresholds concentrate near about 10–12 deg under favorable geometry (sufficient altitude and small azimuth difference).
A conservative allowance of 14 deg covers marginal geometry (lower altitude at best time, greater azimuth separation, or reduced transparency).

Using 12 deg as “typical” and 14 deg as “generous” makes the latest dates later (conservative) and does not change the earliest boundaries (which depend on delta_min, not Delta).

F) Error audit and refinements (Wednesday anchor fully applied)

The Wednesday requirement is now explicit: both Nisan 1 and Tishri 1 are Wednesdays, hence the “moon underfoot” is always evaluated on a Wednesday evening. The discrete sets for Delta_N and delta enforce this.
The 364‑day link is delta ≈ Delta_N − 4.4 deg (182 d vs 186.4 d), not the −9.2 deg used in the lunar case. This has been applied consistently here.
D(2025) = 24.2 deg (± ~1 deg) and the precession scale 1 deg ≈ 71.6 years are unchanged and re‑used correctly.
Crescent thresholds 12 and 14 deg are documented from the visibility literature (typical vs generous).
The “phase filter” note is added: since the 364‑day calendar does not start months by the moon, only those Wednesday Tishri 1’s that happen to have Delta ≥ 12 deg will realize the scene. This filter reduces frequency within the window but does not materially move the boundaries beyond the ±72‑year sensitivity.

G) One‑line “recipes” (Wednesdays only)

Use degrees throughout; 1 day is treated as 1 deg here.

Earliest year (retrograde):
earliest_year ≈ 2025 − ( D(2025) − delta_min ) * 71.6.
With 364‑day Strict: delta_min = −4.4 deg.
With 364‑day Middle: delta_min = −11.4 deg.
Last year (forward limit):
last_year ≈ 2025 − ( D(2025) − ( Delta + delta_max ) ) * 71.6.
With 364‑day rules: delta_max = +1.6 deg.

Sensitivity: ±1 deg in D(2025) or in the assumed delta_min/delta_max shifts dates by about ±72 years.

Bottom line (364‑day, Wednesday‑anchored)

Earliest before Christ (all Wednesdays):
• Strict (Nisan‑after‑VE): about 23 BC.
• Middle (Nisan up to one week before VE): about 525 BC.
Latest (already past):
• With Delta = 12–14 deg, the last attainable Wednesday Tishri 1 with Sun west of Spica and a visible crescent Moon east of Spica is AD 1266–1409.
The Wednesday requirement for both Nisan 1 and Tishri 1 is now fully integrated; the results above are Wednesday‑only windows, with the lunar‑visibility threshold explicitly applied.

Supplemental 2 — What if Tishri 1 is delayed by one night (atmospheric or sighting delay)?

Short answer: A one-night delay of the crescent (i.e., declaring 1 Tishri one day later than the earliest possible evening) typically increases the Sun–Moon elongation Δ by about 12.2 deg, which translates — given precession ≈ 71.6 years/deg — to roughly +873 years later for the Spica-anchored hard-stop. So a single delayed evening has a large cumulative effect on the long-term cutoff because the Sun–Moon geometry advances rapidly (~12 deg/day) while precession is slow (~72 years/deg).

This supplemental is for comparison only. Our main analysis assumes first-visibility practice (no systematic delays) because we treat the Rev.12 sign as an observational/“first-sighting” sign. Still, it is useful to quantify the delayed scenarios so readers can see how sensitive the horizon is to one easily imaginable change (clouds, extinction, missed witnesses, or conservative local practice).

Why consider a one-night delay?

Reasons a 1-night delay can happen (each is historically documented):

Weather (cloud cover, haze): prevents observation of a crescent that is otherwise theoretically visible.
Low Moon altitude / poor geometry: even if the crescent is physically present, it may be too low above the horizon and drowned in twilight.
High extinction / dust / volcanic aerosols: raises visibility threshold.
Human/legal factors: missed witnesses, court delays, or conservative local practice could delay the declaration deliberately.
Tight schedules / religious policy: some communities wait an extra night to be sure.

All of the above can convert a first-possible crescent evening (Δ ≈ 11–14 deg) into the actual declaration evening of the month (Δ larger, often by ~12 deg per night).

Physics of the change: how much does Δ increase per day?

Moon’s mean daily motion ≈ 13.176 deg/day eastward.
Sun’s mean daily motion ≈ 0.986 deg/day eastward.
Relative increase in elongation (Moon minus Sun) ≈ 13.176 − 0.986 ≈ 12.19 deg per day.

Thus, one additional night of waiting typically increases Δ by ≈12.2 deg (rule-of-thumb; exact value depends on instantaneous orbital geometry, but this number is the conventional average used in crescent-visibility work).

How that maps into years (precession sensitivity)

Precession moves Spica vs the equinox ≈ 1 deg every 71.6 years.
So 1 day delay → +12.19 deg → + (12.19 × 71.6) ≈ +873 years shift in the hard-stop epoch.

We can also express this as:

Per degree of Δ increase, the hard stop shifts by ~71.6 years.
Per day of delay (Δ ≈ +12.19 deg) the shift is ~873 years.

Worked examples

Constants used

D(2025) = 24.2 deg (Spica east of AE).
Precession = 71.6 years per degree.
Ancient observational δ_max = 20.3 deg (one lunation after VE).
Modern fixed δ_max ≈ 11.8 … 12.8 deg (empirical today).
Relative elongation growth ≈ 12.19 deg/day.

Example A — Ancient / observational baseline (no delay)

Typical first-sighting Δ = 12 deg.
D* = Δ + δ_max = 12 + 20.3 = 32.3 deg.
Hard-stop year ≈ 2025 + (32.3 − 24.2) × 71.6 = AD 2605 (≈ our baseline).

Example B — Ancient / observational with a 1-night delay

One-night delay adds ≈ 12.19 deg to Δ → Δ ≈ 24.19 deg.
D* = 24.19 + 20.3 = 44.49 deg.
Hard-stop year ≈ 2025 + (44.49 − 24.2) × 71.6 = AD 3478 (≈ AD 3480).
Net shift: ≈ +873 years relative to the no-delay case.

Example C — Modern fixed baseline (no delay)

Typical Δ = 12 deg, δ_max ≈ 11.8 … 12.8 deg.
D* ≈ 23.8 … 24.8 deg ⇒ Hard-stop ≈ AD 1996 … AD 2068 (as before).

Example D — Modern fixed with 1-night delay

Δ ≈ 12 + 12.19 = 24.19 deg.
D* ≈ 24.19 + (11.8 … 12.8) = 36.0 … 37.0 deg.
Hard-stop ≈ AD 2869 … AD 2941 (centuries to a millennium later than modern baseline).

Practical notes (how to read these numbers)

These delayed scenarios are for comparison. They model what happens if the actual declared new month is one day later than the earliest possible evening. They do not claim this was standard practice.
One night is a big lever. Because precession is slow, a small change in elongation (tens of degrees) maps to centuries. That’s why a single night of delay can move the hard-stop from ~AD 2600 to ~AD 3480.
Not all delays are equally plausible. Occasional cloud delays are common; consistent systematic delays of 1–3 nights across many years (enough to push the last possible year centuries) require either recurrent adverse conditions or deliberate legal practice. If you think a given historical community always delayed, the late-millennium conclusions are valid for that assumption; otherwise treat them as sensitivity cases.

Sources / supporting references (short)

Synodic month = 29.53059 d; lunar mean motion ≈ 13.176 deg/day; solar mean motion ≈ 0.9856 deg/day.
(These are the standard references used throughout the article; cite Yallop/USNO for visibility and standard astronomical constants for motion rates.)

Yallop, B. D., NAO Technical Note 69 (crescent visibility parameterization).

Doggett & Schaefer; Odeh; Sultan – modern crescent visibility studies.

USNO crescent-visibility summaries.

Hard-stop years (Δ tiers → D* = Δ + δ_max → approximate last possible year)

Δ (deg)	D* (ancient = Δ+20.3)	Last year (ancient)	D* (modern = Δ+11.8)	Last year (modern, low)	D* (modern = Δ+12.8)	Last year (modern, high)
11	31.3	AD 2533	22.8	AD 1925	23.8	AD 1996
12	32.3	AD 2605	23.8	AD 1996	24.8	AD 2068
14	34.3	AD 2748	25.8	AD 2140	26.8	AD 2211
22	42.3	AD 3321	33.8	AD 2712	34.8	AD 2784
26	46.3	AD 3607	37.8	AD 2999	38.8	AD 3070
30	50.3	AD 3894	41.8	AD 3285	42.8	AD 3357
34	54.3	AD 4180	45.8	AD 3572	46.8	AD 3643

(Years rounded to nearest whole year.)

How to read the table (brief)

Rows show plausible Δ choices (Δ ≈ 11–14 deg = first-sighting; Δ ≈ 22–34 deg = 1–3 evenings late).
“Last year (ancient)” answers: if the ancients insisted on first-sighting except for occasional cloud delays, the latest time the Spica-anchored scene could be realized is the year shown in column 3 for that Δ.
If you allow Δ ≈ 34 deg (a ~3-day-old crescent), the ancient hard stop moves to ~AD 4180 — exactly where your Regulus/4150 snapshot sits.
For the modern fixed calendar, because δ_max is much smaller (~11.8–12.8 deg today), the late limits are much earlier (often already past or in next few centuries).