Chapter 16 evidence and calculation methods

This supplement to The Cross at the Center of Time makes the numerical evidence for Chapter 16 available for examination. It preserves the supplied calculations and documents their settings. The checks performed while preparing this supplement verified arithmetic and retained-file integrity; no fresh ephemeris calculation or astronomical observation is claimed.

Downloads and scope

Download the public calculation files. The download contains numerical results, the full-minute scan, scientific calculation code, cached NASA/JPL request and response pairs, and checks for the retained data. It contains only evidence and methods relevant to this supplement.

Calendar and model settings

All ancient civil dates here are Julian. The reference instant is May 15, AD 33, 13:00 Jerusalem local mean solar time (LMT), equivalent to 10:39:04 UT rounded to the nearest second. Julian day UT is 1733245.9437916668. TT = UT + 10,202 seconds. LMT = UT + 2 hours 20 minutes 56.4 seconds, from longitude 35.235° east. These clocks are model coordinates, not recovered first-century event times.

The supplied calculation uses pyswisseph 2.10.3.2, Swiss Ephemeris 2.10.03, explicit built-in Moshier mode, and scipy 1.17.0. Geocentric positions are apparent tropical ecliptic-of-date longitudes and latitudes. Horizon calculations use Jerusalem 31.778° north, 35.235° east, elevation 786 m. The level astronomical horizon has no terrain or extinction model. Pressure 927 hPa and temperature 15°C apply where apparent limb/refraction settings are used. The common seven-body interval instead uses geometric topocentric centers without refraction.

Reference longitudes and unequal gaps

At the reference instant, the supplied seven-body positions are:

The directed Venus-to-Saturn span is 101.62358031°. Its six successive gaps are 22.06584264°, 22.66814056°, 16.68120155°, 13.88310971°, 10.50960669°, 15.81567917°. Their mean is 16.93726339°. They are unequal: E = max(|gap − mean|) / mean = 0.37949795, exceeding 0.20. The Moon's fractional position from Venus toward the Sun is 0.49326800; 0.5 would be the exact midpoint.

The full May 15 LMT scan retains 1,441 boundary-inclusive rows, at one-minute steps from 00:00 to the next 00:00. The first 1,440 represent 00:00–23:59. A local numerical refinement accompanies the sampled minimum; this is not an analytic proof of a continuous global minimum. The CSV preserves the spacing calculations for inspection.

Common horizon interval

The interval opens with Saturn rising at 0033-05-15 08:56:03 and closes with Venus setting at 0033-05-15 15:06:47. Its computed duration is 6.17882276 hours. Approximate seconds record numerical output. This is neither a visibility claim nor the recorded duration or hour of the Ascension.

Spring events and April 5 dawn

The equinox is the root at which the Sun's apparent geocentric tropical longitude is 0°. The selected inferior conjunction is equality of Venus and Sun longitudes, not zero angular separation; Venus has nonzero ecliptic latitude.

For April 5, the supplied dawn calculation solves topocentric geometric solar-center altitudes of −12°, −6°, and 0°. At −6°, the local mean solar time is 05:20:58; Venus has altitude 9.9571°, solar elongation 21.9885°, and modeled magnitude approximately −4.46. This does not recover a human first sighting.

April 3 eclipse and horizon definitions

The supplied apparent upper-limb Moonrise is 18:18:00 LMT; the airless geometric-center Moonrise is 18:21:44 LMT. Apparent solar upper-limb sunset is 18:18:10 LMT. They use different horizon criteria from the seven-body center interval. The NASA contact record gives the following global predictions in UT:

Credit: eclipse predictions by Fred Espenak and Jean Meeus, NASA GSFC. NASA century catalog and April 3 AD 33 contact plot. Delta T uncertainty, local terrain, extinction and atmospheric conditions limit historical visibility inference. See NASA uncertainty guidance.

NASA JPL comparison

The supplied NASA/JPL Horizons comparison uses geocentric observer coordinates at the same TT instants. Sun, Moon, Mercury and Venus use target IDs 10, 301, 199 and 299. Mars, Jupiter, Saturn and Uranus use DE441 system barycenters 4, 5, 6 and 7; they must not be relabeled planet-center targets. The source manifest records exact request and response hashes. Modern IAU constellation labels are distinct from tropical longitude signs.

The largest retained longitude difference is 0.01758902°, for the Moon. This is a comparison between calculated ephemerides, not an independent historical observation.

Reproduction instructions

Extract the public ZIP into a directory. Run python3 check_retained_data.py for standard-library arithmetic and file-integrity checks. Run python3 crosscheck_horizons.py to reconstruct the JPL comparison from cached records without network access. Fresh summaries are written to output; source records are not overwritten.

For a new scientific run, install the pinned dependencies in requirements-astronomy.txt and run python3 calculate_astronomy.py --output output-new. The script requests the official fixed-star catalog if it is absent. The required catalog SHA-256 is 18b0dcafbe5b7240773daba2c038a325f5b3fc4163f61e0a7f4e92abd4f517c6. It refuses a changed catalog. To use an existing matching file without downloads, add --star-catalog /path/to/sefstars.txt --offline. No external ephemeris binaries or fixed-star catalog are distributed here. A new run is not automatically substituted for the published results.

The scripts were adapted only to use this supplement's standalone directory layout. During supplement preparation, retained-data checks and offline cached JPL reconstruction were run. The scientific calculator was syntax-checked but not rerun. Its model, source inputs and numerical results remain those supplied for Chapter 16.

Pleiades corpus sources for note 26

Note 26 concerns textual evidence rather than an ephemeris. The supplied evidence used indexed scholarly corpus text; direct ORACC origin pages were unavailable at that review. This supplement does not upgrade those records into a fresh inspection of complete origin texts.

• MUL.APIN electronic edition, displayed line 42 associates Bristle with the divine Seven. The adjacent Bull of Heaven entry does not itself call the cluster a bull's mane or a woman's seat.
• SAA 8 507, reverse 1–4 associates the Pleiades with the Seven and describes a favorable omen. The association therefore does not make every Pleiades tradition demonic.
• Sebettu corpus glossary distinguishes a demonic-group sense and a Pleiades sense. This is lexical annotation whose meaning depends on individual contexts.

These sources support the stated associations and their qualifications. They do not independently establish the proposed bull-mane/Harlot identity.

Sources and limits

Swiss Ephemeris programming documentation, JPL Horizons manual, Horizons API documentation, JPL ephemerides, and fixed-star catalog source.

The supplement reports supplied numerical evidence and distinguishes the checks actually performed on it. It does not calculate an AD 29 companion scene. That scene would require its own date, settings and calculation. Native 364-day measures and common 360-day representations remain different units. The author's proposed heavenly meaning extends beyond what the calculation measures or what an observer on earth could have seen.

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