Document ID: E_4_04
Section: E_Cataclysms_and_Chronology
Keywords: mathematical encoding, precessional numbers, 72, 108, 432000, 25920, 360, precession, Hamlet Mill, Santillana, von Dechend, base-60, sexagesimal, Sumerian mathematics, celestial mechanics, precessional cycle, ecliptic, equinox, processional drift, Vedic kalpa, Norse mythology, Einherjar, Valhalla, Egyptian, Osiris conspiracy, Edfu, Dendera zodiac, Maya Long Count, baktun, grand cycle, sacred geometry, sacred numbers, mythology as science, archeoastronomy, Hipparchus
Category Tags: cataclysms, chronology, mathematics, mythology, religion
Cross-References: A_1_03 — Apkallu · B_2_04 — Ancient Lifespans · D_5_03 — Sacred Geometry · D_5_05 — Archaeoastronomy · E_4_01 — Precession · Q_1_03 — Ancient Cosmology · Q_3_02 — Ancient-Modern Parallels · F_4_04 — Knowledge Preservation
Reliability Tier: Tier 1-2 (established with some scholarly debate)
Last Updated: Feb 27, 2026 | Source Count: 0 | Weighted Score: 0 | Source Confidence: [1/5] | Confidence: High (established with some scholarly debate)

QUICK SUMMARY

Certain numbers appear with suspicious regularity across ancient mythologies worldwide: 72 (Egyptian conspirators against Osiris, degrees of precessional shift per degree), 108 (Hindu/Buddhist sacred number, suitors of Penelope), 432,000 (Sumerian King List total pre-flood years, Norse Einherjar warriors, Hindu Kali Yuga years), 25,920 (full precessional cycle in years). These are ALL derivable from the precession of the equinoxes — Earth's ~25,920-year axial wobble. Hamlet's Mill (1969) argued this proves ancient civilizations understood precession THOUSANDS of years before Hipparchus (127 BCE). The statistical improbability of these identical, mathematically interrelated numbers appearing independently in Sumerian, Hindu, Norse, Egyptian, and Mesoamerican traditions demands an explanation: either widespread cultural diffusion from a common source, independent discovery of the same astronomical phenomenon, or deliberate encoding by a lost civilization. This document catalogs every known instance, examines the underlying mathematics, and evaluates the evidence for and against intentional encoding.

1. VERIFIED CLAIMS (Tier 1 — Peer-Reviewed / Established Science)

1.1 The Precessional Mathematics

Precession of the equinoxes is an established astronomical phenomenon — the slow westward drift of the vernal equinox point along the ecliptic, caused by the gravitational torque of the Sun and Moon on Earth's equatorial bulge. The key values:

The traditional value (25,920) is the BASE from which ALL other "sacred" numbers derive through simple arithmetic:

25,920 ÷ 360    = 72           (years per degree)
72 × 5           = 360          (degrees in a circle)
72 × 6           = 432
432 × 1,000      = 432,000      (Kali Yuga, Einherjar, Sumerian King List)
432 × 10,000     = 4,320,000    (Mahayuga)
432 × 10,000,000 = 4,320,000,000 (kalpa / day of Brahma)
72 + 36           = 108          (half of 72 added: 108)
72 × 1.5          = 108
72 × 30           = 2,160        (years in one zodiacal age)
2,160 × 12        = 25,920       (full cycle, 12 ages)
25,920 ÷ 5        = 5,184        (one-fifth cycle)
25,920 ÷ 2        = 12,960       (half cycle — ~Younger Dryas interval?)

KEY FINDING Every single "sacred number" from mythological traditions can be generated from ONE astronomical fact (25,920-year precession) using only basic arithmetic and factors of the base-60 system.

1.2 The Sexagesimal (Base-60) Connection

The Sumerian sexagesimal system — base-60, invented ~3500 BCE — is the mathematical framework that ties these numbers together:

The base-60 system is uniquely suited for astronomical calculation because 60 has twelve factors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) — more than any smaller number. This makes it ideal for dividing circles, tracking celestial cycles, and expressing ratios without fractions.

1.3 Hipparchus and the "Official" Discovery

• Hipparchus of Nicaea (~190–120 BCE) is officially credited with discovering precession, circa 127 BCE
• He compared his own stellar observations with those of Timocharis (~280 BCE) and Aristyllus, finding a systematic shift of ~1° per century (close to the actual ~1° per 72 years)
• Ptolemy (c. 150 CE, Almagest) later reported Hipparchus's finding and slightly underestimated the rate at 1° per 100 years
• The critical question: If precession was truly "discovered" in 127 BCE, why do numbers encoding it appear in texts and traditions THOUSANDS of years older?

1.4 Where the Numbers Verifiably Appear

The following instances are textually confirmed in primary sources or well-attested traditions:

THE NUMBER 72

THE NUMBER 108

THE NUMBER 432,000

THE NUMBER 25,920

THE NUMBER 360

THE NUMBERS 12 AND 60

2. CREDIBLE CLAIMS (Tier 2 — Academic / Debated but Supported)

2.1 Hamlet's Mill — Myth as Encoded Science

Hamlet's Mill: An Essay on Myth and the Frame of Time (1969) by Giorgio de Santillana (MIT professor of history of science) and Hertha von Dechend (University of Frankfurt) remains the foundational academic argument for precessional encoding in mythology.

Core Thesis:

Myth is not primitive superstition but the TECHNICAL LANGUAGE of a pre-literate astronomical science. The narratives of gods, heroes, and cosmic events are carefully constructed to encode the mechanics of precession — the shifting of the celestial frame over millennia.

Key Arguments:

1. The "Mill" motif — Across cultures, a great grinding mill (Grotte in Norse, Sampo in Finnish, the churning of the cosmic ocean in Hindu) represents the celestial axis. When the mill "breaks" or is "displaced," this encodes the precessional shift — the axis points to a new pole star, the equinox moves into a new constellation.
2. Consistent number sets — The same numbers (72, 108, 432,000) appear in mythologies with no documented cultural contact (e.g., Sumerian and Norse, Hindu and Mesoamerican)
3. Constellation imagery — Heroes and gods associated with specific animal forms (bull, ram, fish) correspond to zodiacal ages determined by precession.
4. "Death" of gods — When a god "dies" or a hero is defeated, this often encodes the end of a zodiacal age (Osiris killed → end of Age of Taurus/Orion dominance; Christ the fish/lamb → Pisces replaces Aries).

Reception:

• Mainstream: Respectful but skeptical. Reviewed seriously in academic journals (Isis, Journal for the History of Astronomy) but criticized for selectivity and over-interpretation
• Alternative researchers: Foundational text — cited by Graham Hancock, Robert Bauval, John Anthony West, Randall Carlson
• Current status: Neither fully accepted nor refuted; the core observation about number distribution has never been adequately explained by any competing hypothesis

2.2 The Sumerian King List — Precessional Encoding?

The Sumerian King List (multiple copies; most complete: WB-62 and WB-444) records eight kings ruling before the Flood with impossibly long reigns:

The precessional connection:

• Berossus (3rd c. BCE Babylonian priest) recorded the total as 432,000 years using a different tradition/conversion
• 432,000 = 120 × 3,600 = 120 sars
• Whether the original Sumerian numbers or Berossus's total is "correct," BOTH are multiples of precessional base numbers
• 241,200 = 67 × 3,600 — less clean, but individual reigns (28,800, 36,000, 43,200) all factor neatly: 28,800 = 8 × 3,600; 36,000 = 10 × 3,600; 43,200 = 12 × 3,600

Skeptical position: The King List numbers may simply reflect Sumerian sexagesimal mathematics (everything in base-60 multiples) without intentional precessional encoding. The coincidence arises because base-60 arithmetic naturally generates these factors.

Counter-argument: Why do these SAME base-60-derived numbers appear in Hindu, Norse, and other non-Sumerian traditions? Either there was transmission, or multiple independent cultures encoded the same astronomical phenomenon.

2.3 Norse Einherjar — The 432,000 Warriors

Grímnismál (stanza 23), a poem in the Poetic Edda (compiled c. 1270 CE from older oral tradition), describes Valhalla:

Fimm hundruð dura ok um fjórum togum,
svá hygg ek á Valhöllu vera;
átta hundruð Einherja ganga senn ór einum durum,
þá er þeir fara at vitni at vega.

Translation: "Five hundred doors and forty more / I think are in Valhalla; / Eight hundred Einherjar go at once from each door / When they go forth to fight the Wolf."

540 doors × 800 warriors = 432,000

Arguments for intentional encoding:

• 432,000 is not a "natural" number — it specifically matches the Kali Yuga and Sumerian King List totals
• Norse mythology was transmitted orally for centuries before written compilation; precise number preservation suggests significance
• The compound calculation (540 × 800) is unusual — why not just say "432,000 warriors"? Because the MULTIPLICATION is the encoding mechanism, designed to be memorable and verifiable

Arguments against:

• The Poetic Edda was compiled in 13th-century Iceland — possible late contamination from Eastern sources via Silk Road/Byzantine contact
• 540 and 800 may have independent significance in Norse numerology
• Without pre-Christian written sources, the original numbers cannot be confirmed

2.4 Hindu Yuga Cycles and Precessional Multiples

The Hindu time-cycle system is built ENTIRELY on multiples of 432,000:

Key observation: The base unit (432,000) is identical to the Sumerian/Norse number. The Yuga ratios (1:2:3:4) suggest a system designed, not evolved organically.

Dating controversy: The Surya Siddhanta (astronomical text containing these numbers) is traditionally dated to the Vedic period but the surviving recension is c. 400 CE. The Yuga numbers may be older than the text itself — but how much older is debated.

2.5 The 108 Astronomical Coincidence

The ratio between the Sun, Moon, and Earth shows a remarkable set of near-108 relationships:

The Sun-Earth / Sun-diameter ratio (~107.5) is strikingly close to 108. The Moon ratio (~110.6) is less precise but still in the ballpark. These ratios also explain why the Sun and Moon appear nearly the same apparent size in our sky — enabling total solar eclipses, a phenomenon unique (as far as we know) in the solar system.

Question: Did ancient cultures KNOW these ratios, or is the sacredness of 108 coincidental with the astronomical reality? The fact that 108 = 72 × 1.5 (directly derivable from precession) suggests the precessional derivation, not the astronomical ratio, may be the primary origin — but the coincidence is remarkable.

2.6 Neugebauer and Pre-Hipparchan Knowledge

Otto Neugebauer (1899–1990), the foremost historian of ancient mathematics and astronomy, demonstrated in A History of Ancient Mathematical Astronomy (1975) and Astronomical Cuneiform Texts (1955) that:

• Babylonian astronomers achieved remarkable precision in predicting eclipses and planetary motions by the Seleucid period (3rd–1st c. BCE)
• The Babylonian "System B" lunar theory incorporated corrections that may implicitly account for precessional effects
• Whether Babylonians explicitly recognized precession before Hipparchus remains debated, but their observational precision was sufficient to detect it

Implication: If professional Babylonian astronomers of the 5th–3rd centuries BCE were on the threshold of recognizing precession, it is not inherently implausible that earlier observers (over centuries of accumulated records) could have noticed the drift.

2.7 Graham Hancock's Popularization

Graham Hancock (Fingerprints of the Gods, 1995; Magicians of the Gods, 2015; Netflix's Ancient Apocalypse, 2022) popularized the encoding thesis for a mass audience:

Key claims (as distinct from de Santillana/von Dechend):

• A single advanced civilization existed before the Younger Dryas (~12,800 years ago)
• This civilization encoded precessional knowledge in myths and monuments as a DELIBERATE preservation strategy, anticipating their own destruction
• Göbekli Tepe, Angkor Wat, and Giza are part of a global network encoding precessional data
• The numbers serve as "seeds" — anyone rediscovering them would necessarily recover the astronomical framework

Critical assessment: Hancock's core observation about the numbers is inherited from Hamlet's Mill and is legitimate. His INTERPRETATION (single lost civilization) goes significantly beyond what the number distribution alone can prove. See E_4_01 for detailed precession discussion.

3. SPECULATIVE CLAIMS (Tier 3 — Possible but Unverified)

3.1 A Single Pre-Catastrophe Source Civilization

Hypothesis: A single advanced civilization (pre-Younger Dryas, >12,800 years ago) possessed sophisticated astronomical knowledge, including precise knowledge of precession. Before or during their destruction, they encoded this knowledge in mythological narratives and transmitted it to surviving populations across the globe — explaining the universal distribution of precessional numbers.

Supporting indicators:

• The mathematical precision and consistency of the numbers across cultures
• The appearance of 432,000 in traditions with no documented contact (Sumerian ↔ Norse ↔ Hindu)
• The Younger Dryas impact hypothesis (E_1_01) provides a plausible destruction mechanism
• Knowledge preservation via mythology would be logical for a civilization anticipating catastrophe (see F_4_04)

Problems:

• No direct archaeological evidence of such a civilization has been found
• Cultural diffusion along known trade and migration routes could explain much of the distribution
• The base-60 system's mathematical properties may independently generate these numbers in any culture that adopts it

3.2 Precessional Numbers as Deliberate "Seeds"

Hypothesis: The numbers were not merely recorded but intentionally designed as self-decoding information packets. A civilization that understood precession could embed 72, 108, and 432,000 in myths, knowing that ANY future civilization that rediscovered these numbers and possessed basic astronomical knowledge would inevitably work backward to the precessional cycle.

The logic:

1. Future people find "72" recurring in myths → investigate why
2. They observe precession → calculate ~72 years per degree of shift
3. Connection unlocks the entire framework (432,000, 25,920, etc.)
4. The mythological "packaging" ensures survival through oral tradition even if written records are lost

Assessment: Elegant but unfalsifiable. We cannot distinguish between "intentional seeds" and "coincidentally preserved astronomical observations."

3.3 Precession as a Cosmic Clock for Cataclysmic Cycles

Hypothesis: The half-precessional cycle (~12,960 years) corresponds to recurring cataclysmic periods. The Younger Dryas impact (~12,800 years ago) occurred approximately one half-cycle ago. Ancient astronomers may have tracked precession specifically because it correlated with observed catastrophic cycles.

Observations:

• 25,920 ÷ 2 = 12,960 years — close to the interval since the Younger Dryas
• Researchers (Carlson, Hancock) suggest cataclysmic events may correlate with Earth's passage through specific regions of the galactic plane or encounters with cosmic debris streams (Taurid complex)
• The Maya "Grand Cycle" of ~25,627 years (close to the precessional cycle) ends/resets — potentially encoding a cycle of destruction and renewal

Problems: The Younger Dryas timing is suggestive but a single data point. No confirmed mechanism links precession to cataclysmic periodicity. See E_1_01 and E_1_04 for detailed analysis.

3.4 Göbekli Tepe as Precessional Observatory

Hypothesis: Göbekli Tepe (c. 9600–8000 BCE, ~7,000 years before Hipparchus) was designed partly to observe and record precessional shift.

Evidence cited:

• Martin Sweatman's interpretation of Pillar 43 (Enclosure D) as encoding the date ~10,950 BCE via stellar positions (see D_1_01)
• The site's precise astronomical alignments — pillars oriented to specific stellar positions that would have been accurate at the time of construction
• If Sweatman is correct, the builders were tracking stellar positions with sufficient precision to imply precessional awareness

Assessment (Tier 3): Sweatman's interpretation is published but heavily debated. Even if Pillar 43 does encode a specific date, this demonstrates calendrical astronomy, not necessarily precessional knowledge per se.

3.5 The Dendera Zodiac as Precessional Record

The Dendera Zodiac (ceiling relief in the Temple of Hathor, Dendera, Egypt; c. 50 BCE) is the only known complete ancient Egyptian representation of the zodiacal constellations.

Claims:

• The zodiac's orientation may encode precessional shift relative to known baselines
• The presence of ALL zodiacal signs suggests awareness of the full precessional cycle
• However, dating to c. 50 BCE places it AFTER Hipparchus — so it cannot independently prove pre-Hipparchan knowledge

3.6 The Edfu Building Texts

The Edfu Temple inscriptions (Ptolemaic period, but claiming to copy much older documents) describe the founding of Egyptian temples by the "Shebtiw" — primeval sages who came from an island destroyed by flood.

Possible connection: If the Edfu texts preserve genuine pre-Dynastic traditions, the described "primeval sages" may be the same tradition as the Sumerian Apkallu (see A_1_03) — knowledge-bringers who taught astronomy, including precessional knowledge, to post-catastrophe populations.

4. DUBIOUS CLAIMS (Tier 4 — No Credible Source / Contradicted by Evidence)

4.1 DEBUNKED "Ancient People Could Not Have Known Precession"

This dismissal is itself unsupported. Babylonian astronomical records demonstrate precision sufficient to detect precessional drift over centuries of accumulated observation. The claim rests on the assumption that only Greek-style theoretical astronomy counts as "knowledge" — ignoring the possibility of observational/empirical detection over long time periods, transmitted through cultural memory.

4.2 DEBUNKED "Every Large Number in Mythology Is Precessional"

The encoding thesis is sometimes over-applied. Critics (and honest proponents) note:

• Not every large number in myth fits the framework (e.g., 7, 40, 1,000 are also common mythological numbers with no precessional connection)
• Cherry-picking risk: With enough mythologies and enough numbers, statistical coincidences are inevitable
• The strongest cases are the EXACT matches (432,000 in Sumerian, Norse, AND Hindu); less exact matches should be treated with caution

4.3 DEBUNKED "The Numbers Prove Alien Contact"

Some fringe sources attribute the universal distribution of precessional numbers to extraterrestrial origin. This claim goes far beyond the evidence: shared astronomical encoding can be explained by human astronomical observation + cultural transmission without invoking non-human intelligence. The numbers themselves demonstrate nothing beyond sophisticated human astronomy.

THE NUMBERS TABLE — Complete Catalog

Master Reference: All Precessional Numbers and Their Appearances

The "Impossible Coincidence" Summary

The probability question at the heart of this research:

What are the odds that Sumerian, Hindu, and Norse traditions — separated by thousands of miles and years — would independently arrive at the EXACT same number (432,000) for their most cosmologically significant calculations?

Three possible explanations:

THE MATHEMATICS — Worked Examples

How 72 Generates Everything

Starting from ONE observation — the equinox shifts 1° in ~72 years:

STEP 1:  72 years per degree (observed)
STEP 2:  72 × 360 = 25,920 (full cycle — one complete wobble)
STEP 3:  72 × 6 = 432
STEP 4:  432 × 1,000 = 432,000 (Kali Yuga, Einherjar, King List)
STEP 5:  432 × 10,000 = 4,320,000 (Mahayuga)
STEP 6:  72 × 1.5 = 108 (sacred number, mala beads)
STEP 7:  72 × 2 = 144 (→ 144,000 in Revelation)
STEP 8:  72 × 30 = 2,160 (one zodiacal age)
STEP 9:  72 ÷ 2 = 36 (Egyptian decans)
STEP 10: 72 × 5 = 360 (degrees in circle, days in base year)

The Base-60 Framework

Why base-60 is the KEY to precessional encoding:

60 × 1     =     60    (base)
60 × 6     =    360    (circle degrees)
60 × 60    =  3,600    (one sar; one hour in seconds)
60 × 360   = 21,600    (= 6 × 3,600)
60 × 432   = 25,920    (FULL PRECESSIONAL CYCLE)
60 × 7,200 = 432,000   (Kali Yuga / Einherjar / King List)

Every precessional number is a PRODUCT of factors of 60. This is the fundamental connection between Sumerian mathematics and the encoding hypothesis: the base-60 system is the natural language for expressing precessional astronomy.

The Maya Connection

The Maya Long Count calendar uses a modified base-20/base-18 system:

Key observation: The tun (360 days) breaks the base-20 pattern by using 18 instead of 20 — SPECIFICALLY to generate 360. This is the same number as the Sumerian circle and the Egyptian administrative year. The b'ak'tun (144,000 days = 72 × 2,000) is a direct multiple of 72. The Grand Cycle of 1,872,000 days ≈ 5,125 years — close to one-fifth of the precessional cycle.

CRITICAL ASSESSMENT — Strengths and Weaknesses

Strengths of the Encoding Thesis

1. Mathematical precision: The numbers are not approximate — they are EXACT matches across cultures (432,000 appears identically in Sumerian, Norse, and Hindu contexts)
2. Internal consistency: All the numbers derive from a single framework through simple arithmetic
3. Physical basis: The numbers correspond to a REAL astronomical phenomenon (precession), not an arbitrary schema
4. Cross-cultural distribution: The numbers appear in traditions with no documented contact during the periods when the myths were formed
5. Scholarly foundation: The thesis originates with a tenured MIT professor (de Santillana), not a fringe researcher.

Weaknesses and Counterarguments

1. Selection bias / cherry-picking: Proponents catalog numbers that fit and ignore those that don't (7, 13, 40, 1,000 are equally "sacred" in many traditions but have no precessional significance)
2. Base-60 artifact: Any culture using or influenced by Sumerian base-60 mathematics will naturally generate multiples of 12, 60, 360, and 3,600 — these numbers are built into the mathematical system, not necessarily "encoded"
3. Late textual attestation: Many of the key texts (Plutarch on Osiris, Poetic Edda, surviving Surya Siddhanta) were written down AFTER Hipparchus — raising the possibility of post-Hipparchan contamination
4. No "smoking gun": No ancient text explicitly states, "We are encoding precessional knowledge in this myth." The encoding interpretation is inferred, never confirmed by source material
5. Unfalsifiability: Any number that fits is claimed as evidence; any that doesn't is dismissed as noise. This makes the thesis difficult to test rigorously

CROSS-REFERENCE INDEX

Counter-Arguments & Criticisms

The hypothesis that ancient myths encode precise mathematical or astronomical constants has been critiqued for methodological problems. Skeptics note that with sufficient numerical flexibility, almost any mythological narrative can be made to "encode" mathematical relationships, creating a form of data mining or numerology. De Santillana and von Dechend’s Hamlet’s Mill (1969), the seminal text in this field, has been criticized by classicists and historians of astronomy for selective evidence and speculative interpretation. While some ancient cultures demonstrably embedded astronomical information in myths, extending this to universal mathematical encoding lacks rigorous statistical controls for coincidence.

IMAGES

BIBLIOGRAPHY

• de Santillana, Giorgio, and Hertha von Dechend. Hamlet's Mill: An Essay on Myth and the Frame of Time. Gambit, 1969. DOI: 10.1086/ahr/75.7.2009
• Neugebauer, Otto. A History of Ancient Mathematical Astronomy. Springer, 1975.
• Neugebauer, Otto. Astronomical Cuneiform Texts. Lund Humphries, 1955. DOI: 10.1007/978-1-4612-5507-9
• Plutarch. De Iside et Osiride (On Isis and Osiris). c. 100 CE. ISBN: 9788881470716. DOI: 10.1515/9783050092270.135
• Jacobsen, Thorkild. The Sumerian King List. University of Chicago Press, 1939. DOI: 10.1017/s0035869x00097501
• Berossus. Babyloniaca. c. 280 BCE (fragments via Alexander Polyhistor and Syncellus).
• Hancock, Graham. Fingerprints of the Gods. Crown, 1995.
• Hancock, Graham. Magicians of the Gods. Coronet, 2015. ISBN: 9781444779677
• Sweatman, Martin B., and Dimitrios Tsikritsis. "Decoding Göbekli Tepe with Archaeoastronomy: What Does the Fox Say?" Mediterranean Archaeology and Archaeometry 17, no. 1 (2017): 233–250.
• Burgess, Ebenezer (trans.). Surya Siddhanta: A Text-Book of Hindu Astronomy. 1860; reprinted Motilal Banarsidass. DOI: 10.2307/592174
• Larrington, Carolyne (trans.). The Poetic Edda. Oxford World's Classics, 2014.
• Waerden, B. L. van der. "The Great Year in Greek, Persian and Hindu Astronomy." Archive for History of Exact Sciences 18, no. 4 (1978): 359–383.
• Hunger, Hermann, and David Pingree. Astral Sciences in Mesopotamia. Brill, 1999.
• Rochberg, Francesca. The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture. Cambridge University Press, 2004.
• Aveni, Anthony F. Skywatchers of Ancient Mexico. University of Texas Press, 1980. ISBN: 9780292775572

RESEARCH GAPS

Consolidated from [1] AI source. Last Updated: Feb 27, 2026

Corrections

• Hancock, Graham — invalid ISBN 9784881353486 removed. No verified replacement could be found, and supplying an unverified number would be worse than none. The entry's author, title, publisher and year are unchanged.
• Hunger, Hermann, and David Pingree — invalid ISBN 9789004101272 removed. No verified replacement could be found, and supplying an unverified number would be worse than none. The entry's author, title, publisher and year are unchanged.

• Larrington, Carolyne (trans.) — invalid ISBN 1420957058 removed. No verified replacement could be found, and supplying an unverified number would be worse than none. The entry's author, title, publisher and year are unchanged.