Sigillum Dei Aemeth: History, Provenance, Debate, and the E47 Computational Hypothesis

Sigillum Dei Aemeth: History, Provenance, Debate, and the E47 Computational Hypothesis

Executive summary

The Sigillum Dei—“Seal of God,” and in John Dee’s later vocabulary Sigillum Dei Aemeth/Emeth, “Seal of God: Truth”—is best understood not as a single immutable diagram but as a transmitted family of ritual diagrams whose geometry, inscriptions, orientation, and claimed functions changed across manuscript traditions. Its deepest securely documentable layer belongs to the medieval Liber iuratus Honorii (Sworn Book of Honorius), but the date, authorship, and early textual history of that work remain contested. Jean-Patrice Boudet emphasizes the unusual preservation and dating problems of the Liber iuratus and identifies British Library Sloane MS 3854, copied in the mid-fourteenth century, as the oldest and best of the principal surviving witnesses he examined. This is an important correction to the common internet claim that Sloane MS 313 is simply “the oldest manuscript.” Sloane 313 is exceptionally important for a different reason: it is the principal Liber iuratus witness that actually preserves both the text and a drawing of the seal, at fol. 4r. 

The medieval seal combines circular boundaries with fivefold and sevenfold structures, divine and angelic names, and a form of the Great Schemhamphoras/Shem ha-Mephorash. It was not merely decorative. In the Liber iuratus tradition it belongs to ritual programs concerned with theurgy, spirit operations, and, at the most elevated level, the acquisition of a vision of God. Robert Mathiesen, Boudet, Gösta Hedegård, Katelyn Mesler, Frank Klaassen, L. S. Chardonnens, and Jan R. Veenstra have all contributed to placing that material within medieval learned ritual magic rather than treating it as an isolated occult emblem. 

The evidence also shows that there was no single mechanically copied medieval archetype. Chardonnens and Veenstra document significant variation among Sloane 313, Sloane 3853, Berengario Ganell’s Summa sacre magice, later Solomonic witnesses, and the physical lead seal rediscovered at Doornenburg Castle. Some variants shift syllables, change angelic names, add elements, or alter how fivefold and sevenfold components are drawn. Their 2014 study argues that the late-medieval Doornenburg seal combines features associated with both Northwest-European Liber iuratus transmission and a more southern Ganell tradition. 

John Dee did not invent the Sigillum Dei. What he did in 1582 was more historically interesting: he inherited a disputed manuscript tradition, compared variants, and within his recorded angelic conferences developed a substantially revised, operational version. British Library Sloane MS 3188 preserves Dee’s first five books of conferences from 22 December 1581 to 30 May 1583; a Sigillum drawing used for comparison by modern scholars occurs at fol. 30r. The British Library explicitly describes the manuscript as records of messages delivered through Dee’s angelic sessions. Thus the phrase Mysteriorum Libri Quinti should not be treated as a sixteenth-century “printed source”: the primary object is manuscript Sloane 3188; modern printed editions and transcriptions are secondary publication layers. 

Dee’s royal connection is real but routinely exaggerated. Scholarship documents his close relationship with Elizabeth I and her patronage environment; recent historical work describes him as operating through court networks and as an adviser associated with Elizabeth. What this investigation did not find is primary evidence that Dee formally presented the Sigillum Dei Aemeth itself to Elizabeth I, that Elizabeth owned it, or that the seal was a piece of royal regalia. The secure connection is Dee ↔ Elizabethan court, not Sigillum ↔ royal ownership. The British Library’s Royal MS 17 A XLII, meanwhile, is genuinely part of the Royal manuscript collection and preserves a fifteenth-century English/Latin Sworn Book witness, but its royal-library provenance likewise does not demonstrate a monarch’s ritual use of the seal. 

The physical objects traditionally identified as Dee’s magical equipment require equal caution. The British Museum holds three wax discs associated with Dee, but Silke Ackermann and Louise Devoy’s detailed provenance study concluded that a direct Dee provenance for the group remained to be proven. The associated obsidian “spirit mirror” has generated a parallel—and especially revealing—debate. A 2021 Antiquity study used portable X-ray fluorescence to demonstrate that the mirror is made from Mexican obsidian, specifically material associated with the Pachuca source. That finding recasts an iconic “Elizabethan magical” object within the history of Indigenous Mesoamerican manufacture, colonial movement of objects, European collecting, and subsequent reinterpretation. The researchers stress both the changing cultural biography of the object and the uncertainty surrounding exactly how Dee acquired it. DOI: 10.1016/j.shpsa.2011.11.007 for Ackermann and Devoy; DOI: 10.15184/aqy.2021.132 for Campbell et al. 

The Plate-City E47 invariant belongs to an entirely different evidentiary category. As supplied in the Plate-City material, it begins with a (125)-dimensional carrier

[ V=V_2^{\otimes3},\qquad \dim V=5^3=125, ]

and a self-adjoint Casimir-like operator (C) with eigenvalue/multiplicity data

[ \begin{array}{c|rrrrrrr} C&0&2&6&12&20&30&42\ \hline \dim E_C&1&9&25&28&27&22&13. \end{array} ]

The polynomial filter

[ K=(C-6I)(C-30I) ]

therefore has

[ E_{47}:=\ker K=E_6\oplus E_{30}, ]

so, conditional on those premises,

[ \boxed{\dim E_{47}=25+22=47}, \qquad \boxed{\Omega_{47}=\frac{47}{125}=0.376}. ]

That is an internally exact algebraic construction. It is not presently a historical property of the Sigillum Dei. No medieval or Dee-era evidence reviewed here provides a natural (125)-state carrier, a Casimir with those multiplicities, or an intentional 47-dimensional sector. Therefore any statement that the historical Sigillum “encodes E47” would currently outrun the evidence.

There is, however, a legitimate research program hiding inside the comparison. A Sigillum witness can be treated as a measured symbolic-geometric object: image coordinates become vertices, predeclared relationships become edges, an adjacency matrix (A) produces a graph Laplacian (L=D-A), and eigendecomposition reveals modes associated with rotation, repeated inscriptions, or other structural regularities. A projector

[ P_E=U_EU_E^{\mathsf T} ]

can then isolate a pre-specified spectral subspace. This can test whether sevenfold or other cyclic symmetries persist across witnesses. What cannot legitimately be done is choose the representation, graph, filter, and eigenspaces after inspecting the result until “47” appears. A valid E47 test must independently justify the (125)-state representation and pre-register what would count as a 47-dimensional invariant before the spectral computation is run.

The strongest overall conclusion is therefore twofold:

[ \boxed{\text{The Sigillum is historically a transmitted ritual-symbolic system.}} ]

[ \boxed{\text{E47 is, at present, a modern mathematical hypothesis about representations of such systems.}} ]

Their intersection can be scientifically productive only when manuscript history and computational modeling remain explicitly separated.

Manuscripts, primary evidence, and textual witnesses

The surviving evidence is more complex than a straight line from “medieval seal” to “Dee seal.” It consists of at least three interacting bodies of material: Liber iuratusmanuscripts; southern or Solomonic variants such as Ganell and later Clavicula Salomonis witnesses; and Dee’s own angelic diaries and surviving artifacts. Boudet’s work is particularly valuable because it prevents the chronology from being built around whichever digitized image happens to be most familiar online. 

WitnessDate / locationProvenance and statusSigillum evidence and principal differencesBL Sloane MS 3854, ff. 112ra–139raMid-14th c.; British LibraryBoudet’s oldest and best-quality principal Liber iuratus witness.Important textual witness for construction and ritual, but not one of the principal witnesses preserving a drawn Sigillum. It is therefore critical for distinguishing textual prescription from later images. BL Sloane MS 313, Sigillum at f. 4rBL catalog gives broad 14th–16th c.; Chardonnens/Veenstra place it in the second half of the 14th c.British Library Sloane Collection. Ownership/annotation evidence has been associated with both John Dee and Ben Jonson; the exact sequence of ownership should be checked against codicological evidence rather than repeated from secondary summaries.Exceptionally important because Chardonnens/Veenstra call it the sole Liber iuratus manuscript containing both the text and a drawn seal. Several spellings and placements diverge from the presumed prescription; the study shows how scribal misunderstandings could migrate from prose directions into geometry. BL Sloane MS 3853, Sigillum at f. 127v16th c.; British LibraryEarly-modern magical miscellany in English and Latin.Recontextualizes the seal explicitly in a Solomonic frame; the relevant text calls it a divine seal connected to King Solomon. It adds features absent from some earlier versions, including repeated Hebrew divine-name material. Chardonnens/Veenstra regard it as evidence of post-medieval transformation. BL Sloane MS 3885, ff. 58–96Mid-16th c. in Boudet’s stemmatic discussion; British LibraryOne of Boudet’s principal Liber iuratuswitnesses.Preserves textual variants but is not among the key surviving drawn seals. Its readings are important in critical reconstruction precisely because image and prose traditions do not always coincide. BL Royal MS 17 A XLII15th c.; British Library Royal CollectionOfficial BL record identifies it as Sworne Book of Honorius or Liber iuratus Honorii; English and Latin.ff. 2r–15r preserve chapters of the Sworn Book; subsequent folios include suffumigations, angel/spirit lists, and ritual material. It is textually important but does not provide the same drawn Sigillum witness as Sloane 313. Its membership in the Royal Collection is a provenance fact, not evidence of royal ritual practice. Kassel, 4º MS astron. 3, Ganell’s Summa sacre magice, Sigillum at f. 104rManuscript 15th c.; work composed c. 1346Chardonnens/Veenstra report that this manuscript belonged to John Dee.Represents a southern-European line associated with Berengario Ganell. Its Sigillum often corresponds more closely to detailed construction instructions than the Sloane 313 image does. It is crucial evidence that the history is not purely English. BL Sloane MS 3188, drawing compared by scholars at f. 30rDee’s conferences, 22 Dec. 1581–30 May 1583Passed through later owners including Elias Ashmole; eventually through Hans Sloane and the Sloane collection into the national collections. The current BL catalog provides a digital-item record, but its images are presently marked unavailable during recovery of BL systems.This is the Dee layer, not a medieval archetype. Dee inherited older Sigillum material but the angelic conferences generated a significantly revised operational form. The manuscript is the primary record behind the Mysteriorum Libri Quinti designation. Bodleian MS Michael 276Early-modern Italian Clavicula Salomoniswitness; often dated to the 17th c., but an item-level Bodleian date was not independently confirmed in the catalog interface located for this reportPart of the Michael manuscript collection; the Bodleian states that Heimann Joseph Michael’s manuscript collection was purchased in 1848.A later Solomonic comparator. Chardonnens/Veenstra use Michael 276 repeatedly to compare readings; some of its angel-name and syllabic sequences are notably divergent. It should not be treated as a direct copy of Sloane 313. Bodleian MS Aubrey 24John Aubrey copy, 1674Bodleian Aubrey collection; catalogued as a manuscript copied by Aubrey from an Italian source.A late reception witness. Chardonnens/Veenstra show that it preserves some older sequences but also changes geometry: a hexagram appears where the earlier comparison requires fivefold material, forcing duplication of letters to fill the added angle. That makes it particularly valuable for studying diagrammatic mutation. 

A particularly significant material witness lies outside these manuscript repositories. In 2011 researchers re-examined a lead disc concealed in a brick at Doornenburg Castle in the Netherlands and identified it as a late-medieval or early-sixteenth-century Sigillum Dei. The associated brick was tentatively dated to the first decade of the sixteenth century, while palaeographic assessment placed the seal itself approximately in the fifteenth or early sixteenth century. Its combination of textual and visual features makes it powerful evidence that physical Sigilla circulated before Dee’s 1582 redesign. 

The Doornenburg artifact also changes the question of function. It had been fixed into a brick and concealed, so it could no longer have been manipulated in the ways required by the rituals in the Liber iuratus or Ganell. Chardonnens and Veenstra therefore consider possibilities such as protective deposition or deliberate concealment while explicitly acknowledging that its original purpose cannot be established. 

For printed comparators, Athanasius Kircher reproduced and interpreted the Sigillum in Oedipus Aegyptiacus, vol. II.2, p. 480, published within the 1652–54 Oedipus sequence. Chardonnens and Veenstra find errors in Kircher’s version but also features connecting it to a Hispano-Italian transmission line. This makes Kircher valuable evidence for seventeenth-century learned reception, not a neutral reproduction of Dee. 

For modern editions, Gösta Hedegård’s Liber Iuratus Honorii: A Critical Edition of the Latin Version of the Sworn Book of Honorius (2002) is the key philological edition. Boudet regarded its textual work as valuable while arguing that dating and historical interpretation still required further investigation. 

The primary-access situation in 2026 is uneven. The British Library catalog currently describes itself as an interim system recovering from its cyberattack, and records such as Sloane 3188 and Royal 17 A XLII show digitized-content links whose images are presently unavailable. The manuscripts remain catalogued and may be requested under the Library’s current reading-room procedures. The Bodleian’s Digital Bodleian provides high-resolution access to many Michael holdings, but this research did not locate a public Digital Bodleian object page specifically for Michael 276; therefore it would be unsafe to say that this particular manuscript is fully digitized. 

Provenance, transmission, and royal or elite connections

A rigorous provenance narrative has to distinguish textual transmission, ownership, and patronage. They are not interchangeable.

13th–14th centuriesFormation of theLiber iuratustradition remainsdebatedmid-14th centurySloane 3854,oldest/bestprincipal survivingLiber iuratus witnessin Boudet's studyc. 1346Berengario Ganellcomposes Summasacre magicelater 14th centurySloane 313preserves text plus adrawn Sigillum Dei15th centuryRoyal MS 17 A XLIIpreserves anEnglish/Latin SwornBook witness15th–early 16thcenturyDoornenburg leadSigillum probablymanufactured1581–1583Dee records firstfive books of angelicconferences inSloane 31881582Dee's revisedSigillum Emethemerges within theangelic-operationcontext1652–1654Kircher prints andinterprets a Sigillumin OedipusAegyptiacus1659Casaubon printslater portions ofDee's angelicrecords1672Elias Ashmoleacquires themanuscript nowSloane 31881674John Aubrey copiesthe material nowBodleian MS Aubrey241753Sloane's collectionsenter the newBritish Museum byparliamentarypurchase1848Bodleian purchasesHeimann JosephMichael's manuscriptcollection2011Doornenburg seal isreidentified andinvestigated2014Chardonnens andVeenstra publishdetailedcomparative study2016Royal College ofPhysicians stagesmajor John Deelibrary exhibition2021pXRF studyestablishes Mexicangeological source ofDee-associatedobsidian mirror2026BL manuscriptcatalog is online;several legacydigitized imagesremain temporarilyunavailableSigillum Dei: transmission, ownership, and modern study

Show code

The medieval milestones and witness dating above follow Boudet, the British Library catalog, and Chardonnens/Veenstra; the Dee manuscript history and current digital status follow the British Library’s Sloane 3188 record.  The modern milestones are documented by the Royal College of Physicians, Bodleian, and Antiquity. 

The medieval “Honorius” layer. The Liber iuratuspresents itself under the authority of Honorius of Thebes/Honorius son of Euclid, but modern historians do not treat this persona like the verified author of a conventional scholastic treatise. Boudet stresses serious problems of dating, preservation, and historical interpretation. Mathiesen’s work argues for a thirteenth-century ritual stratum centered on the beatific vision, but the oldest surviving manuscript evidence is later. The responsible formulation is therefore “a medieval Liber iuratus tradition attributed to Honorius,” not “a book demonstrably written by Honorius son of Euclid in year X.” 

The Dee layer. Dee occupied a genuinely elite intellectual environment. Scholarship on his patronage emphasizes Elizabeth I as a particularly important patron and shows Dee constructing intellectual and political projects in relation to the Tudor court. The 2021 Antiquity study, synthesizing Dee scholarship, describes him as scientific adviser and astrologer to Elizabeth and places him in European court and diplomatic networks. 

That does not prove a royal Sigillum. Sloane 3188 documents the seal in an angelic-working context with Edward Kelley and other scrying arrangements, not as an item commissioned by or formally delivered to Elizabeth. In the sources reviewed for this report, no inventory, presentation record, royal warrant, gift entry, or Elizabethan ownership mark was found documenting a presentation of the Sigillum itself to Elizabeth I. The distinction matters because popular retellings often silently transform “Dee advised Elizabeth” into “Elizabeth possessed or authorized Dee’s magical apparatus.” The former is supported; the latter has not been demonstrated here. 

Royal MS 17 A XLII supplies a different kind of royal connection. It is now officially part of the British Library Royal Collection and contains the Sworne Book of Honorius. That is meaningful provenance, but there is no warrant for interpreting the shelfmark as proof that a particular English sovereign commissioned, read, or ritually used its Sigillum material. 

Elite collectors are much more securely documented. Sloane 3188’s later history involves Elias Ashmole and Sir Hans Sloane. The British Library record notes its passage through several owners before Sloane and explains that the Sloane manuscripts entered the national collection in 1753 through the parliamentary acquisition establishing the British Museum. This is one reason modern “Dee provenance” is itself layered: the object we now consult is partly the product of seventeenth- and eighteenth-century antiquarian collecting. 

Sloane 313 is similarly associated in scholarship with both Dee and playwright Ben Jonson. Because secondary descriptions of the sequence of ownership are not always consistent, this is precisely the sort of provenance point that should be checked directly against ownership inscriptions and Roberts and Watson’s reconstruction of Dee’s library before a definitive transfer chronology is printed. Chardonnens and Veenstra nevertheless establish the importance of the manuscript to the Dee-related transmission. 

Dee’s European contacts supply still another elite context. The literature places him amid Habsburg and Central European intellectual circles; Campbell and colleagues even note a scholarly suggestion that acquisition of an obsidian object by Emperor Rudolf II may have been influenced by knowledge of Dee’s mirror. That proposition concerns a related magical object and cultural milieu, not documentary proof that Rudolf possessed Dee’s Sigillum. 

Scholarship, origin, and the debate over what the seal “does”

The modern scholarly trajectory has progressively moved the Sigillum away from two misleading extremes: treating it as a purely decorative piece of “sacred geometry,” or treating every detail in modern occult reconstructions as a stable secret code handed down unchanged from antiquity.

Boudet and the dating problem. Jean-Patrice Boudet’s 2002 study remains foundational because it treats the Liber sacratus sive juratus as a difficult historical source rather than as a transparent manual. He emphasizes the scarcity and complicated state of the witnesses and identifies Sloane 3854 as the mid-fourteenth-century manuscript of highest quality among the principal copies. His title—linking theurgy, angelology, and beatific vision—also accurately reflects the theological ambition of parts of the work. DOI: 10.3406/mefr.2002.9254. 

Hedegård and philological reconstruction. Gösta Hedegård’s 2002 critical Latin edition created the indispensable textual base for comparing variant readings. Its importance is precisely that the Sigillum’s inscriptions are unstable: one cannot infer symbolism reliably from a modern redrawn seal without first asking which manuscript reading is being represented. 

Mathiesen, Fanger, Mesler, and medieval ritual magic. Mathiesen’s influential study of the ritual for attaining the beatific vision placed the Sworn Bookwithin medieval learned magical practice, while scholarship collected by Claire Fanger and later work by Mesler examine its angelological and Christian-theurgical dimensions. Chardonnens and Veenstra explicitly situate their material study in dialogue with this scholarship and with Frank Klaassen’s broader history of illicit learned magic. 

The implication is important: calling the Sigillum “a device for summoning angels” is not entirely wrong, but it is incomplete. The textual tradition contains a hierarchy of operations and claims, including theurgic aspirations to divine vision as well as operations involving celestial and other spirits. Its meaning is therefore generated by the diagram plus ritual text plus preparation plus theological assumptions, not by geometry alone. 

Chardonnens and Veenstra and material transmission. Their article, “Carved in Lead and Concealed in Stone,” Magic, Ritual, and Witchcraft 9.2 (2014), pp. 117–156, DOI 10.1353/mrw.2014.0015, is especially important for the present inquiry because it compares manuscript geometry at high granularity rather than simply reproducing a canonical modern seal. Their tables show specific orthographic differences in the first heptagon, Creator names, angelic names, pentagram spaces, and other sectors. They conclude that younger witnesses often drift farther from particular Honorius readings and that the Doornenburg artifact crosses apparent textual families. 

That finding cuts directly against a naive “perfect invariant diagram” model. The historical object displays structured persistence under mutation, not pixel-perfect invariance. Fivefold/sevenfold architecture can persist while spellings, assignments, orientations, and local structures change. For computational work, that suggests that a meaningful invariant—if one exists—would more plausibly be a structural or equivalence-class invariant than an invariant requiring every letter to occupy one immutable coordinate.

Dee scholarship and the meaning of his revision.Deborah Harkness’s John Dee’s Conversations with Angels: Cabala, Alchemy, and the End of Naturesituates the angelic conversations within Dee’s broader search for authoritative knowledge rather than treating them as an eccentric appendage to an otherwise “scientific” career. Her account emphasizes his library, learned sources, salvific ambitions, and intellectual networks. Book DOI: 10.1017/CBO9781107340909. 

Stephen Clucas’s edited John Dee: Interdisciplinary Studies in English Renaissance Thought likewise treats Dee’s mathematics, natural philosophy, religion, and occult interests within the same Renaissance intellectual world rather than projecting a modern science/magic binary backward. DOI: 10.1007/1-4020-4246-9. 

The critical point for the Sigillum is that Dee was both a receiver and a transformer of tradition. Chardonnens/Veenstra and modern transcriptions of the Dee diaries indicate that he knew older Sigillum material and encountered discrepancies. The angelic sessions did not simply certify one medieval diagram; they generated a distinctly Dee-specific reworking. 

Kircher’s interpretation belongs to still another intellectual mode. His seventeenth-century treatment tries to explain the sigil within his enormous comparative program of Egyptian, Hebrew, Christian, Arabic, and other symbolic traditions. Chardonnens/Veenstra find genuine transmitted material in his image but also errors. Kircher therefore shows how a diagram can acquire a new scholarly interpretation while retaining recognizable inherited geometry. 

Taken together, the scholarship supports four propositions:

First, the Sigillum is older than Dee. Second, Dee’s Aemeth form is a consequential revision, not the medieval original. Third, the manuscript tradition is variant and geographically distributed, not a single perfectly reproduced schema. Fourth, its historically documented function is ritual and theurgical, whereas treating it as a matrix, automaton, spectral filter, or computational device is a modern analytical transformation and must be labeled as such. 

Modern controversies, archival access, and renewed interest

The most consequential modern controversy is not a dramatic manuscript forgery scandal. It is the quieter and academically more important question of how securely famous “Dee objects” can actually be tied to Dee, and how much later collectors and curators shaped their identities.

Ackermann and Devoy reviewed six British Museum objects associated with Dee—including three wax seals, an obsidian mirror, a gold disc, and a crystal ball—and concluded that direct association of the objects with Dee remained incompletely proven. Their method is exemplary: rather than assuming inherited labels are facts, they compare object features, collection histories, and Dee’s manuscript descriptions. DOI: 10.1016/j.shpsa.2011.11.007. 

The British Museum’s wax discs are consequently better described as objects historically associated with Dee whose relationship to the manuscript instructions is strong enough to warrant study, but whose complete chain of custody is not demonstrable back to Dee in every respect. This is more precise than simply captioning them “John Dee’s original seals.” 

The obsidian mirror sharpens that methodological problem. Campbell and colleagues note that the exact path by which the mirror reached Dee is unknown and that doubts had previously been raised even about whether the object was genuinely Dee’s or might be a later copy. Their pXRF work demonstrated a Mexican geological origin, with Dee’s mirror matching the Pachuca source. They argue that this strengthens the historical interpretation while simultaneously demanding a wider history: Indigenous Mexican manufacture, Spanish colonial transfer, European collecting, Dee’s appropriation of the unfamiliar object, and modern museum display. DOI: 10.15184/aqy.2021.132. 

That is also the clearest ethical-cultural issuesurrounding the broader Dee assemblage. It would be misleading to allow the charismatic “English magician” story to erase the pre-European biography of an Indigenous Mesoamerican object. Campbell et al. explicitly emphasize how collecting and display create new meanings as objects cross cultural settings. This issue pertains directly to the mirror and related Mexican artifacts; it should not be projected onto the European manuscript Sigillum itself as though the medieval seal were Mesoamerican. 

A second controversy concerns reconstruction fidelity. Chardonnens and Veenstra noted in 2014 that the British Museum’s online image of a large wax sigil was then displayed in an orientation opposite to Sloane 3188 f. 30r. More broadly, their comparison demonstrates that a redrawn “canonical Sigillum” can silently combine readings from different witnesses. Even when no fraudulent intent exists, normalization can erase precisely the errors, shifts, and variants that matter historically. 

This leads to a useful distinction among three categories:

Facsimile means a faithful reproduction of one identified witness.

Critical reconstruction means an editorial diagram that explicitly chooses readings among witnesses.

Modern symbolic reconstruction means a new diagram inspired by the historical form for occult, artistic, mathematical, or computational purposes.

Conflating those categories is one of the largest sources of misinformation about the Sigillum.

I found no credible evidence in this research that Sloane MS 3188 or Sloane MS 313 themselves are modern forgeries. “Forgery controversy” should therefore not be presented as though the core manuscripts are suspect. The stronger attribution controversy concerns museum artifacts and modern derivative diagrams, while textual criticism concerns which readings are early, secondary, erroneous, or recontextualized. 

Renewed academic and public attention is nevertheless unmistakable. The Doornenburg object was newly identified and researched in the 2010s; the Royal College of Physicians staged “Scholar, courtier, magician: the lost library of John Dee” in 2016; British Library digitization initiatives made Dee material much easier to inspect before the library’s recent infrastructure disruption; SloaneLab has developed digital approaches to the Sloane collections; and the 2021 mirror study showed how laboratory archaeology can transform the biography of a famous magical artifact. 

There is also renewed commercial and popular occult interest. A representative 2026 commercial page, for example, presents the Sigillum as intrinsically protective and safe to use. Such material is valuable evidence for modern reception, but it is not evidence for medieval function, Dee’s intentions, or the precise textual history of the diagram. 

The archival picture as of September 2026 is therefore:

RepositoryRelevant materialCurrent research statusBritish LibrarySloane 313, 3188, 3853, 3854, 3885; Royal 17 A XLII; additional Dee MSSCatalog records online. Some legacy digitized viewers, including Sloane 3188 and Royal 17 A XLII, are currently marked unavailable during recovery from the BL cyberattack. Bodleian LibrariesAubrey 24, Michael 276 and related Solomonic materialCatalog infrastructure online; Michael collection background is documented. This search did not find full public Digital Bodleian imaging specifically for Michael 276, so digital availability should be verified before a project depends on it. British MuseumWax discs and other objects traditionally associated with Dee, including obsidian mirrorOnline object records; mirror is a major focus of provenance and archaeometric research. Doornenburg Castle / scholarly publicationLead Sigillum in brickArchaeological/material witness published in detail, providing pre-Dee physical evidence. 

E47 and a rigorous computational reading of the Sigillum

The E47 question becomes much clearer once three mathematical layers are separated:

[ \boxed{\text{historical diagram}} \neq \boxed{\text{chosen mathematical representation}} \neq \boxed{\text{resulting invariant}}. ]

What E47 means in the Plate-City formulation

Taking the Plate-City specification supplied in this project as its formal definition,

[ V=V_2^{\otimes3}, \qquad \dim V=5^3=125. ]

The listed Casimir eigenvalues are

[ \sigma(C)={0,2,6,12,20,30,42}, ]

with respective total eigenspace dimensions

[ (1,9,25,28,27,22,13). ]

These add correctly:

[ 1+9+25+28+27+22+13=125. ]

The values themselves have the familiar quadratic form

[ j(j+1),\qquad j=0,1,\ldots,6, ]

and the dimensions correspond to representation multiplicities

[ 1,;3,;5,;4,;3,;2,;1 ]

times (2j+1). Thus the stated spectral decomposition is algebraically coherent.

Now choose

[ K=(C-6I)(C-30I). ]

For any (C)-eigenvector with eigenvalue (c),

[ Kv=(c-6)(c-30)v. ]

Hence precisely the (c=6) and (c=30) sectors are annihilated:

[ \ker K=E_6\oplus E_{30}. ]

Since

[ \dim E_6=25,\qquad \dim E_{30}=22, ]

one obtains

[ \boxed{ E_{47}:=\ker K,\qquad \dim E_{47}=47. } ]

The orthogonal projector is

[ \boxed{ P_{47}=P_6+P_{30}, \quad P_{47}^2=P_{47}, \quad KP_{47}=0, \quad \operatorname{rank}P_{47}=47. } ]

And

[ \boxed{ \Omega_{47}

\frac{\dim E_{47}}{\dim V}

\frac{47}{125}

0.376. } ]

There is also a useful error correction to preserve in any future E47 graphic. On the seven listed (C)-eigenvalues,

[ K^2: \quad 32400,;12544,;0,;11664,;19600,;0,;186624. ]

Thus

[ \lambda_{\max}(K^2)=186624. ]

For

[ \Gamma_\epsilon=I-\epsilon K^2, ]

strict spectral contraction of every non-kernel mode requires

[ |1-\epsilon\lambda|<1, ]

hence

[ \boxed{ 0<\epsilon< \frac{2}{186624}

\frac{1}{93312}. } ]

If one instead demands non-oscillatory decay, the stricter condition is

[ \boxed{ 0<\epsilon\le \frac{1}{186624}. } ]

This parallels the earlier distinction in the sevenfold consensus model between the full stability interval (2/\lambda_{\max}) and the stricter no-sign-reversal interval (1/\lambda_{\max}).

Where the Sigillum comparison is legitimate

The historical Sigillum gives us observable structures that can reasonably motivate mathematical questions: circles, cyclic letter sequences, repeated sevenfold relations, fivefold geometry, adjacency along drawn lines, and repeated groups of names. Chardonnens and Veenstra’s cross-witness comparison demonstrates that several of these structures persist while individual textual placements vary. That is a sound reason to ask whether the tradition contains measurable structural invariants under scribal transformation. 

A neutral graph-spectral model could therefore begin with

[ G=(V,E,W) ]

where (V) is a set of identified symbols or geometric landmarks, (E) is a predeclared relationship such as drawn connection or cyclic succession, and (W) optionally represents geometric distance or another explicitly defined weight.

Then

[ A=(a_{ij}), \qquad D_{ii}=\sum_j a_{ij}, \qquad L=D-A. ]

For a symmetric graph,

[ L=U\Lambda U^{\mathsf T}. ]

A candidate eigenspace (E) represented by columns (U_E) has orthogonal projector

[ \boxed{ P_E=U_EU_E^{\mathsf T}. } ]

This is the mathematically clean sense in which one can ask whether a measured Sigillum has an “invariant spectral sector.”

What must not happen is:

[ \text{Sigillum} \longrightarrow \text{choose arbitrary 125 states} \longrightarrow \text{adjust graph/filter} \longrightarrow 47 \longrightarrow \text{claim ancient encoding}. ]

That is numerology by model selection.

What an E47 hypothesis would actually test

A serious study could test increasingly strong hypotheses.

The weakest and most plausible hypothesis is that sevenfold geometry produces expected cyclic spectral degeneracies. If seven equally related nodes form (C_7), the Laplacian spectrum contains paired Fourier modes because clockwise and counterclockwise harmonics have equal eigenvalues.

A stronger hypothesis would ask whether inscriptional patterns are phase-correlated with the sevenfold geometry more strongly than expected under constrained random permutations of the same letters or names.

Stronger still would be a cross-witness invariant hypothesis: after registering Sloane 313, Ganell, Sloane 3853, Dee f. 30r, Michael 276, Aubrey 24, and the Doornenburg seal into a common structural ontology, does a low-dimensional spectral subspace survive their textual mutations? Chardonnens/Veenstra’s evidence makes this a historically meaningful question because they already demonstrate both persistence and mutation across those witnesses. 

The specifically E47 hypothesis is stronger again:

There exists an independently motivated 125-dimensional state representation of the Sigillum tradition and an independently defined operator whose invariant sector has rank 47.

At present, the historical literature reviewed here supplies no independent reason for 125 states. The obvious historical counts instead include fivefold and sevenfold geometries and a large outer name/letter sequence. Therefore (125=5^3) must currently be regarded as a Plate-City representational choice, not a manuscript-derived constant.

That is not fatal to the research program. It simply changes the language from

“We discovered E47 in Dee’s seal”

to

“We are testing whether a pre-specified E47 representation can model some structural features of the seal better than competing representations.”

That version is scientifically testable.

Computational pipeline

No

Yes

Exact manuscript witness
high-resolution image

Image registration
center, scale, orientation

Symbol and geometry segmentation
with uncertainty labels

Predeclared node ontology
letters, names, vertices, intersections

Predeclared edge rule

Adjacency A
or multiplex adjacency

Degree D and Laplacian
L = D - A

Eigendecomposition
L = U Λ Uᵀ

Pre-registered candidate modes

Projector
P = U_E U_Eᵀ

Null models
shuffle / rotation / perturbation

Cross-witness replication

Independent
125-state rationale?

Report spectral structure
without E47 claim

Test rank-47 hypothesis
against controls

Show code

Small synthetic example

Take seven abstract symbols with coordinates

[ x_j= \left( \cos \frac{2\pi j}{7}, \sin \frac{2\pi j}{7} \right), \qquad j=0,\ldots,6. ]

Define adjacency only between cyclic neighbors,

[ A_{jk}= \begin{cases} 1,&k=j\pm1\pmod7,\ 0,&\text{otherwise}. \end{cases} ]

Every vertex has degree two, so

[ D=2I, \qquad L=2I-A. ]

The exact eigenvalue formula is

[ \lambda_m

2-2\cos\left(\frac{2\pi m}{7}\right), \qquad m=0,\ldots,6. ]

Numerically, the generated example gives

[ \boxed{ \sigma(L)= { 0,; 0.7530203963,; 0.7530203963,; 2.4450418679,; 2.4450418679,; 3.8019377358,; 3.8019377358 }. } ]

The zero eigenspace is

[ \ker L

\operatorname{span}{\mathbf1}. ]

Its projector is

[ \boxed{ P_0= \frac17\mathbf1\mathbf1^{\mathsf T}. } ]

Therefore every entry of (P_0) is (1/7), exactly as the generated computation confirms.

Download the synthetic geometry plot

The paired Laplacian eigenvalues are the spectral signature of the ideal cyclic symmetry:

Download the synthetic spectrum plot

This example demonstrates the full logic

[ \boxed{ \text{coordinates} \to A \to L \to \sigma(L) \to \ker L \to P_0 } ]

without smuggling in a desired output.

It also illustrates the main warning: an authentic sevenfold Sigillum layer naturally gives a one-dimensional constant Laplacian kernel in this simple model, not (E_{47}). To obtain E47, a genuinely different and independently justified 125-state operator must be introduced.

Methodological checklist for an actual manuscript study

StageRequired procedureFailure conditionWitness controlTreat Sloane 313, Ganell, Sloane 3853, Sloane 3188, Michael 276, Aubrey 24, Doornenburg, etc. as separate datasets.Combining them into a synthetic “perfect seal” before analysis.ImagingUse high-resolution archival images; preserve folio, shelfmark, crop, orientation, pixel scale, and repository metadata.Working from Pinterest/Wikipedia redrawings without source registration.TranscriptionRecord every glyph with confidence score; preserve illegible and uncertain readings rather than silently correcting them.Normalizing spellings before measuring variation.GeometryEstimate center, ring radii, polygon vertices, crossings, and angular locations with error bars.Hand-selecting “ideal” coordinates that erase scribal variation.OntologyDecide before spectral analysis what counts as a node: characters, whole names, vertices, intersections, or layers.Changing node definitions until a desired dimension appears.AdjacencyPredeclare edge rules: drawn line, ring-neighbor, common region, textual succession, etc. Prefer a multiplex graph when relations differ.Treating semantic and geometric connections as interchangeable.Spectral testCompute (A,D,L,\Lambda,U); predefine candidate symmetry statistics.Searching all possible spectra for attractive numbers.Null modelsShuffle labels while preserving frequencies; rotate layers; perturb coordinates within measurement error; compare against degree-preserving random graphs.Calling any degeneracy “significant” without a baseline.Cross-witness validationFit hypotheses on one group of witnesses and test on independent witnesses.Using every manuscript to construct and test the same hypothesis.E47 pre-registrationSpecify the 125 states, operator (C) or (K), and criterion “rank = 47” before seeing the target spectrum.Choosing (K) retrospectively because two eigenspaces happen to sum to 47.ReproducibilityPublish image identifiers, coordinate CSV/JSON, transcription table, code, environment lockfile, random seeds, and source hashes.A result that can only be reproduced from an unpublished hand-cleaned image.Historical interpretationPhrase output as “modern model detects X in witness Y.”Recasting a statistical pattern as Dee’s or Honorius’s conscious intention without documentary evidence.

Conclusions, source priorities, and unresolved questions

The history is stronger than the mythology and more interesting than the simplified story.

The medieval Sigillum Dei was already a sophisticated combination of geometry, sacred names, and ritual prescription before Dee. Sloane 3854 anchors the principal Liber iuratus tradition in the mid-fourteenth century; Sloane 313 supplies the crucial surviving drawn seal at fol. 4r; Ganell shows a related southern tradition; Sloane 3853 demonstrates early-modern Solomonic recontextualization; the Doornenburg lead object establishes material use outside the manuscript page; and Dee’s Sloane 3188 documents a major 1582 transformation into the form later remembered as the Sigillum Dei Aemeth. 

The documentary evidence supports elite networks, but not the stronger folklore that the seal itself was an Elizabethan royal instrument. Dee’s relationship with Elizabeth I is historically substantive and worthy of study, yet no evidence located here establishes that Elizabeth commissioned, received, possessed, or used the Sigillum. The most defensible phrasing is that the Aemeth seal arose within the work of a scholar operating in Elizabethan court and patronage networks. 

The modern artifact story is equally conditional. Ackermann and Devoy show why labels such as “Dee’s wax seal” need provenance qualification, while the archaeometric study of the obsidian mirror demonstrates how a scientific test can simultaneously strengthen one attributional story and reveal a much older, non-European material biography. Those studies are models for how the E47 investigation should proceed: measure first, separate evidence classes, test alternatives, and allow the result to contradict the attractive story. 

For the E47 framework, the precise conclusion is:

[ \boxed{ E_{47}=\ker[(C-6I)(C-30I)] } ]

is an exact invariant inside the specified Plate-City (125)-dimensional representation because the designated eigenspaces have dimensions (25) and (22). Its ratio

[ \boxed{\frac{47}{125}=0.376} ]

is consequently exact inside that model.

But the historical Sigillum presently supplies neither

[ 125 ]

nor

[ 47 ]

as independently established manuscript invariants.

What it does supply is a highly promising object for graph-spectral investigation: cyclic orders, multiple nested layers, strong sevenfold organization, fivefold organization, repeated symbolic categories, textual variations, and multiple witnesses that permit genuine out-of-sample comparison. Chardonnens and Veenstra’s manuscript tables effectively provide the beginnings of exactly the kind of variant dataset that a modern computational study would need. 

Accordingly, the best first computational target is not “prove E47.” It is:

[ \boxed{ \text{Determine which geometric and symbolic modes remain invariant across independently transmitted Sigillum witnesses.} } ]

Only after that analysis should one ask whether those empirically stable modes admit a representation naturally equivalent to the Plate-City E47 sector.

The most important source priorities for such a project are:

Primary archival layer: British Library Sloane 313, Sloane 3854, Sloane 3853, Sloane 3885, Sloane 3188, and Royal 17 A XLII; Bodleian Michael 276 and Aubrey 24; the Kassel Ganell manuscript; and the Doornenburg artifact. The British Library and Bodleian catalog records should govern shelfmark/date/access claims over derivative websites. 

Critical-edition layer: Hedegård for the Latin Liber iuratus, Boudet for dating and historical interpretation, and manuscript-specific transcriptions checked against folios rather than relying on normalized occult editions. 

Comparative-material layer: Chardonnens and Veenstra, “Carved in Lead and Concealed in Stone,” DOI 10.1353/mrw.2014.0015, because it directly compares inscriptions, geometry, regional traditions, and a physical pre-Dee artifact. 

Dee intellectual-history layer: Deborah Harkness, John Dee’s Conversations with Angels, DOI 10.1017/CBO9781107340909; Stephen Clucas’s interdisciplinary Dee scholarship, DOI 10.1007/1-4020-4246-9; and scholarship on Dee’s patronage rather than popular “royal magician” biographies. 

Material-provenance layer: Ackermann and Devoy, DOI 10.1016/j.shpsa.2011.11.007, and Campbell et al., DOI 10.15184/aqy.2021.132. 

Several gaps remain genuinely unresolved rather than merely unresearched. The early composition date of the Liber iuratus is not fixed with the precision often claimed online; “Honorius of Thebes” is not a straightforward documented historical author; the exact paths connecting southern and northwestern Sigillum traditions are partly reconstructive; the complete ownership sequence of some individual manuscripts requires codicological verification; Dee-associated museum objects do not all possess uninterrupted sixteenth-century provenances; and the British Library’s present technical state limits immediate online rechecking of some digitized folios. 

The E47 question adds one further unresolved problem, but a productive one:

[ \boxed{ \text{Can a representation be derived from the manuscripts that predicts 47 before 47 is inserted into the model?} } ]

That is the decisive criterion separating a discovered invariant from an imposed correspondence. At present, E47 is a mathematically coherent Plate-City construction and the Sigillum is a historically coherent cyclic-symbolic object; the proposed bridge between them is a testable research hypothesis, not yet a historical finding