One Thousand and One Conjectures

The modern capital campaign — where a museum or university secures a headline anchor gift or star acquisition just before asking everyone else for money — is here read back into the medieval church. Relic translations, the ceremonial installation of a saint's…

In the 13th century, English law adopted a rule for how far apart markets must be — the spacing derived in the classic legal reckoning from a day's return journey on foot, about 6.6 miles. The conjecture joins this statute to the…

The medieval Champagne fairs ran as a fixed annual cycle of six fairs in four towns, and the merchants of Flanders and Italy worked the whole circuit. Seen with modern eyes, scheduling that cycle is a traveling-merchant optimization: fair dates and durations…

The Shapley value, cooperative game theory's canonical answer to fair division, pays each member of a coalition its average marginal contribution to the coalition's worth. The Hanseatic League was such a coalition: member cities jointly controlled Baltic and North Sea trade routes,…

This joins medieval pilgrimage history to tribology, the physics of wear. Every pilgrim who crossed a church threshold removed a microscopic layer of stone, and centuries of feet turned steps into shallow basins; the missing volume is a footfall counter that no…

The Bass diffusion model, the workhorse of new-technology adoption studies, splits uptake into two forces: an innovation coefficient p (adopters persuaded by external influence) and an imitation coefficient q (adopters copying their neighbours). Medieval Europe's watermill boom is a textbook diffusion process,…

Joins stream-power hydrology to the great fiscal cadastre of 1086: the Domesday survey, in recording what each water-mill rendered to its lord, unwittingly logged a physics meter across England. A mill's earning power was set by the hydraulic power of its site…

Vertical-monopoly pricing from industrial organization shows that a chain of independent monopolists along one route charges more in total than a single owner would, because each ignores the damage its markup does to the others' traffic. This conjecture reads the toll castles…

Common-value auction theory predicts the winner's curse — the highest bidder is the one who most overestimated the shared value — and that experienced bidders learn to shade their bids downward. This conjecture finds the earliest documented correction in Venetian state finance:…

Indulgences — remissions of penance measured in days and years — famously inflated across the later Middle Ages. The conjecture is that the inflation had exactly one source: canon law capped each bishop's grant at forty days, and that cap held, so…

Every relic in a church treasury carried a tiny parchment tag — an 'authentic' — naming the saint. Churches did not label continuously; they labeled when an altar was opened, a shrine translated, or an inventory ordered. The conjecture is therefore that…

Gratian's Decretum, the twelfth century's great canon-law textbook, was augmented after its making with inserted passages called paleae; the next century's decretal collections (the Liber Extra) codified the new case law flowing through the papal courts. The conjecture is that the paleae…

Inquisition registers record vernacular testimony in notarial Latin, but the Latin skin tears in predictable places, letting Occitan words through. The conjecture is twofold: the tear-points cluster in domains where Latin genuinely lacked equivalents — kinship terms, foodstuffs, and the heretics' own…

Byzantine monastic founders wrote typika — charters specifying, among much else, perpetual commemorations for themselves and their donors. Each generation added obligations; none subtracted its predecessors'. The conjecture is that this created a genuine liturgical debt crisis with a paper trail: as…

Early medieval charters routinely ended by cursing violators — anathema, the fate of Judas, eternal fire — while later charters mostly dropped the curses. The conjecture is that the curse was a substitute enforcement technology whose use varied inversely with access to…

The famous illustrated Exultet rolls of southern Italy — liturgical scrolls sung once a year at the Easter vigil — are usually explained by display aesthetics. This conjecture ties the roll format instead to the region's notarial economy: Exultet rolls were produced…

A tonary is a Carolingian book that sorts hundreds of chants into eight modal bins; a polyptych is a Carolingian estate survey that sorts hundreds of holdings into fiscal bins. This conjecture claims they are the same administrative technology in two departments:…

Stray neumes turn up on the backs and margins of charters and on flyleaves, and they are catalogued as pen trials. This conjecture claims a legal function for a distinct subset: neumes were added to property documents that were contested or vulnerable,…

Tropes — optional festal additions wrapped around the fixed chants of the mass — flourished from the tenth to twelfth centuries and then withered, a rise and fall usually explained by liturgical reform. This conjecture explains it economically: troping is surplus-absorbing ornament,…

Rome sang two chants: the 'Old Roman' dialect surviving in a handful of city manuscripts, and the Gregorian that conquered Europe and eventually Rome itself. This conjecture claims the survival pattern inside Rome was a property fact: churches that kept Old Roman…

The plenary missal — one volume merging the prayers, readings, and chants that older practice split across sacramentary, lectionary, and gradual — took over Latin Europe between 1000 and 1300, and liturgists explain it by the rise of private masses. This conjecture…

Byzantium lost southern Italy to the Normans in the eleventh century, and by intuition, political loss should mean textual loss. This conjecture says the opposite happened: Greek manuscripts produced in Italo-Greek scriptoria survive at higher rates than their Constantinopolitan contemporaries, because Norman…

Greek Gospels survive in two forms: the continuous text, which anyone might own, and the lectionary, rearranged for reading at services — altar equipment that only a functioning church needs. This conjecture says the ratio between them is a census: the lectionary…

Greek medical compendia — Galenic handbooks, hospital recipe books — were copied in bursts. This conjecture says the bursts ride hospital endowments: new medical witnesses cluster in the decades after the foundation or refoundation of endowed xenones, most visibly the Pantokrator hospital…

An imperial chrysobull — the gold-sealed charter confirming a monastery's estates — looks like agrarian history, not book history. This conjecture says it was a preservation subsidy: houses holding surviving early charters possess manuscript collections with systematically older age profiles than comparable…

Monastic forgery of Anglo-Saxon charters is usually pictured as a slow pious habit; this conjecture joins it instead to legal procedure, the sequence of royal challenges that made written title the winning move in court. The claim is that forgery was a…

Historians often read the rising count of English private charters as a gauge of the land market or of spreading literacy; this conjecture joins the charter-production curve instead to the menu of royal remedies. The claim is that ordinary people bought documentation…

The wax seal and the witness list were the two proof technologies carried by the same single-sheet deed, and this conjecture treats them as substitutes with a measurable exchange rate. As sealing spread down the English social ladder in the twelfth and…

We estimate medieval government output from surviving acta, but survival was decided by the recipients, not the chancery — and this conjecture joins the diplomatists' category of deperdita (documents known only because something else mentions them) to the sociology of who could…

This conjecture joins the purported dates written into forged charters with the shape of the forging house's own genuine holdings. The claim is that forgers dated their fabrications into the decades from which their archive held few or no authentic documents —…

A cartulary — the bound book into which a monastery copied its loose charters — is usually treated as a photocopier; this conjecture treats it as an investment portfolio. Copying cost scribal labour, so the compiler triaged by future litigation value: perpetual…

This conjecture imports burstiness statistics — the tools used to describe irregular human communication patterns — into the study of itinerant medieval kingship. An itinerant chancery issued documents where and when the king was available: acta came in bursts at assemblies, sieges,…

This conjecture joins forgery to risk management: whose name do you dare to fake? A diploma attributed to a living ruler or his recent line could be checked against a functioning chancery, its personnel, and its registers; a diploma of a long-extinct…

Diplomatists distinguish two forgery technologies: doctoring a genuine old charter (interpolation) and fabricating one wholesale. This conjecture maps that choice onto archival wealth: a house with deep muniments had authentic parchment, scripts, and formulae to modify, while a burned or refounded house…

English private deeds of the twelfth and thirteenth centuries are famously undated, and then dating clauses flood back around 1300; this conjecture joins that curiosity to limitation law. A date on a deed was legally inert while courts reckoned title by living…

The chirograph — a deed written out twice on one sheet and then cut apart in a wavy or lettered line, so the matching halves authenticate each other — is a physical checksum, and this conjecture joins the choice of that format…

Anglo-Saxon royal charters pair a Latin dispositive text with an Old English boundary clause, and this conjecture reads the pairing as two proof regimes fossilized in one object. The Latin grant was proof-as-relic — its authority lay in being verbally unchanged —…

An archive fire or a viking sack is usually where a documentary story ends; this conjecture makes it where one begins. A house that lost its muniments still held its lands — and now held them without proof — so documented archive…

This conjecture joins the chronology of English famines to the typology of English charters. In subsistence crises smallholders sell land to eat, and the buyer of a desperate seller insists on parchment precisely because hungry men's kin come back to court later;…

Clauses recording a wife's consent to her husband's land sales are usually read as sentiment about family property; this conjecture reads them as buyer's insurance and joins their frequency to the enforcement of dower. A consent clause is worth drafting only once…

Witnessing a deed looks like a neighbourly duty, but this conjecture claims late thirteenth-century England grew a semi-professional attestor class: the same small set of local names recurring across many unrelated parties' deeds, clustered around scribes and courts. As proof of deeds…

Counts of medieval government output lean on surviving original documents, but archives curated by impressiveness: a great sealed privilege on fine parchment was a treasure and a permanent legal weapon, while a small mandate was scrap the day it was obeyed. This…

In a personal monarchy, beneficiaries feared their rights lapsed with the grantor's last breath, so each accession triggered a rush to have old grants confirmed. This conjecture turns that rush into a gauge: confirmations as a share of chancery output should spike…

Medieval dating clauses encode the date redundantly — indiction, regnal year, year of the incarnation — and the redundancy lets us catch clerks in errors. This conjecture claims the internal-inconsistency rate of dating elements in royal and imperial acta is a chancery-stress…

A vacancy of the throne or of the papal see stopped the sealing but not the wanting: petitions and unrenewed privileges accumulated. This conjecture models medieval chanceries as queueing systems and claims their output shows a measurable overshoot after every long interregnum…

A genuine charter's content could survive perfectly well as a copy in a cartulary; a forgery's whole point was frequently the exhibitable object — venerable-looking script, an old seal — to be produced at an inquest or in court. This conjecture therefore…

The backs of medieval charters carry archival endorsements — shelfmarks, one-line summaries, notes like 'inutile' — added whenever someone reorganized the muniments. This conjecture claims endorsement was not steady housekeeping but crisis behaviour: the endorsing hands on a house's single sheets should…

Assyriology, sitting on hundreds of thousands of digitized tablets, learned to treat administrative writing as a statistical population: text types and formulae in the Ur III archives follow heavy-tailed frequency distributions with stable shape parameters. Medieval English charters, digitized in the DEEDS…

The Ur III state of Mesopotamia (around 2100 BCE) left roughly a hundred thousand administrative tablets, and Assyriologists learned to reconstruct its bureaucratic hierarchy statistically — disambiguating names and inferring rank from who appears with whom, and in what position, across thousands…