Where this sits. Book X is the floor of the first ten. The series descends from frontier mathematics in Volumes I and II, through matter, formal theory and the people who built it, to logic and philosophy in Volume IX · Omega Point — and lands here, on custody, transmission, and the continent. The floor is not linear: Book X returns to the question Book I’s reader came from, which is who holds a thing and on what terms.
Finished, and not. Six chapters are written, each with its own sources. ch06 carries a producing script; the other five do not yet and under R6 they owe one. Chapter 6’s gap P3 — Moyo against the coordination argument — is the one genuinely unfinished argument here and is marked open in the text rather than resolved. No contract is cited and no party is accused. The claim type throughout is definitions, measurables and sourced history.
The handshake. Nothing is asserted beyond what its own page supports. Where a claim is proved there is a link to the proof; where it is cited it says so; where it is open it says that too. A reader who wants the series starts at the Series Hub; one who wants to check rather than read starts at the Master Index, where each page carries its evidence tags and the kernel-checked declarations it names, linked to the Lean. If you find a number no script produces, or a proof that does not resolve at the path given, that is a defect worth reporting — the series is built to be audited, and this is the volume that argues why that matters.
This volume opened as political economy — what a producing country has committed away, for how long, and to whom. It is becoming something larger, because the question turned out not to be about commodities.
Ask what share of a country's iron ore is spoken for and you are asking who holds a claim on a thing, under what instrument, and for how long. Ask where the Ishango bone is and you are asking the same three things about a carved fibula from Lake Edward. In both cases there is a public number for where the thing is and no public number for the terms it is held under. In both cases the terms are what decide whether the position is reversible.
Custody and commitment are the same relation seen from two ends. A holder acquires an option — to keep, to lend, to interpret, to refuse — and the party from whom it came loses the corresponding one. Where the loss is written into a contract, we call it offtake. Where it is written into a museum statute, we call it a collection. The accounting is identical and neither side books it.
| Axis | The question | What is usually missing |
|---|---|---|
| History of science | What was known on the continent, where, and when — read from the objects and the records rather than from later summaries of them. | The primary object, which is frequently not in the country that produced it, and often not on the continent. |
| Custody | Who holds it now. Under what instrument. Whether return is possible at all, and if not, what specifically bars it. | The instrument. Location is catalogued; terms of holding are not aggregated anywhere. |
| Transmission | How it moved — in both directions — and whether the record of the movement survived the movement. | The middle of the chain. Endpoints are documented; the passage between them is where attribution is lost. |
The three are not separable in practice. A history of science written without custody is a history of whatever happened to stay accessible. A custody question without transmission is a property dispute. Transmission without either is a story.
This is not a regional volume and should not be read as one. Every lineage of modern humans traces to Africa; so, necessarily, does the first instance of every human cognitive practice — counting, marking, measuring, recording, inferring. A history of science that begins in Africa is not a chapter of the subject. It is the subject's first chapter, and the rest of the discipline has spent a long time treating it as an appendix.
The volume takes that literally rather than rhetorically. The claim to be tested in each chapter is narrow and checkable: what does this object show, where is it, who holds it, and what would it take for the people best placed to interpret it to be in a room with it.
Four quantities. None is published today. Each is constructible from records institutions already keep.
| # | Quantity | Settles | Status |
|---|---|---|---|
| 1 | Encumbrance — committed volume over national output, with counterparty concentration and weighted term | Whether a producer's dependence is commercial or constitutional. Indistinguishable in trade statistics; only one is reversible. | Open |
| 2 | Custody — share of a category of heritage held outside its continent of origin, by instrument of holding and by whether return is statutorily barred | Whether a collection is a loan with a long fuse or a transfer with no term. The locations are catalogued; the instruments are not aggregated. | Open |
| 3 | Asymmetry α — directional imbalance of a market connection | Whether a connection between two economies is complete, or whether exposure and co-movement both land on one side. | Open |
| 4 | Interval τ — years from first discussion to first operation | Whether the length of construction is the cost of a cross-border institution or the mechanism that makes it survive. | Open |
Quantity 3 is argued in WP-121; quantity 4 in WP-118. Quantities 1 and 2 open this volume, in chapters 1 and 2.
Alongside the chapters there is a standing forum where these questions are argued before they are written up: the G6 Chamber. It is deliberately not a terminal — no subscription, no seat fee, no data licence, and no requirement to hold a chair in order to take the floor. It carries the volume's three measurables as live threads and the house rule that this work cannot fix anyone's country and does not propose to. Access is by invitation while the room is small: write to the convenor.
| Ch. | Title | What it establishes |
|---|---|---|
| 01 | The Encumbrance Ratio | Separates destination concentration from contractual commitment; defines E, C, T; shows that a long-horizon supply commitment is the sale of an unrecorded option. |
| 02 | The Ishango Bone Is in Brussels | The oldest mathematical object in the volume, and the custody instrument that holds it. Shows the museum statute is an encumbrance in Chapter 1's exact sense, with indefinite term. |
| 03 | The Numbers in Dead Aid | Forty figures from Moyo (2009) with their page numbers, the case against them at full strength, and the third instance of the instrument — aid substitutes a counterparty who is not the citizen, extinguishing the only option most people hold over a state. |
| 04 | Receiving Capacity Is Measured Every Year, Under Another Name | Corrects WP-41: 1.52bn border crossings absorbed in 2025 against a claim that receiving capacity does not exist. Names the second way a number goes missing — collected for another purpose, by people who do not know they hold it. |
| 05 | The Notebooks and What Reached Us | Ramanujan wrote down over a hundred class invariants with no proofs and no statement of what they were. What the recovery recovered was not proofs. On disk since before this table was last written, and not linked from it until 2026-09-19. |
| 06 | The Price of the Thing | Previously linked here under chapter 4's title. The link worked and the label did not. |
| 07 | Up Before Right | Gapminder's respondents score 18.3 % on three-option questions where chance gives 33.3 %, and 15 % get all twelve wrong against a chance rate of 0.77 % — 19.5 times. Then Rosling's ordering claim on four World Bank series for South Korea: child survival 1970.8, fertility 1975.0, life expectancy 1984.7, income 1999.5. |
| 08 | You Never Asked | Sirolli's tomatoes grew; the hippos ate them; nobody had been asked. Every channel ran donor-to-recipient. Marks this volume's own “two hundred hippos” as not located rather than repeating it a third time. |
Chapters open when a measurable or a sourced object is ready, not before. This table is short on purpose and is expected to be written by more than one hand.
This volume is not a new direction. It is a commitment being redeemed, and the commitment has an address.
“Brazil proposes the adoption of the CEFR → TO/TOGT framework (IMPA Edition) as a unified, scalable, culturally adaptable model of learning… Africa is proposed as the first priority for international implementation, given its youth demographics, cultural richness, and historical ties with Brazil.”
Principia Orthogona, Appendix L — Letters and Diplomatic, §L.2. Source file Principia_Orthogona_Complete_v8.pdf, sha256 96971cc0b760ac99…, 3,974,068 bytes. §L.3 is a draft Memorandum of Understanding for Brazil–Africa cooperation.
That was written, addressed to foreign ministries, and then nothing was built on it. A commitment with no address is not a commitment, which is this series' rule applied to its own promises rather than to its theorems. Book X is the address.
One thing has moved since and should be said rather than smoothed: L.2 says BRICS. The structure this volume now works with is BRIX — Russia out by decision, and Africa entering whole rather than through one of its states. That is a revision of the author's own earlier position, not a continuation of it.
In 1971 Italian volunteers taught Zambians in the Zambezi valley to grow magnificent tomatoes. Two hundred hippos ate the crop overnight. The Zambians had always known. “You never asked.”
The story is Ernesto Sirolli's, and his method — “you never initiate anything, you never motivate anybody… you become a servant of the local passion” — is the one this volume is trying to copy. It has no view about what anyone else should be researching and will not acquire one. The chapters below are the author's own work, offered as examples of a standard rather than as a direction.
We cannot fix the problems in Russia, nor in Mexico, nor in Africa. Nobody outside a country ever has. What is available is narrower and worth more: listen to the people inside the problem, help with what they say they need, and then do the one thing distance is good for — publish the number they are not placed to publish for themselves.
That last clause is the whole of the offer. A person inside a problem is usually a party to it: the aggregate that describes it runs against their own counterparty, their own ministry or their own employer, and assembling it is unpaid work taking months. Someone at a distance with no position to protect can do exactly that. It is the only contribution here that does not require pretending to know better, and it is why every chapter ends in a measurable rather than a recommendation.
The conditions for the questions in this volume to be answered already exist. What is usually missing is not capability but that nobody asked, and that nobody published the answer at an address. Supplying the address is the service. How to write a chapter →
The rest of this series was written by one author working through one argument. This volume cannot be, and should not be. Custody and transmission are questions whose evidence is distributed across archives, collections, field sites and institutions on several continents, and most of it is held by people who are not the present author and know considerably more.
So Book X is open. A chapter here is not a submission to be judged and published; it is a piece of study carried out in the open, with its sources, its uncertainties and its corrections on the page while the work is happening. The standard is the series standard and nothing more: every claim resolves to an address or is marked open.
If the custody instruments turn out to be aggregated somewhere already — if some registry does record, for a class of objects, the legal basis of holding and whether return is barred — then chapter 2's premise fails and the work is to publicise that registry rather than to build one. Finding it would be the most useful possible outcome and nobody should be attached to its absence.