A page of checked mathematics invites a question it rarely answers: checked against what? A number that comes out right proves the arithmetic. It does not prove the page means what its title says. This desk has met that failure more than once, a result that is true and unrelated to its own name, and the working rule since is to print the limit beside the claim.
The ten pages follow that rule. The Book 7 Scientist Gallery gained four: the geometric Langlands programme, the Kloosterman sums, Feigin–Frenkel duality and four quantum oracles. A new set of five chapters, with an index, walks the mathematics those oracles run on, from a single qubit to braiding. Page 2 lists the gallery pages and Page 3 the quantum set. Every link is given in full.
What a script does here is narrow and worth saying exactly. It computes a stated quantity, shows that a deliberately wrong version fails, and exits non-zero when anything disagrees. The Frenkel page, for example, compares central charges across 16 Lie algebra types; the Provers page tests the size bound on Kloosterman sums over 30 primes. Neither claims more than that.
Two pages were corrected rather than added, and Page 4 says what was wrong in each: wording about the cost of a constant-entropy path, which was too strong, in Book 3 chapter 6 and in Book 4 chapter 21. The correction sits inside the page, at the top of the section it changes, and has a date.
Page 5 carries a finance concept, Ponte Nova, with what this desk could and could not confirm. The Reading Room, Page 6, carries Part 7 of the serial, set from its source.
In the CHSH game a classical strategy can reach a correlation score of 2, a quantum one reaches 2√2, and no quantum strategy goes further. Cirel’son proved the bound in 1980. QM2 reproduces it, and says in the same place that a box allowed to reach 4 respects no-signalling and is still not quantum.
All ten were committed and pushed before this issue was set. The live site had not been opened at the time of writing; the links work once GitHub Pages has rebuilt.
Book 7 is the Scientist Gallery. Four pages joined it. The description beside each link is what the page checks, as the page itself states it.
| Page | What it checks |
|---|---|
| Drinfeld & Beilinson | The geometric Langlands programme, with a check of the mass formula for rank-2 bundles on the projective line. |
| The Provers | Kloosterman sums and the size bound on them, checked numerically over 30 primes. |
| Edward Frenkel | Feigin–Frenkel duality, checked on central charges across 16 Lie algebra types. |
| Four Quantum Oracles | Deutsch, Deutsch–Jozsa, Bernstein–Vazirani and Grover, run on explicit amplitude vectors and sourced against Nielsen & Chuang and Cleve et al. |
A word on the last row. “Sourced” means the statements were compared with the text of the named works, Nielsen & Chuang and Cleve et al., and the page records which comparisons were made. It does not mean the page is endorsed by either.
Not claimed: that a numerical check of a formula is a proof of the programme it comes from. The Drinfeld–Beilinson page checks a mass formula for rank-2 bundles on the projective line, one small case, and does not touch geometric Langlands in general.
The set is five chapters and an index. It is meant to be read in order by someone who wants the mathematics behind the four oracles on the previous page. Start with the index.
| Chapter | Covers |
|---|---|
| Index | Start here. |
| QM1 · States, gates, tensor products | Qubits, the Pauli algebra, the Bloch sphere, no-cloning. |
| QM2 · Measurement and CHSH | The Born rule, entanglement, CHSH reaching 2√2 and no further, the CHSH game, and Cirel’son’s 1980 theorem. |
| QM3 · The Fourier transform and phase estimation | The quantum Fourier transform, phase estimation, continued fractions. |
| QM4 · Order finding and the arithmetic of Shor | Shor’s algorithm, with simulated runs including the 33 = 3 × 11 case from his paper. |
| QM5 · Braiding: Fibonacci and Ising | Anyons, the golden ratio, and why one braid group is universal and the other is not. |
Two details a reader can test. QM2 reaches 2√2 and no further, and it also reproduces Cirel’son’s 1980 theorem on realisable correlations. QM4 runs simulated order-finding, including the 33 = 3 × 11 case from Shor’s own paper.
Each chapter has a script and says what it checks and what it does not. These pages teach standard material from the literature. They are not a result of this corpus, and nothing on them tests the corpus’s own claims.
Two pages already in the corpus were wrong in one respect and were repaired in place, not replaced. Both carry a dated correction box at the top of the corrected section, so a reader who arrives from an old link sees the change before the text.
| Page | Where |
|---|---|
| The Term You Set to Zero | Book 3, chapter 6 |
| Chapter 21, The Closing Field | Book 4, section 21.8 |
What was wrong. The two pages described the constant-entropy path as free of cost, and a path on which the contact form vanishes as reversible. Neither follows. With dS = 0 and heat given up (dQ < 0) the entropy produced, −dQ/T, is positive. And a system at 300 K receiving one unit of heat from a reservoir at 400 K has zero contact form along its own path, yet the total entropy produced is 1/300 − 1/400 = 1/1200, so the process is irreversible. What the form does say is that the path is quasi-static for the system. Whether it is reversible overall also depends on the reservoir.
What the repair is not. It is not a claim that any physical system is described by the corpus form. The rewritten script checks the algebra and the two counterexamples, and the Clausius inequality it leans on is stated as an input, not derived.
The ten new pages are not yet linked from the site’s own indexes or the book gallery page, because those are generated pages and were left alone. All ten were committed and pushed, but the live site had not been opened, so the links work once GitHub Pages has rebuilt. A Lean file for the qubit algebra is in the repository; it has not been compiled and the main library does not import it, so nothing in the quantum set rests on it. A sentence in Book 4 chapter 28 inherited the first error and carries an inline marker; that chapter’s own audit is pending.
Every “just download the app” service assumes a smartphone, a data plan, a bank account and a credit card. The concept starts from the people who have none of them, and the page names them as immigrant, low-income and elderly households. For them a digital wallet is a wall, and for the cash economy it is useless on the first day, because there is no way to put cash in or take it out.
The precedents. Three countries built public, near-free instant rails, and none ran on the card networks. PIX in Brazil (2020) is free for individuals and keyed to a phone number. M-Pesa in Kenya (2007) ran over USSD on a basic phone, with corner-shop agents handling cash. UPI in India (2016) is an open rail that now runs billions of transactions a month. The United States has had its own rail since FedNow launched on 20 July 2023. The page’s argument is that the road exists and the on-ramp does not.
The design. Four choices carry it. Funds settle over FedNow through a chartered sponsor bank, the same arrangement Cash App and Chime use. The front door is SMS, USSD and a voice line, so a basic phone works and the app is optional. A cash bridge runs through neighbourhood anchors such as bodegas, libraries and immigrant-serving nonprofits. And the fee is near zero, with no card-network interchange on a small payment, though the payments stay traceable and compliant. The page says plainly that this is freedom from a private toll, not anonymity.
Payments and capital. Moving money is half of inclusion, and the page pairs it with small collateral-free credit on the Grameen model. It is candid about the record. Rigorous trials of microfinance found modest average effects, and the 2010 Andhra Pradesh crisis showed what over-lending does. It cites an MDRC evaluation of Grameen America as evidence that the model translates to the United States.
The honest path. To operate, Ponte Nova would need state money-transmitter licensing (New Jersey first) and FinCEN registration, a full BSA/AML/KYC programme, a sponsor-bank partnership for FedNow access and custody, and a funded team. The page proposes a first pilot in New Jersey as a public-private partnership. The name belongs to Ponte Nova in Minas Gerais, where the founder’s family is from.
Confirmed. FedNow launched on 20 July 2023 (a Covington client alert is dated to the launch). The MDRC evaluation of Grameen America reports lower material hardship and higher credit scores, business ownership, earnings and non-retirement savings. That matches the page, and only the headline of the release was read.
Not confirmed. The page says Grameen America has operated in New Jersey since 2014 and reached 6,000+ women. This desk did not find either figure. A Grameen post from August 2021 is titled as the opening of a new New Jersey branch for Trenton and Camden, which suggests that part is later than 2014. Treat both numbers as the page’s own until the author supplies a source.
Not checked. The ~2–3% card toll, the PIX, M-Pesa and UPI descriptions, and the comparison with Cash App and Chime are the page’s statements and were not tested here.
Not an offer of financial services, a solicitation or financial advice. “Ponte Nova” is a working name.
A disguise, Fermat came to understand, was not a single decision made once at a dock in La Rochelle. It was a decision that had to be made again every single day, for months, against an enemy far more patient than any king's man: the ordinary, grinding sameness of shipboard life, which left no corner of a person unexamined for long.
The first difficulty was water. A ship's crew bathed rarely and carelessly, in full view of one another, and a clerk who never once joined them, who always found some pressing errand of the commissioner's at exactly the hour the men stripped down on deck, was the kind of oddity that sailors — who had nothing to do for months but notice things about each other — eventually noticed.
The second difficulty was her hands. Marie's disguise held up remarkably well from a distance: the cut hair, the borrowed coat, the deliberate slouch she had practiced in the mirror above the chandler's shop until it looked less like a performance and more like a habit. But her hands had spent twenty years being a court lady's hands, soft in a way that no clerk's hands ever were, and by the second month the ropes and the ledgers between them had roughened them, but not nearly enough, not fast enough, and Fermat found himself inventing reasons — an injury, a rash, a family superstition about gloves — faster than he was entirely comfortable inventing them.
The third difficulty, which he had genuinely failed to calculate for, arriving at it only with a kind of belated, mortified respect for a variable his own life had never required him to consider, was that a woman's body did not stop being a woman's body simply because a coat had been put over it. There were days, each month, when Marie disappeared entirely into the small cabin Fermat had commandeered "for commission papers requiring privacy," and did not emerge, and Fermat stood outside that door inventing commissioner's business for anyone who asked, and understood, with the same clear-eyed precision he brought to everything else, that this was the one part of the entire scheme he could not solve with arithmetic. He could only stand guard over it.
The man who noticed first was Bertrand, the ship's carpenter, a quiet sort who noticed everything and said very little, which Fermat had at first mistaken for stupidity and later came to recognize, with some alarm, as the opposite.
"Your clerk," Bertrand said to him one evening, not quite a question, "keeps unusual hours."
"My clerk," Fermat said, "keeps my hours, which are the hours of a man arranging a colonial commission from a berth too small for the paperwork it requires."
Bertrand said nothing further that night. But Fermat noticed, after that, how Bertrand's eyes followed the boy across the deck — not with suspicion exactly, not yet, but with the specific attention of a man doing sums in his head and not yet certain of the total.
Others followed. A sailor remarked, within Fermat's hearing but not quite to him, that the commissioner's clerk had a voice too gentle for the work he claimed to do. The cook, who fed the crew twice daily from a single vantage point that saw everyone eat or fail to eat, noted that the boy ate like someone raised at a table with linen on it, small bites, an economy of motion no clerk's upbringing had ever produced.
Fermat could not silence a whole crew's worth of small observations. He could only, with the same calculated patience he had once used to secure a royal commission from a minister who didn't want the posting, make the cost of speaking aloud higher than the cost of staying quiet — an extra ration here, a debt quietly forgiven there, a private word to Bertrand specifically that a commissioner grateful for a carpenter's discretion was a commissioner who remembered such things when postings and favors were handed out in the colony.
It worked, in the sense that no one said anything. It did not work in the sense that mattered most: by the fourth month, there was not a man on that ship who fully believed the clerk was a clerk, and a belief that goes unspoken for months does not disappear. It only waits, gathering a kind of quiet resentment at having been made to pretend, for the moment when pretending no longer serves any purpose at all — the moment, say, when a ship is breaking apart on a reef, and a crew already halfway convinced they had been lied to for four months finds it remarkably easy to row away and let the liars manage the consequences themselves.
Part 7 of 18 · Fiction, drawn from the documented record; what is invented and what is not is set out in the series’ own note on fact and fiction. © 2026 Pablo Nogueira Grossi · G6 LLC.
Rights notice. Pierre et Mademoiselle is not covered by this issue’s CC BY 4.0 licence. The serial and the work it belongs to — a limited series in development — are © 2026 Pablo Nogueira Grossi / G6 LLC, all rights reserved. No licence to reproduce, adapt, translate or perform it is granted here.
Documented. Only the frame. Fermat died at Castres on 12 January 1665, the record this serial sails away from, and the French Atlantic corridor from La Rochelle toward Cayenne and Maranhão was a working route in those years.
Invented. Everything aboard. Bertrand the ship’s carpenter, the sailor, the cook and the crew’s suspicion; the cabin kept “for commission papers requiring privacy”; the three difficulties of the disguise. The carpenter is not Bertrand d’Ogeron, the governor of Tortuga named in the ledger for No. 6; the shared first name is a coincidence of the page and nothing more.
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tools/corpus_count.py · tools/self_reference.py — entity-aware counting, and the vicious-circle test. Both standard library only.sorry, standard axioms only.