Questions nobody has answered yet.

🜁Is there an element of order 4 on the plane the walk lives on?

🜁Is there a move on this plane that comes back to the start only after four turns?

R4☿ = ℤ/2 × ℤ/2 has no element of order 4 — 1, A, B, AB have orders 1, 2, 2, 2. Poisson summation needs F with F² = parity and F⁴ = I, generating ℤ/4, checked at ‖F²−parity‖ = 8.75e−14 and ‖F⁴−I‖ = 1.23e−13. So the model holds the functional equation as a consequence without its cause.

R4☿ has four moves: 1, A, B and AB. Do any one of them twice and you are back at the start. None of them needs four turns to come back. Poisson summation needs a move F where doing it twice gives parity and doing it four times gives the identity. That F was checked by machine: ‖F²−parity‖ = 8.75e−14 and ‖F⁴−I‖ = 1.23e−13. So the model gets the functional equation as a result without holding the reason for it.

What would answer it: exhibit such an element on the right plane, generating the functional equation rather than assuming it — or show none can exist there, which falsifies the ΑΔΩ Hypothesis outright.

What would answer it: show such a move on the right plane, so the functional equation follows instead of being assumed. Or show that no such move can exist there. That second answer would prove the ΑΔΩ Hypothesis wrong outright.

One ℤ/4 is already known in the flow, Q: (Y,Z) → (−Z,Y), with the flow Q-equivariant. It is on the wrong plane.

One four-turn move is already known in the flow. It is Q: (Y,Z) → (−Z,Y), and the flow keeps its shape under it. It sits on the wrong plane.

🜁Is generalisation reachable from this architecture at all?

🜁Can this design ever read text it was never given?

On material never fed, next-word reading is 0.0133 with delimiters skipped and 0.0193 with them kept — about 1–2% either way, N = 828 per cell, Δ/V·001 fed — on the shipped holdout☿. Merging corpora☿ does not transfer: a field scored about 2% on a book it had not seen and about 92% after being fed it. Feeding more makes more material known; it does not improve the unknown.

On material it was never fed, it gets the next word right 0.0133 of the time with delimiters skipped, and 0.0193 with them kept. Both are about 1–2%. There were 828 probes in each case, with Δ/V·001 fed. That is on the shipped holdout☿. Merging corpora☿ does not transfer. Feeding it more makes more material known. It does not improve the unknown.

What would answer it: any mechanism that raises unseen reading without raising the false-claim rate. Several were tried and came back inert — those attempts belong on this page.

What would answer it: any mechanism that improves reading on unseen material without making it claim things falsely more often. Several were tried and did nothing. Those attempts belong on this page.

🜁Does the address-collision rate scale with ledger size?

🜁As the record grows, do two different things land on the same address more often?

On the ten-book benchmark — 5.94 MB fed, 1,077,603 states, window☿ 11 — the false-claim rate is 0.003, and inspection showed the errors are collisions rather than fabrication: two different contexts landing on the same address☿, and the field reporting what lives there.

On the ten-book benchmark — 5.94 MB fed, 1,077,603 states, window☿ 11 — the false-claim rate is 0.003. The errors were looked at one by one. They are clashes, not invented text. Two different pieces of context land on the same address☿, and the field reports what sits there.

What would answer it: the same measurement at 10×, 100× and 1000× the ledger☿, with the collision rate plotted against state count. If it grows, the address space needs more depth and the admission gate☿ needs a size-aware threshold.

What would answer it: run the same measurement with a ledger☿ 10×, 100× and 1000× as large. Plot the clash rate against the number of states. If it grows, the addresses need to go deeper, and the admission gate☿ needs a limit that changes with size.

🜁Can a gate of exactly zero false claims ever be satisfied?

🜁Can anything ever pass a gate that allows exactly zero false claims?

The admission gate requires zero claims on foreign material. Run against the shipped holdout, the flagship corpus itself fails: three claims on Pride and Prejudice, none on Frankenstein or Moby-Dick, out of the 336 probes the gate draws — gates.js · probes(book, 120, 400). All three returned a word from its own ledger rather than invented text — but they are not one phenomenon, and the three were opened individually on 2026-08-18. One is an address collision: the query's full 12-trit key is present in the trie, leftover comes back 0.0000, and at the resolution the doorway reads at that genuinely is the same passage. The other two are pole-threshold false positives on partial prefixes: they agree with the trie to depth 9 of 12 and depth 7 of 12, never reach a full key, and pass only because leftover — 0.2246 and 0.1469 — lands on the near side of the boundary at 0.2853. Calling all three collisions hid the harder of the two problems.

The admission gate allows no claims at all on material from outside. Run against the shipped holdout, the flagship corpus itself fails. It made three claims on Pride and Prejudice, none on Frankenstein and none on Moby-Dick, out of the 336 probes the gate draws — gates.js · probes(book, 120, 400). All three handed back a word from its own ledger rather than invented text. But they are not the same thing, and each was opened up on 2026-08-18. One is an address clash. The query’s whole 12-symbol key is in the index, leftover comes back 0.0000, and at the resolution the doorway reads at, that really is the same passage. The other two are threshold mistakes on partial matches. They agree with the index to depth 9 of 12 and depth 7 of 12. Neither ever reaches a full key. They pass only because leftover, at 0.2246 and 0.1469, lands on the near side of the boundary at 0.2853. Calling all three clashes hid the harder of the two problems.

And the mechanism is not settled. The standing claim that this is fixable only by finer addresses was tested directly: raising DEPTH from 12 to 16 and then to 24 changed nothing at all — three false claims in every case — and keying the trie on the whole face-0 address instead of its first symbol made it ten, spread across all three books. Finer addresses did not help, and in one test tripled the failure.

And nobody knows the mechanism yet. The standing claim is that only finer addresses can fix this. That was tested directly. Raising DEPTH from 12 to 16 and then to 24 changed nothing: three false claims every time. Keying the index on the whole face-0 address instead of just its first symbol made it ten, spread over all three books. Finer addresses did not help. In one test they made it more than three times worse.

What would answer it: a rule that separates a genuine collision from a partial match that merely cleared the pole, and an account of why the pole sits where it does on foreign material. Two of the three are the second kind, so a bar of exactly zero is unreachable in principle at any size, and the gate rejects material it should admit.

What would answer it: a rule that tells a real clash apart from a partial match that only just cleared the pole, and an account of why the pole falls where it does on foreign material. Two of the three are the second kind. So a bar of exactly zero cannot be met at any size, and the gate turns away material it should let in.

🜁Why does agreement depth 9 have no states and depth 8 exactly one?

🜁Why does depth 9 hold no states at all, while depth 8 holds exactly one?

Across 15,538 states aligned after a walk, the agreement-depth distribution runs θ = 14 with 4,847 states, 13 with 1,025, 12 with 581, 11 with 1,436, 10 with 3,512 — then 9 with none at all, 8 with exactly one, 7 with 607, 6 with 341.

15,538 states were lined up after a walk. Counting how deep each one agreed gives: 14 with 4,847 states, 13 with 1,025, 12 with 581, 11 with 1,436, 10 with 3,512. Then 9 with none at all, 8 with exactly one, 7 with 607, and 6 with 341.

What would answer it: a reason for the gap, or a demonstration that it is an artefact of this corpus. A hole that clean in a distribution of 15,538 is unlikely to be nothing, and nobody has chased it.

What would answer it: a reason for the gap, or a showing that it is a quirk of this corpus alone. A hole that clean, in a count of 15,538, is unlikely to mean nothing. Nobody has chased it.

🜁Is interpolation reachable, given the point set is finite?

🜁Can the field make a point between two others, when the points are finite in number?

Each face is a pseudo-ultrametric where every triangle is isosceles, so there is no betweenness inside one — that is a theorem about such trees, not a defect. Summing three faces breaks it: 44.01% of triples still satisfy the strong inequality. But a finite metric space has essentially no betweenness whatever metric it carries, so the break separates addresses without establishing interpolation.

Inside one face, every triangle has two sides of equal length. That means nothing can sit between two other things there. It is a proved property of shapes like this, not a fault. Adding the three faces together breaks that property: 44.01% of triples still obey the strong rule. But a space with a finite number of points has almost no betweenness under any measure. So the break tells addresses apart. It does not show that filling in between them is possible.

What would answer it: either a construction that interpolates on a finite address set, or an argument that it cannot be done and the question should be retired.

What would answer it: either a method that fills in between points on a finite set of addresses, or an argument that it cannot be done and the question should be dropped.

🜁Is the scale-ladder collapse still justified after the architecture changed?

🜁The design has changed. Does the old decision to use one scale still hold?

The collapse to a single rung was made before the trie or the directions existed. The log records that it has not been re-tested since and may no longer hold.

The decision to use a single rung was made before the index or the directions existed. The log says it has not been re-tested since, and it may no longer hold.

What would answer it: re-run the collapse against the current engine. This is a small, well-specified job and a good first contribution.

What would answer it: run that test again against the current engine. It is a small, clearly stated job, and a good first thing to contribute.

🜁What should a field do in the presence of novelty?

🜁What should a field do when it meets something new?

It recognises its own material and refuses what it has never seen. Between those is the middle verdict☿ — the words are its own but the order is not — and what the right behaviour is there has never been settled. The control that moves that boundary is bounded by the field's own two poles☿, but where inside them it should sit is not answered by anything measured.

It knows its own material, and it refuses what it has never seen. In between sits the middle verdict☿: the words are its own, but the order is not. What it should do there has never been settled. The control that moves that line can only move between the field’s own two poles☿. Where it should sit between them is not answered by anything measured.

What would answer it: a principled position for the boundary, derived rather than chosen, or a demonstration that it is genuinely a matter of preference and belongs to whoever is using it.

What would answer it: a place for the line that follows from the work rather than being picked, or a showing that it really is a matter of taste and belongs to whoever is using the system.