Why this page exists
Research that is only ever reported once it has survived gives a false impression of how it was made. It suggests a straight line from question to result. The line is not straight, and the discarded branches carry most of the information about how reliable the surviving ones are.
So every claim made in this work and later withdrawn is listed here, with the reason it died. Several were withdrawn within hours of being made. Several were withdrawn because a second system checked them and found them wrong. One was withdrawn because it turned out to have been answered seven weeks earlier, more sharply, in this same programme.
None of these are open questions. Each one is settled — settled against the claim. Where a weaker statement survived, it is given.
1. Four on quotient admissibility
Withdrawn on 8 September 2026. The question behind all four: when can you throw away part of a description of a physical process without losing the process?
| withdrawn claim | why it died |
|---|---|
| reduction commutes with gluing if and only if the interface carries charge | four of eight gradings lose nothing, including the interface bond itself — so the condition is not necessary |
| a quotient is admissible if and only if some declared instrument breaks the grading | a counterexample breaks the grading and still spans only 52 of the required directions — so the condition is not sufficient |
| the slack ceiling proves no syntactic criterion can decide admissibility | it refutes one criterion, not the class; a better algebraic criterion was not excluded, and a block decomposition pointed straight at one |
| universal conjecture: span equals the dimension of the generated algebra | compatible with all seven frozen cases, and false outside the model — a single qubit with one Hamiltonian and one instrument has algebra 4 and span 3 |
One cause, four deaths. All four tried to read a decomposition off the generators. A decomposition is not visible there. That is worth more than any of the four claims would have been.
What survived, with a proof: if the dephased Hamiltonian and every declared instrument preserve a grading, the closure is confined to the block-diagonal subspace and the quotient is inadmissible. Breaking the grading is necessary but not sufficient. In its corrected form the criterion is about reachability rather than syntax: a quotient is admissible exactly when its discarded redundancy is a union of invariant components not containing the identity.
2. Six during the locality study
Made and withdrawn in the same session, during the work that became the register-hub locality paper.
| withdrawn claim | why it died |
|---|---|
| "the total-singlet constraint destroys spatial locality" | every disjoint restricted pair operator commutes and every overlapping one does not. The sector has a perfectly good local commuting structure. The constraint was innocent. |
| "does a causal cone survive a global constraint?" — posed as an open problem | answered yes by a two-line invariant-subspace argument, then confirmed numerically. It was never open. |
| "the register-only depth test matches the earlier local-probe setup" | the register term directly controls the distant bonds. It is not a local probe. |
| "there is a light cone in closure depth; geometry lives in time" | a rediscovery of an earlier note from seven weeks before, which was sharper — and it did not survive being tested in the setup that actually matched that note |
| "the interface contribution is unbounded, so the area-law route is closed" | the numbers behind it are two finite-size algebraic rank differences, not an entropy and not an asymptotic statement. Retained as measurements, withdrawn as a conclusion. |
| "general relativity's Hamiltonian constraint is 'the total is fixed'" | it is a local family smeared by lapse functions, with a non-trivial algebra encoding refoliation. The analogy was simply wrong. |
3. Three from external review
Raised by two independent review sessions on 9 September 2026, the same day the work was opened for review. Recorded rather than folded silently into the text.
| withdrawn claim | why it died |
|---|---|
| the study tests the model's own Hamiltonian | it uses a plain Heisenberg chain, which is not that Hamiltonian. The correct scope is a statement about the sector, tested with a local Hamiltonian — not about the model, whose Hamiltonian is not local. The phrasing conflated sector with model and is withdrawn. |
| the measured velocity supplies the propagation scale an earlier truncation bound needs | that bound is stated in terms of a generator norm and a specified support order, not a fitted wavefront velocity. Different quantities; a fitted number must not be transferred between models as if it were one of them. |
| the restriction inequality holds with equality | an initial search for a counterexample found none at three sizes, which was reported as suggestive. A later search found one. Equality is false in general; only the inequality holds. |
The same review produced the strongest positive item in that study — an independent reimplementation using a different sector construction, a different norm and a different notion of the full space, agreeing to eight decimals at every bond distance, using an instrument that is both cheaper and better than the original.
4. What the pattern shows
Three lessons come out of these thirteen, and they are the durable part.
An algebraic statistic is not a physical probe. In the same model and the same sector, a closure-depth statistic showed no causal cone while the physical commutator norm showed a textbook one. Every locality conclusion drawn from closure statistics was withdrawn on that basis. Exact-membership depth in an operator closure does not probe causal structure.
A mixed-instrument comparison is a defect, not a measurement. One run reported thirty apparent violations of a theorem. The cause was mixing exact decomposition for small matrices with iterative approximation for large ones, where the iteration converges from below by a fraction of a per cent. Not physics. It was caught only because a violated theorem is loud — a mixed instrument that merely shifts a number slightly would have passed unnoticed.
Test a criterion at the boundary of its sample, not the middle. Two of the four quotient criteria died the same day. One had held on twenty-five of twenty-six cases. A badly wrong proxy is caught immediately; a proxy that is ninety-six per cent correct becomes a claim.
A related correction sits outside these thirteen because it is a priority error rather than a mathematical one. A counterexample to the Jacobian conjecture recorded here as a local discovery was in fact the counterexample presented publicly two days earlier. It is genuine mathematics and it is not ours; see the verification note. The missing step was a literature check before the verification effort rather than after it.