Open topics v1

Date: 26 October 2026 Status: maintained working queue Machine authority: open-topic register Detector map: detector and frontier atlas

The register contains 55 independently closable topics: 46 remain live and nine are closed with retained evidence. The whole-corpus scope and ranked execution order are summarized in the frontier exhaustion checkpoint.

Operating rule

An open topic stays on this list until one of four things happens:

• its closure condition is met and linked;
• its kill test fires and the topic becomes a retained no-go;
• a dependency proves it unreachable and it becomes blocked;
• it is split into sharper child topics, with the parent marked superseded.

“Interesting” is not a status. Every topic has a next action, detector bundle, closure condition and kill test in the machine register.

P0 — active conductor

P0 — gated executable work

AZ-058 turns OT-006 into a measured bandwidth rather than a request for “more optical data.” The published Hall tensor ends at 1.5 THz. A 0.1–1 µm force experiment samples a characteristic 24–239 THz (0.099–0.987 eV), so the missing off-diagonal band begins 15.9 times above the current ceiling. The nearest experiment is same-film spectroscopy; force metrology follows only after a no-refit resolvability calculation.

AZ-059 closes OT-010's specification layer. The exact hub record has rank two; a resolved centred detuning releases rank four; weak breaking produces quadratic memory; and a physical outer-port exchange flips the oriented contrast cubic. All 5,000 frozen tolerance draws retain the declared gap, visibility and rank conditioning. OT-010 remains active for construction and blind execution, not for another dimensionless redesign.

P1 — executable development and mandatory audits

P2 — gated translation problems

Wave 7.72 and AZ-082 now separate two questions that previously looked like one. The pinned Claimipedia relationship capture still has zero of 43 edges directly admissible as scientific transformations. Separately, four authored D02 research paths, with sixteen named steps, pass the active Sourcery v1 protocol and retain assumptions, losses, evidence, bounded authority, fourteen zero-candidate negative queries and fifteen rejected-rule fixtures. A source-native executable workflow therefore exists; a graph-derived Jordan algebra does not. OT-026 and OT-027 now reopen at the narrower boundary. AZ-083 closes that dimension gate for the primary four-step path at the honest dimensionless record layer, and shows that missing or inconsistent dimension metadata kills the path. AZ-084 extends the result to all four families: sixteen steps pass, fourteen negative queries remain empty and fifteen invalid rules remain rejected. Declared loss-bearing projections preserve live v1 execution. Record-level migration is closed. AZ-085 then closes the first quantity-level witness: a calibrated passive RC network carries siemens through Schur elimination, converts volts to amperes through a declared operator and predicts a computationally held-out current recovered by an independent Kirchhoff solve. OT-027 is narrowed to source-native measured data and a rule generating both operator and detector map. OT-026 remains open: no Jordan product or identity has been extracted from relation composition.

AZ-086 extends the physical bridge to extract-positive-operator-measure. The RC pole becomes a positive atom in siemens per second, and its held-out Stieltjes contribution is recovered independently. The atom correctly loses the coupling sign. This closes the scalar measure translation, not general operator reconstruction or graph-to-Jordan extraction. The next datum must be a source-native measured response or a non-imported product identity.

AZ-111 now changes the strongest reading of that boundary. The reversible Spin--Temple block induces an exact special Jordan product: transpose fixes a three-dimensional $H_2(\mathbb Q)$ face, and determinant and matrix rank come with it. Reaching the face discards the 30-dimensional path radical, folds two relation labels into one symmetric coordinate and supplies positive order from the real matrix representation. OT-026 remains gated on a source-native order that survives the radical and predicts a withheld composition or physical record.

AZ-112 tests that order at its source. None of the four aggregate relation-generator transposes belongs to the 35-dimensional predecessor-closed algebra. Across all 24 permutations of the relation labels, global edge reversal recovers at most two of seventeen records: the local Spin--Temple pair. The Jordan face is therefore exact but quotient-local. Reopening now requires an authored dagger, a provenance-bearing nonlocal anti-automorphism, or a held-out prediction that selects one.

AZ-124 closes the finite translation grammar without weakening that no-go. Every weighted edge supplies a rank-one boundary atom of $H_2(\mathbb R)^+$; incidence glues these atoms into $D-A$ or $D+A$; Schur elimination compiles hidden paths into an effective two-port face. A complex edge coordinate is gauge-removable on a tree. The first intrinsic phase appears on a cycle, and the $H_3(\mathbb C)$ determinant reads its cosine while an orientation-odd detector is required for its sine. OT-026 now lacks neither a mathematical compiler nor a precise failure location. It remains gated because Claimipedia has not generated the dagger, positive kernel and boundary partition before the desired quotient was inspected, and no held-out record has been predicted.

AZ-125 executes that collision against the hash-matched live captured source. Counting measure and incidence derive a positive kernel, but reversing every arrow or permuting every relation label leaves it unchanged. Schur reduction gives an exact Spin--Temple rank-one face, yet its conductance is two when reciprocal authored records are counted separately and one when they are treated as one undirected relation. Positivity is therefore support-native but not semantic. The nearest nontrivial source cycle is instead the all-DependsOn river flow--calibration--nitrate triangle; its current evidence is fixture-only and contains no maps or held-out numerical record, so it defines the next honest experiment rather than closing the translation.

AZ-126 shows that AZ-125's loss was caused by an early quotient rather than positivity itself. On the free node by source/target rail by relation-type carrier, the Gram kernel is positive and its source--target blocks reconstruct all 41 distinct directed typed records. Rail swap is exactly equivariant with global arrow reversal. Identifying the rails and type channels recovers the ordinary rank-33 Laplacian from the rank-41 lift, localizing an eight-direction quotient scar. This closes faithful positive representation, not the required path product or semantic star operation; no physical boundary or prediction is yet source-selected.

AZ-129 then classifies the local motion that the mirror could support. Complex, split-complex and dual-number generators are the negative-square, positive-square and square-zero branches of one symplectic family. The rail swap is anti-symplectic as a discrete exchange but generates a symplectic hyperbolic flow after exponentiation. This supplies a precise candidate grammar, not the missing source semantics: OT-026 must still derive which square class, if any, the authored path composition selects. A signed two-port trace curvature is the smallest proposed held-out discriminator.

AZ-130 closes the universal local algebra more strongly. An anticommuting negative- square quarter-turn and positive-square mirror generate $Cl(1,1)\cong M_2(\mathbb R)$, while their two null mixtures are directed square-zero rungs. This set the decisive source-native test: derive the negative-square partner and check anticommutation with the existing rail swap. AZ-131 subsequently passes that algebraic test, so OT-026 no longer waits on the local operator; it waits on response closure, path semantics and a held-out orientation record.

AZ-131 passes that source-native test. The authored source/target grading \(G\) and rail mirror \(J\) anticommute, so \(I=GJ\) is a canonical negative-square operator and its null mixtures are within-fibre rail transfers. The result does not close OT-026 because \(I\) carries the signed incidence kernel to an unsigned co-incidence kernel rather than preserving it. The next object is a doubled response with both channels, an authored path product and a semantic adjoint.

AZ-132 then exhausts the vocabulary across the corpus. It finds the complete local grammar independently on the Claimipedia rails, neutral Peirce/selector planes, bi-symplectic recursion and Furey--Higgs aggregate plane, while keeping antiunitary, KO-sign and lone-nilpotent neighbours separate. This closes semantic propagation, not the cross-carrier intertwiner.

AZ-133 derives the doubled response. Incidence and co-incidence descend to the ordinary and signless Laplacians with ranks 33 and 35. Their rank difference is exactly the two connected components containing odd cycles, so the second channel detects an alternating-sign topological obstruction rather than an extra dimension.

AZ-134 then exhausts all 24 type permutations and all 10 involutions. The best rule reverses only the Spin--Temple Supports/Qualifies pair and leaves 41 of 43 records unmatched. The current-source path-adjoint route is therefore closed negatively. OT-026 reopens only with independently authored reverse semantics, an external contravariant functor or a device dictionary predicting held-out reverse-path records.

AZ-142 supplies the nearest physical calibration without pretending that relation labels are forces. Three programmable resonators realize node amplitudes as carrier, coupling parity as selector and loop parity as detector. The two flux sectors have identical trace and quadratic spectral moment, but their pole-product determinants differ by exactly $4\kappa_{12}\kappa_{23}\kappa_{31}$. This makes AZ-142 an executable precursor for OT-024; success validates the detector grammar inside ordinary mechanics, while only a controlled residual can reopen fundamental physics.

AZ-113

AZ-114 proves that the exact dimension-five map into the three W-associated amplitude coordinates has null direction \((0,0,2,1)\), and that arbitrary same-process differential or linearly folded detector records inherit it. This closes finer binning of the same process as the sixth-coordinate strategy without closing the three-coordinate factorial amplitude test.

AZ-115 restores the omitted hypercharge and gluon anomaly shifts. The five-coordinate current quotient plus three direct gauge labels has rank seven, with exact null \((\Delta A_2,\Delta c_{WW},\Delta c_{BB})=(2,1,-1)\). A neutral-gauge record supplies the missing row only after a direct-operator slice is declared; the unrestricted EFT should be fitted in basis-invariant coordinates rather than asked to reveal an unobservable origin label.

AZ-116 identifies the conditional detector pair and its remaining loss. Charged weak and diphoton amplitudes invert \((A_2,c_{WW})\) when \(c_{BB}=0\), but their separate rates retain two relative-sign branches. A coherent reference, full width model and nuisance-profiled joint likelihood are the exact remaining experimental inputs.

AZ-117 provides the coherent-reference statistic: paired mass bins about the ALP pole isolate the odd real interference term, and a sign-weighted moment reverses with the resonant source residue. The remaining gate is no longer conceptual; it is the source-complete continuum/resonance helicity calculation and detector convolution for one declared channel. audits the nearest official collider implementation. Its CaPhi control fixes the normalized top and bottom ALP couplings to opposite signs, while CWtil supplies the direct weak-boson control. The resulting intervention map has rank two: only nine of the twenty-seven signed settings are reachable, and a general six-coefficient quadratic kernel collapses to three combinations. The file is valid for that two-control slice; it cannot execute the corpus's three-source test. This is an implementation-rank boundary, not a physical no-go.

AZ-087 supplies that first measured response. A checksum-identified Zenodo EIS file is split before fitting; a nonnegative passive circuit family predicts fifteen held-out complex impedances with 0.462% median and 3.575% maximum relative error. This closes one-cell translation, not uncertainty, detector likelihood, cross-cell generalization or dynamics.

AZ-088 runs the frozen protocol across all 54 cells. Every cell passes; the worst cellwise maximum held-out error is 3.914%. This establishes population-wide adequacy under per-cell calibration. A shared population law, covariance and generated dynamics remain open.

AZ-089 tests that stronger law without target-cell recalibration. The other 53 cells' median parameter vector passes 53 of 54 unseen cells, but ID07 reaches 5.575% median error and fails the frozen 5% ceiling. The common passive shape is therefore nearly population-wide, while one localized heterogeneity prevents closure. The next honest object is a preregistered hierarchical predictive distribution with independent covariates or a minimal calibration record plus replicate and fixture covariance—not a post-hoc refit or a new-physics label.

AZ-090 proves that simply widening this to the other cells' pointwise min-max range does not supply that object. Its 52/54 scalar coverage is forced by ranks. The informative residue is cross-frequency coherence: ID07 is real-part extreme at all fifteen evaluation frequencies, while ID52 is repeatedly imaginary-part extreme. OT-027 now requires a donor-selected latent cell state and simultaneous spectral coverage, not independent pointwise bars.

AZ-091 tests the smallest calibration record. A nested neighbour model using one fixed 10 kHz complex point passes 53 of 54 cells but leaves ID07 at 5.250% median error. Solving only series resistance and inductance from that point passes just 36 of 54. One point is informative but does not span the relaxation state; the next record needs a second, separated frequency.

AZ-092 closes that point-prediction gate. Nested donor-only selection pairs 10 kHz with 2.8219349 Hz for 51 targets, and all 54 cells pass on fifteen untouched frequencies. The result is a two-tone population-state bridge, not yet a joint predictive distribution, external replication, detector likelihood or dynamics.

AZ-093 removes the remaining adaptation. The globally fixed 10 kHz / 2.8219349 Hz, three-neighbour rule still passes all 54 cells and improves the worst median error to 2.290%. It is now a reproducible within-batch point predictor; joint uncertainty, fixture covariance and external-batch replication remain open.

AZ-094 tests the whole predicted curve as one object. A donor-only maximum-error score across all fifteen untouched frequencies covers 49/54 spectra at nominal 90% and 52/54 at nominal 95%; ID07 and ID12 remain outside the latter. This is useful internal uncertainty engineering, but the overlapping nested fits do not provide an independent split-conformal or external coverage guarantee. OT-027 now asks for a new batch with fixed calibration/test partitions, repeat and fixture covariance, and a separately generated action for dynamics.

Wave 7.73 sharpens OT-050 without closing it. The reduced free-Majorana (T1/S1) action is complete on the ten even spin sectors. A lone absolute (\pi/4) phase depends on a common anomaly trivialization, while the (T1) fixed-square/two-cycle ratio and (S1) odd--odd/even--even fixed ratio are both invariantly (i). The next datum is no longer another free-theta enumeration: it is the genus-two fermionic Baby-Monster spin family, followed by a coherent relative-sector detector map and one complete gravitational route.

The Moonshine/program/lattice audit sharpens OT-045 and OT-050 without adding a duplicate topic. The Monster Lie algebra grading plane embeds exactly as the diagonal integral \(II_{1,1}\subset H_2(\mathbb R)\), but this is a kinematic carrier slice, not a Monster action on the full cone. On the cyclic Golay image the exact identity \((1+\sigma)^{89}=\sigma^2\) isolates the order-23 cyclic symmetry, while the remaining order-89 factor proves that Rule 60 itself cannot be a Monster element. The scalar lift now closes: the determinant-23 Leech fixed lattice has Gram matrix \(\left(\begin{smallmatrix}4&1\\1&6\end{smallmatrix}\right)\), and its normalized theta/eta trace is exactly the common 23A/23B McKay--Thompson series. The inverse nonprincipal discriminant-\(-23\) forms have the same scalar theta series, so the record provably forgets orientation. Before that loss, however, reducing the Gaussian period on the two degree-eleven Golay factors gives \(0\) and \(1\), contracting them to the conjugate ideals \((2,\alpha)\) and \((2,\alpha+1)\). Thus the oriented arithmetic lift is canonical relative to a declared primitive root; the unresolved convention is which resulting Monster generator is called 23A. On the 529 sector labels, the fifth-power exchange and modular quarter-turn generate the exact dicyclic group \(\mathrm{Dic}_{11}\) of order 44. This is a reversible label calculus, not a Monster subgroup or physical dynamics. Projectivizing removes its central sign and gives \(D_{11}\) of order 22, with the pure axes separated from all 22 mixed directions. The finite action embeds in \(Sp(4,23)\cong Spin(5,23)\), but this preserves algebraic type rather than the real signature, cone or time orientation. Current work sharpens that reopening again: Volpato's September 2026 preprint supplies a self-orbifold \(23AB\) channel with 529 sectors, \(q(a,b)=ab/23\), the \(U(23)\) discriminant form, an embedded \(P(23)\) parafermion algebra and a Tambara--Yamagami duality defect exchanging twist and charge. Ordinary genus-one charge projection still collapses all twenty-two nonzero charges to one series. A separate conditional construction predicts twelve \(\operatorname{Rep}(\mathfrak{so}(3)_{23})\) defect lines with \(\Gamma_1(25)\) invariance; \(X_1(25)\) has genus twelve, an exact but unexplained rank/genus coincidence. A modular-orbit audit further shows that the 529 entries are not independent: the 528 nonzero labels are one \(SL_2(\mathbb F_{23})\) orbit, while \(\Gamma_0(23)\) invariance collapses their scalar realizations to 24 projective branches, each shared by 22 labels. Fricke invariance turns the branches into \(T_{23}((\tau+r)/23)\), and Fourier projection filters coefficients by \(n\equiv ab\pmod{23}\); all 529 module characters thereby reduce to 25 scalar types. Volpato's commutant inversion now yields three verified terms for each of the twelve required even-\(l\) characters. The scalar duality-defect trace is now assembled through \(q^4\) and remains invariant under fifth-power exchange, so it closes negatively as an orientation detector. The full commuting-insertion census now closes the scalar version of that proposal. For an order-23 element the centralizer is \(C_{23}\times S_4\); its five insertion classes yield cyclic products of orders \(23,46,46,69,92\), and every corresponding A/B McKay--Thompson pair is equal. The order-24 Monster anomaly transgresses trivially along the order-23 twist, so the centralizer action is linearisable; the five class traces determine the full graded \(S_4\) module, and scalar word traces add nothing. The next finite work must therefore construct cross-grade VOA or defect composition, identify the corpus cycle with an oriented 23A/23B generator, and sew the channel at genus two. The off-diagonal physical Jordan response and a gravitational action remain separate gates.

P3 — fundamental firewall

Closed with retained evidence

Cross-cutting unknowns

The queue exposes nine recurring unknowns that should be reported for every new arm:

1. carrier: what physical degrees of freedom hold the state?
2. admission: which constraints define allowed states and transformations?
3. dynamics: what generates motion, attraction, switching or decay?
4. orientation: what physical reference retains a sign or phase lift?
5. memory: where is history stored and how long does it persist?
6. detector: which records separate the leading mechanisms after nuisance folding?
7. scale: which conclusions survive size, time, frequency and coarse-graining limits?
8. translation: what typed map connects formal structures to physical operators and observations?
9. record law: which completely positive instrument decides what becomes a retained record, and is it selected or merely one member of an admitted family?

Stop rules

• Do not add another abstract selector before OT-002 and OT-003 are instantiated on a carrier.
• Do not interpret two-current rank before OT-008 closes its low-frequency limits.
• Do not infer Berry curvature from thermal Hall without OT-011's independently measured gap, moving-crossing intervention and joint mixture test; clean-limit persistence does not exclude intrinsic many-body skew scattering.
• Do not infer a material Casimir bridge before OT-006 and OT-007 close without refitting.
• Do not promote relation, Leech, Golay, Jordan, \(Spin(2,3)\) or \(E_8\) contact without OT-024–OT-027.
• Do not reopen torsion coefficient selection without the explicit datum in OT-029.
• Do not call a finite spectral scan a mass-gap result without OT-031.
• OT-054 closes the direct identification: the current OPH source has no canonical invariant H_2(R) corner, adjacent updates retain schedule order and the record laws are non-injective. Use OT-055 for the narrower emulator and scheduler-qualified quotient question.

The maintained list is intentionally finite. New topics should be added only when they introduce a distinct carrier, detector, boundary, translation or falsifier not already represented here.

AZ-056 deliberately adds no duplicate topic. Its exact kernel-invariance and defect-composition calculus is physically instantiated by AZ-099, which closes OT-019's stated construction. Its commutator no-go still sharpens OT-027 and OT-038; its detector-intersection law sharpens OT-034; and its unresolved modular-forms signpost remains behind OT-045. Repetition of the diagram without a source-native arrow does not create a new frontier.

The three-carrier programme checkpoint also adds no duplicate topic. Its exact A8 mixed interface sharpens OT-019; the closed F05 slice concentrates OT-024, OT-027 and OT-038 into a single co-realization task; the refused F01 lift sharpens OT-003 and OT-034; and the 39-entry instrument atlas assigns concrete decision surfaces across the existing queue. The remaining frontier is execution, scale survival and source-native provenance, not another relabelling of the same finite map.