The programme’s own open questions, each with what would discharge it. Generated from its register, not written for this page — 9 stand open.
PO-30the curves own dynamics -- A GENERATIVE LAW FOR THE MATTER CONTENTr3882: P08 sec:open states it and no register row carried it. The bend-density identity is EXACT but it states WHAT the bend is, not WHY a cut bends as it does: the slicing operator is KINEMATIC, generating the stress-energy from the curve and not the curves own dynamics. P08 narrows it sharply and the narrowing is the papers own -- the confined case IS exhibited; the boundary at which free radiation begins IS the range papers wall, and beyond it the framework leaves GR UNCHANGED so the general inhomogeneous evolution is ordinary leaf evolution with its canonical form in P10; and the branch-point crossing IS well posed, with the worldline taken up in P16. What is left after all of that is one thing: the matter contents own generative law where the construction does not supply one, a dynamics for the curve itself as against the ordinary leaf evolution that carries it -- which P08 calls the distinction between a complete dynamical theory and a kinematical one, and the deepest question this construction opens onto. ITS LEDGER ROW 11b0140039 POINTED AT PO-6 SINCE r2581, and PO-6s object is the interacting quantum tower: a classical dynamics gap routed to a quantum item, which is why nobody could work it. THE ESTIMATE IS A FLOOR, scored as a build because nothing smaller has been identified, not because a route is known.
PO-26the compact-face fermion sector -- CAN IT BE BUILTr3867: opened r3861 on a WRONG PREMISE -- I framed it as whether a sector can be built on the discrete component, and P14 has built one there. P13 sec:open: two things stay genuinely open and they are distinct; FIRST, the compact-face fermion sector. P14s sector lives on the DISCRETE component and supplies NO equivariant index, its count being a wall-localised leaf index well defined precisely where the bulk index is not. The sector the obstruction acts on is the other one, gauge-acted and isometry-realised on the compact face, and it remains unbuilt -- the major undertaking any geometric gauge-matter route would first have to complete. TRIP-WIRE: forcing the gauge group forces the Higgs representation with it.
PO-43the Weyl-squared coefficient at second order in the shearr4543 OPENED. P10 carries the whole chain and names the entry: the three quadratic invariants collapse to two, the R-squared term at second order is a multiple of Einstein-Hilbert for a transverse-traceless perturbation, Gauss-Bonnet contributes no field equation, and THE SHEAR COSTS EXACTLY ONE NEW COUNTERTERM AND IT IS THE WEYL-SQUARED ONE. So the ledger acquires that entry and the question is at what coefficient. AND PO-23s zeta(0) IS NOT THAT COEFFICIENT: the background is conformally flat so the Weyl-squared invariant vanishes identically on it, and a background computation cannot see the counterterm at all -- what was measured is the log on the degenerate combination. The entry lives at SECOND ORDER in the mode amplitude where the shear is the propagating content. NO COLLISION with the ghost-free result, which P07 scopes as classical in the sentence that states it. A SECOND POSSIBLE ENTRY is chirality-tied and unworked: the Pontryagin density is non-zero at second order for a circularly polarised mode, so whether a parity-odd entry is owed depends on the towers polarisation, on which the corpus has a position in the matter sector. r4545: THE PARITY-ODD SECOND ENTRY IS NOT OWED ON PRESENT GROUNDS, and the tempting chain fails at two separate joins. The five faces give a Z_2 exchanging the helicities and grading fermion chirality, but a map that exchanges two things is a grading and every parity-even theory has one; the corpus own criterion is that NO CONNECTED ACTION COMPLETES the reflection, applied to the radiating sector and never to this tower. And independently, a counterterm answers to a parity-odd divergence of the EFFECTIVE ACTION and not to a basis mode, so a mode-level evaluation cannot fix it in either direction -- P10 caveat bounds its own instrument. AND EVEN IF OWED IT IS A DIFFERENT KIND OF THING: the density is a total derivative contributing no field equation, so whether it is a ledger entry is a question about whether the audit counts topological terms. TWO INDEPENDENT QUESTIONS REPLACE IT: whether a connected isometry of the closed layer identifies the two helicities of an S3 tensor harmonic, and whether the ledger counts topological terms. DISCHARGED BY: the Weyl-squared coefficient at second order in the shear with the sub-leading heat-kernel coefficients, which is the instrument P10 names and stopped short of running.
PO-23the mode sums beyond the free static caser4537: THE NUMBER IS COMPUTED AND IT IS NOT ZERO. On the towers own spectrum -- eigenvalues n(n+2)-2 with degeneracy 2(n-1)(n+3), which P10 derives from Peter-Weyl rather than importing -- the spectral zeta at zero is 10 EXACTLY, the asymptotic series terminating at s=0 so it is an identity and not an estimate; and the zero-point sums log-scale coefficient is the residue, 39/4. THE TOWERS AND NOT THE SCHEMES: a hard cutoff with no zeta function in it returns 9.749 against 39/4, and 39/4 is independently the 1/m coefficient of the summands own expansion -- two regulators sharing no machinery agreeing to a part in ten thousand. SO THE MODE SUMS SPEND ONE DIMENSIONLESS CONSTANT, and the no-free-constants claim carries the scoping its own frontier sentence names. AND THE COST WAS ALREADY NAMED: the logarithmic successor goes with curvature-squared invariants, which P10 says is not an entry in this frameworks ledger. WHAT REMAINS: the scope is free and static on the instantaneous spectrum -- time-dependence does not move the leading coefficient, but that the regularisation commutes with the evolution is not established and the couplings are not in it. DISCHARGED BY: the coupled and non-adiabatic computation, which could still return zero; what is excluded is the claim holding trivially on the most favourable case.
PO-13the handover datum, and the rigid phase split beneath itr4519: the candidate mechanism is that the modes are driven twice, on the collapse leg and again on the leaf, which gives the direction, the ordering with peak number and the overshoot together. THE CHECK ON IT CAME BACK NEITHER BRANCH. The transfer never integrates the collapse leg -- it enters as a three-number handover per mode, and THE TWO HALVES ARE READ AT DIFFERENT POINTS OF IT: the photon amplitude carries the closed-form transfer and the potential is left at its primordial value, so the expanding-leg driving is re-applied from a potential already spent. Carrying the decay across does not halve the driving, it doubles it again to 5.14x the control; reading both halves at one point kills the comb. Three codings, three answers, so THE FACTOR OF 2.4 IS A PROPERTY OF THE CHOICE AND NOT YET OF THE CONSTRUCTION. The mechanism is not refuted -- the instrument cannot weigh it. AND BENEATH ALL OF IT: undriven, this arm sits at 1.1273 of the acoustic scale and the control at 0.9158, on opposite sides of the adiabatic value, a 23 per cent split no account of the driving can produce. r4527 LOCATES THE SPLIT: measured without the peak-finder, both arms turn over at exactly one half-period undriven -- control 0.9989-1.0009, the arm 0.9989-1.0001 -- so the oscillator is excluded and the split is not in the acoustic phase or the sound-horizon bookkeeping. And every available change to the handover moves the arm the WRONG way, so the handover is excluded too. THE SPLIT IS IN THE PROJECTION: both arms would sit at unity if the projected peak sat at the sources turnover, and the control lands 8.4 per cent below while the arm lands 12.7 above -- what differs is what rides with the monopole into the source, the potential, integrated and Doppler terms, which the two arms do not carry alike. r4535: THE SUBTRACTION IS DONE AND IT IS NONE OF THE THREE. Removing the integrated term WIDENS the split to 29.4 per cent, the Doppler term leaves 23.8, the monopole leaves 27.5, and switching the diffusion damping off entirely widens it to 26.0. The split never collapses, so what sets the undriven position is common to all three sources and to the envelope. TWO FRAMINGS DISSOLVE: opposite sides of the adiabatic value is a property of the baseline and not of the split, since with the monopole removed both arms sit above it and the split stands; and the ratio is far steadier than its parts, 1.23 to 1.29 across configurations whose peak positions move by up to 30 per cent. r4549: THE VISIBILITY IS EXCLUDED TOO, and the reason nothing moved the ratio then became visible -- l1/lA = k1 rs / pi, THE DISTANCE CANCELS IDENTICALLY, so the ratio was never a projection quantity at all. What it compares is the sound horizon each arm REPORTS against the phase its modes accumulate, and those are different integrals over different intervals here: the control from the start of its run, this arm from its onset. THE INSTRUMENTS OWN COMMENT PREDICTED THE CONFOUND -- that a comparison between the arms confounds the rate with the start. Run symmetrically it largely dissolves: start matched alone overshoots and CHANGES SIGN, start and sound-horizon convention both matched leaves a quarter of the original on the far side of zero, the two mismatches having been partly cancelling. WHAT REMAINS: the residual under matched conventions, measured against a scale this arm pins to the one fitted number while the controls is free. DISCHARGED BY: that last convention stripped -- both arms free or both pinned -- and separately a statement of what the photon perturbation and the potential both are at ONE locus.
PO-24whether the tilt displacement is a tensionr4505 NARROWED -- the computation is done and the verdict is neither of the two expected. A refit of amplitude and tilt absorbs the signature almost entirely in SHAPE, 0.26 per bin over the 185-bin ceiling and less the higher one looks, because over a restricted high-ell range a Gaussian in ell is well approximated by a power law. THE ABSORPTION COSTS a tilt shift of -0.0304 against sigma = 0.00323 from the same covariance that scores the fit, so the signature does not vanish -- it relocates into an inferred parameter. THE EARLY-ISW LEG IS ANSWERED AND SMALL: 0.77 sigma per bin over 700-1296 against 3.49 over 100-1296, so the term the row named as one of two things the answer turns on does not reach the multipoles in question. BOUNDS THAT TRAVEL WITH IT: the shape residual IS an upper bound; the tilt displacement is NOT, since more parameters would share it; and the magnitude is not robust to a factor of three between the data-shape and in-source routes, stated at the weaker bound with closing the factor named as work not done. DISCHARGED BY: whether a displacement of that size in the inferred tilt is a tension, which is a joint fit and is the whole of what remains.
PO-36does the Hubble-Eddington radius track the dynamical mass or the baryonic oner4207 NAME GUARD: the standard literature calls this radius a maximum TURNAROUND radius; in this corpus TURNAROUND is the comoving turnaround, where the worldline turns at r = -(2M alpha^2)^(1/3) on the conjugate leg -- a different locus, and their word is used only in reporting their result. The radius is derived in the standard framework and proposed there as a local test of Lambda, with the same M^(1/3) scaling this construction gives, so the two are DEGENERATE on the radius. The circularity is in how the test has been run: the N-body calibrations are dark-matter-only and the observational masses are dynamical, so which mass sets it is assumed rather than measured. Discharged by the radius measured against independently measured BARYONIC mass. Held at weight: a baryonic-set radius is smaller, which is the OPPOSITE direction from the dark-matter evidence, so this is a discriminating measurement and not a dark-matter explanation
PO-31the progenitor spectrumr3969: family 3 of THE_OPEN_PROBLEMS_LEDGER, and P15 calls it THE GENUINE FRONTIER as against its buildable debts. PO-16 is struck and its own text names this as what stays open beyond the strike, so the object was correctly identified and unregistered since r3012. The strike is sound and is why this is a frontier rather than a gap: the infall thermalizes four orders above the deuterium bottleneck so the progenitors composition is ERASED and the abundances are synthesized in the window, while BARYON NUMBER survives because no dissociation destroys it. So eta is inherited because a conservation law protects it and the abundances are predicted because none protects them. AND THAT CONSTRAINS THE DERIVATION IN KIND: it must reach a CONSERVED CHARGE of the progenitor, not a thermal history. P16 has already excluded one mechanism -- the Euclidean action is odd under the standing conjugation so the two branches carry equal and opposite action, the balance exact rather than approximate.
PO-25the charged bead -- DOES A CHARGED COLLAPSE FORM THE CAUCHY HORIZONr3827: P03 states the obstruction exactly -- with Q nonzero, Q^2/r^2 dominates as r -> 0 so f -> +inf rather than -inf, an inner Cauchy turning point appears, and r=0 becomes a TIMELIKE RN singularity rather than the branch point through which the signed radius passes to the conjugate branch. So the cosmogenetic loop has no branch point to close through when the collapsing matter carries charge. And the limit is SINGULAR: r_inner = M - sqrt(M^2 - Q^2) -> Q^2/2M shrinks to zero as Q^2, but at ANY Q>0 the origin is timelike and only at Q=0 exactly is it a branch point -- the bead closes on a set of measure zero in Q. P03s charged case is the ETERNAL RN-de Sitter geometry, stationary; PO-13s object is the DYNAMICAL collapse. The question is whether a charged collapse forms the eternal inner horizon at all, real collapses being widely held not to, in which case the branch point survives dynamically and the charged case rejoins the bead. HANDS OFF TO PO-13 IN THAT LIMIT. And the arbitrariness objection -- that a loop closing only at Q=0 exactly is a flatness problem in other clothes -- is answered structurally rather than numerically: the sub-Planckian answer is FALSE at cosmological scale, since on 1e80 baryons even the lab bound 1e-21 on