The explicability ledger: every row of the explanation register (block X, "what the construction explains") of every paper ledger of the corpus in one place (65 explicability dividends from 7 sources, 46 with a machine witness). A row keeps the identifiers it has at home: its paper label (35:X13) and its accession key (p35050); the label links to the row in the paper ledger, the key is stable. A dividend stated in more than one paper is listed once, at its first appearance, with the restatements linked from it (5 folded). Where the paper has a validation package, the witness column shows the family that decides the row and whether it passes today.
| # | Explicability dividend | Status | Source · witness · master |
|---|---|---|---|
| 14-entr. De Sitter Entropy Estimates over Finite Holographic Substrate ¶ | |||
| 14:X3p14030 | The age coincidence $t_0H_\Lambda\approx\pi/4$ becomes the octant: $\Omega_\Lambda=\tanh^{2}(3\pi/8)=0.6837$ [ΛCDM] is an output of the realisation set, landing at $0.19\sigma$ on the fitted $0.685\pm0.007$ — never an independent measurement of $\dS$ (same-channel, X6), a zero-freedom derivation in full standing; the $(\Lambda,H_0)$ entailment at the channel-1 $\Lambda$ is this same landing read on $H_0$, not a further prediction. | T R | Lem. 1; est.A1 1/1 |
| 14:X4p14031 | The congruence $\dS$ even acquires a second physical face: it is the existence of the octant sector, hence the well-definedness of the measured age — a structure of the Carrier’s cycle lattice, certified by realisation and read as an observational condition, never an arithmetic property of the numeral. | T | Lem. 1(iv) |
| 14:X5p14032 | The termination of the single-object sequence is a consistency of the wall structure: the typical-density diagonal over-closes at $1.8\times10^{8}M_\odot$ [approx] (sensitivity band $(1.4\text{--}2.8)\times10^{8}$ across fit variants), so every heavier single object continuing the condensed-density sequence is necessarily wall-bound; the supermassive holes are that continuation, not an anomaly beyond it. Classified with the triangle: consistency, not derivation of an observed scale. | T | § 4; tri.D 1/1 |
| 14:X6p14033 | The celebrated sub-percent age agreement is judged: same-channel by the circularity criterion, a restatement of the fitted dark-energy fraction — consistency, not evidence — and the criterion locates exactly which confrontations do carry weight. | T | § 3.3; est.A1 1/1 |
| 14:X7p14034 | The universe-as-black-hole puzzle dissolves: the Hubble radius sits on the black-hole line identically ($\rho_{\mathrm{BH}}(r_H)=\rho_c$ [ΛCDM]), but the Schwarzschild reading consumes an exterior, and the containment argument (A3) makes an exterior incoherent — the totality on its own horizon is the chart’s closing point, not a hole in a background. | T | § 4, [Lineweaver & Patel 2023] |
| 14:X8p14035 | The interior completions weighed: black-hole cosmology keeps the same saturation identity by consuming a parent exterior and a singularity-replacing mechanism (torsion; exclusion pressure); the finite reading consumes neither: the containment argument (A3) closes the chart at $\Om$, and no singularity is available over a finite totality. The registered record-depth bound separates the completions empirically (P2). | T | master: 00:L6 |
| 21-grav. Gravitation as Phase Synchronisation ¶ | |||
| 21:X1p21041 | The cosmological-constant magnitude. $\Lambda\sim1/\Omega$ in Planck units is the curvature of the closed chart, the totality datum, not a vacuum energy requiring cancellation across $122$ orders. The fine-tuning problem is not solved but unasked. | T R | § 1 restated as the small cosmological constant in 32-dark and as the dissolved cosmological-constant problem in 14-entr |
| 21:X2p21042 | No dark-matter particle. The radial acceleration relation is a registration crossover of the resolution floor, not evidence for undetected mass: galactic dynamics require no dark sector beyond the floor already fixed by $\Omega$. | T R | restated: 32:X11 |
| 21:X3p21043 | No horizons, no singularities, no information loss. Collapse ends in a horizonless body, operationally black at $r_f$ (conditional on the fold-transition programme, C12), with an exact saturating interior profile — and information conservation is a theorem citation, not an absence claim: interior data live in offset sectors the drive confines exactly [Akhtman & Voether 2026]: the theory never forfeits predictivity. | T R | Prop. 6.4, 6.2 |
| 21:X4p21044 | Misner’s standing objection dissolves. The exponential metric is derived, not posited as a self-coupled field equation, so the field-equation pathology Misner identified in exponential-metric gravity does not arise here. | T | Rem. 6.7 |
| 21:X5p21045 | No graviton quantisation problem. The radiative field is collective phase synchronisation, not a propagating fundamental quantum: there is no separate field left over to quantise. | T R | § 5.5 |
| 21:X6p21046 | The large-angle microwave anomaly. The anomalously low large-angle correlation ($p\sim1\%$ [Schwarz et al. 2016]) is the signature of the wrapped chart: super-horizon modes are identified, not populated, truncating correlations beyond the horizon scale. This consonance is a number, the primordial spectrum being structural, not transported. | T R | Prop. 7.8; grav.primordial 1/1 |
| 21:X7p21047 | The equivalence principle is an identity, not a postulate. | T | Cor. 4.8 |
| 21:X8p21048 | The weakness of gravity is cardinality dilution, not a hierarchy to be tuned. | T | § 4.4 |
| 22-qm. Quantum Observation over Finite Substrate ¶ | |||
| 22:X1p22044 | The Born rule is a coincidence count, the unique window lift of its carrier shadow, not a postulated quadratic functional — on its stationary domain, where the weights are uniform over the fibres; non-uniform statistics are read through the engineered-core readout (C11). | T | Prop. 5.3, Thm. 5.7, Rem. 5.8 |
| 22:X2p22045 | The complexity of amplitudes is the arithmetic of the shared quarter-turn core, the canonical complex sector $\Z[\It]$; a shell without the internal quarter-turn gives a real-amplitude theory instead. | T | Prop. 6.1 |
| 22:X3p22046 | The preferred basis is the Subject’s own phase anatomy, einselected by the algebra of the frames rather than by a model of the environment. | T | Prop. 4.2 |
| 22:X4p22047 | The dynamical measurement problem dissolves: collapse is the re-metrisation of a relational chart, no disturbance propagates, and distinct Subjects never disagree on what they share. | T | 1/1 |
| 22:X5p22048 | The classical limit has a mechanism, containment, the divisibility of the observer’s frame, exact arithmetic rather than an appeal to a limit. | T | § 8 |
| 22:X6p22049 | Native probability over a finite substrate: the unordered-field obstruction is cleared by keeping counts in the observer’s ledger: a finite-relational provenance theorem for the Born calculus, in which the substrate determines the tally ring, the measurement family, and the readout (calibrated against the counting and cyclotomic precedents in Section 11). | T | § 5 |
| 22:X7p22050 | The Tsirelson boundary is attained as a ring identity, $S=2(\zeta_8+\zeta_8^{-1})=2\sqrt2$, so a relational finite substrate carries full quantum correlation strength, not merely quantum vocabulary. | T | Thm. 7.11; qm.composite 1/1 |
| 22:X8p22051 | Higher-order interference is forbidden exactly: the Sorkin hierarchy is zero with a forbidden neighbourhood, not a small number to be measured down. | T | 1/1 |
| 27-fld. Standard-Model Interactions over Finite Substrate ¶ | |||
| 27:X1p27024 | The gauge group $\U(1)\times\SU(2)\times\SU(3)$ is the gauging of the substrate’s three frame data, the phase, spinor, and colour frames read by the one recipe, not a product of groups chosen to fit. | T | § 5, 6, 7 |
| 27:X2p27025 | Charge quantisation is automatic: electric charge is an integer winding index, so the electron and proton charges match exactly and no fractional residue survives, with no quantisation condition imposed. | T | Prop. 5.2; fld.em1_prototype 1/1 |
| 27:X3p27026 | The photon and its dynamics are forced: masslessness is drive-invariance and the exact rank-one kernel of the broken vacuum, and Maxwell is the unique adjacency-local gauge-invariant quadratic operator, neither put in by hand. | T | 2/2 |
| 27:X4p27027 | The Weinberg angle is the exact rational $\sin^2\sW=3/8$ at the unification point, fixed by the charge spectrum of the realised generation (B5) with the group-theoretic step imported (A4), not a free parameter measured into the theory. | T | 1/1 |
| 27:X5p27028 | The custodial relation $\rho=1$ is the rank-one identity $\det\equiv0$ forced by the spinor-doublet Higgs, not a tree-level accident. | T | 2/2 |
| 27:X6p27029 | Maximal parity violation is the exact decoupling of the Frobenius branch from the drive, so the $V\!-\!A$ current is derived rather than the left-handed doublets assigned by hand. | T | 2/2 |
| 27:X7p27030 | The colour sector is fixed: three colours is the minimal triality-carrying frame, confinement is the compact-group area law from positivity, and asymptotic freedom is the gluon self-coupling, not $N_c=3$ supplemented by an assumed confining phase. | T | 3/3 |
| 27:X8p27031 | One complete generation is the spinor $\mathbf{16}$ of the rank-five internal frame, so its hypercharges, charges, and anomaly freedom follow and a right-handed neutrino is present, with $\SO(10)$ unification forced, rather than a hypercharge assignment whose anomaly cancellation is a coincidence; given B5, the anomaly cancellation is the imported $\SO(10)$ fact (A4) evaluated on the realised content. | T | 3/3 |
| 27:X9p27032 | The interaction and generation counts are the $1+3$ split of the closed primitive-role ladder, so four forces and three families are fixed and a fifth force and a fourth generation are forbidden, not left unexplained. | T | 1/1 |
| 27:X10p27033 | The Koide ratio is exactly $2/3$, the cube-root generation orbit at the self-dual quarter-turn $\rho^2=2^{-1}$, an exact value rather than an unexplained numerical coincidence. | T | Prop. 8.8; fld.koide 1/1 restated: 28:X1 |
| 27:X11p27034 | The strong-CP angle vanishes with no axion: no substrate-native topological term, and Hermitian quark masses with real determinant, give $\bar\theta=0$, so the problem does not arise rather than being tuned away. | T | Prop. 8.9; fld.strongcp 1/1 |
| 28-flav. Fermion Flavour Sector over Finite Substrate ¶ | |||
| 28:X2p28026 | The up-quark Koide value is $5/6$ in framed arithmetic ($0.849$ in the working scheme, $0.832$ with pole masses), the cube-root colour norm $r_u^2=N(1-\omega)=3$ against the colourless $N(1-i)=2$, a ratio where the Standard Model carries no relation at all. | T | Remark 4.5; flv.quark_amp 1/1 |
| 28:X3p28027 | The flavour charges are the role depths $(0,1,2)$ of the closed primitive-role ladder, derived as the three generative roles rather than assigned to fit the hierarchy. | T | § 4.2; flv.tier_b 1/1 |
| 28:X4p28028 | The Cabibbo angle is the Gatto relation $V_{us}=|\sqrt{m_d/m_s}-e^{i\varphi}\sqrt{m_u/m_c}|$ following from the role-depth texture, the leading term at $0.3\%$ and the phase $\varphi$ a kernel datum, so two otherwise-independent observables are tied rather than measured apart. | T | Proposition 4; flv.spurion 1/1 |
| 28:X5p28029 | The Georgi–Jarlskog factor is the colour count $N_c=3$, the $B\!-\!L$ Clebsch of the $\overline{\mathbf{126}}$, not a texture coefficient inserted by hand; its double ratio $9$ against the measured $10.4\pm0.5$ is the open $15\%$ excess of the minimal Clebsch. | T | § 4.3; flv.tier_b 1/1 |
| 28:X6p28030 | The up-sector doubling $m^u_i\sim(m^d_i)^2$ is forced by the $\mathbf{10}\cdot\mathbf{10}$ Yukawa, so the steeper up hierarchy is a consequence rather than a separate assumption. | T | Proposition 3; flv.up_doubling 1/1 |
| 28:X7p28031 | The electron’s extreme lightness is the quarter-turn boundary: the lightest generation sits where the winding amplitude vanishes, massless at leading order, rather than an anomalously small Yukawa tuned by hand. | T | Proposition 6; flv.m10 1/1 |
| 28:X8p28032 | The large-lepton, small-quark mixing split is the lopsided $M_e=M_d^{\mathsf T}$: one off-diagonal feeds the invisible right-handed quark rotation and, transposed, the visible left-handed lepton rotation, so the two mixing matrices are one structure rather than two unrelated ones. | T | § 4.4 |
| 28:X9p28033 | The reactor angle is, at leading order, $\sin\theta_{13}=\sin\theta_C/\sqrt2=0.159$, quark–lepton complementarity through the quarter-turn, $7\%$ above the observed $0.149$ with no correction derived: a leading-order estimate of the mixing parameter, not a prediction. | T | § 6; flv.theta13 1/1 |
| 28:X10p28034 | Near-maximal leptonic CP is the cube-root phase: $\mathrm{Im}\,\omega=\sqrt3/2$ gives the maximal Jarlskog $J=1/(6\sqrt3)$, so the cubic reappears as CP violation rather than a free phase fitted to data. | T | § 6; flv.pmns_cp 1/1 |
| 28:X11p28035 | The neutrino spectrum (a near-massless lightest state, $\sum m_\nu\simeq59\,$meV on the normal branch) follows from colourlessness fixing $Q_\nu=2/3$, the transpose fixed point $M_R\propto m_D$ and the boundary-branch realisation that selects the ordering, rather than three independent neutrino masses. | T | 1/1 |
| 32-dark. The Dark Sector over Finite Substrate ¶ | |||
| 32:X1p32027 | Newton’s inverse-square law and the equivalence principle follow from the discrete Gauss law of the synchronisation flux, the acceleration of a test cluster independent of its mass and composition. | T | Prop. 1; dark.flux_exact 1/1 |
| 32:X2p32028 | The acceleration scale $\az=c\Hzero/2\pi$ is the phase-coherence threshold, the acceleration whose winding frequency reaches the drive’s cyclic rate, the $2\pi$ the radian-to-cycle conversion of the angular Hubble rate, parameter-free, $13\%$ below the fitted value at the entailed $\Hzero$. | T | Eq. (2); dark.deep_mond 1/1 restated: 14:X2 restated as Milgrom's coincidence with zero freedom in 14-entr |
| 32:X3p32029 | Flat rotation curves and the baryonic Tully–Fisher relation $v^{4}=GM\az$ are the deep-regime geometric mean $\geff=\sqrt{\gb\az}$, the amplitude reading of the field below the floor. | T | Eq. (4); dark.deep_mond 1/1 |
| 32:X4p32030 | The radial acceleration relation carries no fitted function: its interpolation is the finite first-passage registration given one declared identification, the amplitude barrier (B8), and it is the curve the data selected. | T | 1/1 |
| 32:X5p32031 | The relation is tight, its intrinsic scatter ($0.04$ dex at the knee, SPARC at fixed $\az$) smallest at high acceleration and rising as $x^{-1/4}$ into the deep regime, the spread of the collective phase. | T | Eq. (9); dark.rar_scatter 1/1 |
| 32:X6p32032 | The external-field effect breaks the strong equivalence principle, the internal dynamics depending on the total field through the registration. | T | Eq. (10) |
| 32:X7p32033 | The merging-cluster lensing offset is a selection: the coherence-weighted enhancement follows the collisionless galaxies and drops the shock-decohered gas ($C_{ij}\to0$), not a coincidence. | T | 1/1 |
| 32:X8p32034 | The cluster-core residual is referred to the coherent amplitude addition $\sqrt{N_{\mathrm{eff}}}$ over the core’s separately virialised composites, the one law that also gives the merger selection (C10); the quantitative closure, with $N_{\mathrm{eff}}$ uncomputed, is the conjecture O1. | T | 1/1 |
| 32:X10p32036 | The dark-matter and dark-energy scales coincide because both are readings of the one cardinality $\Om$, the floor $\az=c\Hzero/2\pi$ and the curvature $\Lambda\sim1/\Om$ fixed together. | T | § 7.1 |
| 35-hadr. Ground-State Light Hadron Spectroscopy over Finite Substrate ¶ | |||
| 35:X1p35038 | The baryon is three quarks because the only colourless escape from the gluon residue $0$ is the determinant $\Lambda^N=\det$, which requires exactly $N=3$. | T | Prop. 2; had.carrier_residue 1/1 |
| 35:X2p35039 | The baryon is colour-neutral as the centre-neutral, triality-$0$ invariant $\varepsilon_{abc}$ of the triality frame, a derived singlet. | T | Prop. 1; had.su3_singlet 1/1 |
| 35:X3p35040 | Baryon number is the Carrier residue $1$, the determinant winding, so its conservation is the invariance of $\Lambda^3$, on the same footing as the photon residue $2$ and the gluon residue $0$. | T | § 3.2; had.carrier_residue 1/1 |
| 35:X4p35041 | The Gell-Mann–Okubo relation is exact, the scale-cancelling identity $2N+2\Xi-3\Lambda-\Sigma=0$ of linear flavour breaking, a derived sum rule. | T | Prop. 3; had.su3f_relations 1/1 |
| 35:X5p35042 | The decuplet is equally spaced because the strange seed enters the wrap additively. | T | Prop. 4; had.su3f_relations 1/1 |
| 35:X6p35043 | The decuplet is heavier than the octet by the colour-magnetic curvature invariant, the colour factor $-8$ times the spin $\half S(S+1)-\tfrac98$, a derived sign and pattern. | T | Prop. 6; had.hyperfine_charsum 1/1 |
| 35:X7p35044 | The proton is stable as the minimal-wrap residue-$1$ state, with no lighter $B=1$ residue to reach. | T | § 3.2; had.carrier_residue 1/1 |
| 35:X8p35045 | The neutron is heavier than the proton because the $d-u$ seed exceeds the charge-squared electromagnetic term ($\sum Q^2=1$ for $p$, $\tfrac23$ for $n$), a derived ordering. | T | § 3.5; had.isospin_cottingham 1/1 |
| 35:X9p35046 | $\Sigma$ is heavier than $\Lambda$ by the spin-$1$ versus spin-$0$ light-pair hyperfine, a derived splitting of two states of identical quark content. | T | § 3.5; had.isospin_cottingham 1/1 |
| 35:X10p35047 | The isospin splittings obey Coleman–Glashow exactly at one body, $(n{-}p)+(\Xi^-{-}\Xi^0)=\Sigma^-{-}\Sigma^+$, a derived identity. | T | Prop. 8; had.isospin_cottingham 1/1 |
| 35:X11p35048 | The heavy baryons follow heavy-quark symmetry, $M_{\Lambda_b}-M_{\Lambda_c}=M_B-M_D$ by spin decoupling, so the baryon and meson heavy-mass differences are one quantity. | T | Prop. 9; had.heavy_flavour 1/1 |
| 35:X12p35049 | The vector mesons equally space, $2M_{K^{*}}=M_\rho+M_\phi$, the meson residue $1$ ($B=0$) on the same frame and scale as the baryons. | T | Prop. 15; had.vector_nonet 1/1 |
| 35:X13p35050 | The spectrum rests on one scale, $\sqrt\sigma=\LQCD$, the lone $\Om$-hard residue; every dimensionless mass ratio is a sub-horizon eigenvalue. | T | 2/2 |
Nothing matches that filter.
Reading the ledger
- T
- Explicability dividend. A fact the standard account postulates, fits or leaves unexplained that the construction derives; each row is a theorem of its paper (T, or T on a declared realisation, T|R), the derivation cited in its source cell.
35:X13- The paper label: the paper's corpus number and the row's label in its ledger; the link opens the row there.
p35050- The accession key, unique across the corpus and stable while labels may move.
- witness
- The validation family that decides the row, linked to its script, green when it passes today.
- master
- The master-ledger rows that carry the dividend.
- restated
- Later papers stating the same dividend; listed here once, at its first appearance.