A Finite-QEC Substrate Program

The shortest map of the current canon. Particle physics and cosmology are modelled as consequences of a quantum-error-correcting register geometry rather than as fields on a pre-assumed continuum: an eight-bit local code, its constrained crystallisation into a register-bearing cubic phase, and a finite service ledger for boundary and bulk correction events. The aim is not to present the framework as closed, but to state clearly what is derived, what is computed, what is conditional, and what has been retired. The strongest current themes: recovery of Standard-Model-like matter structure from the finite code; a now-canonical 28 = 2×14 service clock; a proton-primary route in which the measured proton mass fixes the chiral scale and the framework predicts G, M_P and H₀; a dynamic dark-energy branch w(a) = −1 + a/28; an HBC scalar-clock route to (n_s, A_s) = (27/28, (3/4)α₀⁴); the electroweak/top scale reduced from an unexplained second anchor to a ~10% radiative prediction, v/M_P = α₀⁸/√λ; and a crystallisation/debris sector sharply constrained by embedded-lattice simulations. It is explicit about how it can fail — standing falsification targets include a SH0ES-side resolution of the Hubble tension (the chain predicts H₀ ≈ 67.3 on the CMB side), a robust phantom epoch w < −1, and failure of the proton-anchored G to land inside the CODATA error bar.

States the foundational objects and audit methodology behind the program. The physics is presented not as a continuum field theory with a hidden discretization, but as a finite register system whose ordered crystalline phase supplies the visible substrate and whose correction, strain, and boundary ledgers determine which quantities become physical observables. Since the first version the foundation has sharpened: the eight-bit cell is no longer an assumed starting object — under explicit stable-record hypotheses (binary local records, commuting CSS read/write, balanced self-duality, doubly-even closure, distance-4 erasure protection) the unique minimal cell is forced to be the self-dual doubly-even [8,4,4] code, and the bare service rate α₀ = 1/137 is derived from the symmetric record-pair alphabet (Sym²(16) = 136, plus the idle channel). It also introduces the bi-cubic crystallisation picture, the distinction between syndrome and strain readouts, the 28 = 2×14 service-clock construction, and the rules that classify every claim as locked, computed, foundationally grounded, conditional, retired, or open — with the dressed-α value now a bounded conditional Maxwell-contact candidate — a finite local subtraction 2ΣQ² − 1 = 31 giving α⁻¹ = 137.036, still awaiting the endpoint-covariance → F² normal-ordering theorem, not yet a locked QED prediction. The goal is to make the later physics papers auditable: every coefficient must name its carrier, event unit, scheduler, observable map, and reproducibility check. The methodology's own kill condition is concrete — a companion-paper coefficient that cannot exhibit this ledger is, by the standard set here, not canon.

The matter-sector companion. Collects the finite-code results that produce Standard-Model-like matter bookkeeping, the gauge-structure results that survive current audits, and the spectroscopy results that remain load-bearing after the numerical-search and retraction tests. The central message is deliberately split. The strongest results are exact finite identities: charge bookkeeping, anomaly cancellation, the separation of spatial, colour, generation, and repair-axis roles, and the recovered chiral charge-cube identity ∑Q_L³ = −2/9. The continuum and dynamical results are more mixed but have sharpened: the chiral/mirror-gapping continuum problem is now rigorously reduced to ordinary SU(3) confinement (a standard pure-gauge lattice fact rather than a framework-specific gap); the electroweak/top scale, once an unexplained second anchor, is now a ~10% radiative prediction v/M_P = α₀⁸/√λ with a forced near-critical quartic λ(M_P) = 0; the W/Z sector is a pole-precision map in which the live 2/9 is a post-EWSB LSZ endpoint quotient (the old UV Weinberg-angle 2/9 is retired to a 3/8 charge trace) and α(M_Z) is simply dressed α(0) run up to M_Z; and the neutrino texture yields a sharp near-maximal second-octant prediction θ23 ≈ 45.9°. Spectroscopy still contains several robust anchors, but mass-ratio numerology is actively demoted unless the observable map is unique. The goal is not to declare the matter sector closed, but to state which parts are exact finite arithmetic, which are reproducible computations, and which remain continuum-lift or operator-definition frontiers.

States the current gravity and horizon canon. The preferred presentation is proton-primary: the measured proton mass fixes Λ_P = m_p/(2√2), and the QEC/horizon accounting chain predicts G, M_P and H₀ (a script varies a dummy H₀ tenfold and confirms the final input ledger is unchanged). Two upgrades since the previous draft change the status. First, the local source form is no longer a horizon-input analogy: an explicit service-current T_svc^μν, with Ryu–Takayanagi / first-law entanglement reasoning, gives the linearized Einstein source at continuum-Jacobson grade. Second, the hierarchy coefficient has a sharper operator statement, Z_G = 4α₀²N_lock with T = 8+1+0 = 9, landing M_P at +0.016% before the remaining alpha/Λ precision convention. The horizon side has sharpened further: the Bekenstein severing-channel factor is C = 55/8 (56 directed monogamy incidences modulo the single global-complement blind slot, all-contact severing grounded in the [8,4,4] = Q₃ face lattice); and the absolute flux is now resolved — the near-horizon Bogoliubov spectrum is exactly thermal at the KMS temperature, so the flux is the standard Hawking coefficient (P/P_SB = 1.000 to ~10⁻²⁰), with the (10/27)α₀ source-counting only a 0.29% shortcut. The emitted species are the two-helicity photon plus a computed 11.4% graviton, and fast scrambling is forbidden by finite-range locality (a falsifiable negative). These still fall short of a complete quantum theory of black holes — the Kerr/charge extensions and the full dynamical-collapse lift remain open. Falsification surfaces are explicit: resolving the alpha-convention gate collapses the G window to a single value that must then match CODATA at its 22-ppm precision; the predicted H₀ = 67.27 km s⁻¹ Mpc⁻¹ dies with a SH0ES-side resolution of the Hubble tension; and Ω_Λ = 12π/55 = 0.6854 currently stands +0.1σ from the Planck value.

States the current dark-sector canon. The main cleanup is categorical: the dark sector is not a single hidden particle gas, not a single entropy pressure, and not a single defect network — it now resolves into three separated carriers. A boot-frozen K04 debris mechanism leaves gauge-blind wall defects that gravitate but are pinned, so they are a durable, distinctive relic rather than the dominant mobile halo. An R4/MOND mechanism lets scheduler-clocked line records produce the cubic AQUAL action and the baryonic Tully–Fisher relation under a Poisson line-current theorem. And the mobile, pressureless CMB and halo budget is carried by a conserved R4 zero-mode reservoir together with the 17.7 keV sterile-neutrino branch. The K04 toy configuration model is superseded because it admits non-physical K₃,₃ order; the embedded Z₃ bond-subset ensemble is the physical substrate and crystallises strongly, and the earlier thermodynamic island-floor abundance is now archival (K04-as-halo is killed by pinning). Each live branch carries a stated kill condition: the MOND branch dies if the scheduler premise or the baryonic Tully–Fisher normalisation fails; the zero-mode/CMB completion dies if the reservoir cannot act as pressureless geodesic dust without double-counting the active R4/MOND response; and cluster-scale lensing offsets discriminate pinned from collisionless wall debris.

States the current cosmology-side canon, with stricter labels than its historical papers used — dark energy, horizon thermodynamics, and inflation were the main source of earlier overclaims. The late dark-energy equation of state has been reduced to finite service-instrument theorems plus a homogeneous cosmological lift: w(a) = −1 + a/28, with positive activation excluding phantom behaviour unless an additional negative-rate channel is introduced. Structure-formation corrections are no longer free CPL deformations; paired ledgers show the linear fixed-total-matter correction vanishes and the first allowed term is a variance susceptibility. The HBC inflationary tilt has a conditional mode-local scalar-clock route to n_s = 27/28. The scalar amplitude has advanced from an arbitrary normalization to the specific candidate A_ν = (3/4)α₀⁴, but remains conditional on the absolute scalar-shell service count. The cosmological-constant sector is split into two routes: the historical Λ_QCD³H₀ horizon/Dirac scale relation, and a newer active-demux generation-vertex computation that lands at ρ_Λ ≈ 1.0019 ρ_obs, with the remaining residual now treated as an internal operator-algebra convention rather than an observational fit target. The CMB third-peak problem has likewise changed: a pressureless R4 zero-mode reservoir now supplies the cold-dark-matter budget and a forward Boltzmann run matches the acoustic peak heights, though the acoustic scale and the halo phenomenology remain live gates. The result is a sharper cosmology program, not a closed one.

The relativity companion to the series: special and general relativity recovered as emergent properties of the finite-QEC substrate. Special relativity is the universal reversible propagation clock — the invariant speed c is one lattice step per service tick, and internal observers built from the same reversible walk/QEC clock infer Lorentz symmetry even though the microscopic update has a preferred order. General relativity is the coarse-grained covariance of that clock under substrate strain and record load: the metric encodes how local clocks, causal cones, and rulers renormalise, and matter follows geodesics because its propagation phase is extremised in the distorted clock field. The matter sector is an exactly isotropic massless Weyl cone whose three spatial hops form an anticommuting Clifford triple, forcing the relativistic dispersion at leading order; straining the cone yields the metric perturbation directly — the metric perturbation is the strain field — and the linearised Bianchi identity and the substrate's strain-ledger conservation become one statement, making G_μν = 8πG T_μν a consistent field equation rather than an imposed one. The equivalence principle follows once gravity couples to the full energy (kinetic plus confinement/Yukawa mass), not the bare hopping. Finally, the program's four horizon objects — the Bekenstein area law, the Hawking ladder, the firewall isometry, and the gravitational source — are shown to be one register-syndrome read four ways. Explicit about tiers: the kinematic spine is computed and machine-verified; three steps rest on flagged standard imports (Nielsen–Ninomiya IR restoration, Sakharov induced gravity, Weinberg's soft-graviton theorem).

A focused deep-dive companion to the gravity and black-hole paper: the black-hole horizon as a finite quantum-error-correcting record governed by a single object, the three-cube coboundary δ. Three results. (i) One δ controls the boundary strain record, the firewall isometry, and the single blind degree of freedom — but the Hawking degeneracies and the area coefficient additionally need a register-validity/monogamy ingredient provably independent of δ, so the unification is real but not “one δ controls everything.” (ii) The Bekenstein area law, written in substrate units (node area A_node = a₀²/4, proton-primary G), is exactly equivalent to a microscopic records rate: each horizon node carries ~10³⁸ nats while a single eight-bit cell holds at most 8 ln 2 ≈ 5.5, so the area entropy cannot be stored — standing storage fails by 37–45 orders of magnitude across the black-hole mass range — and must instead flow, at rate H₀ M_P²/(16 Λ_QCD³) = C α₀². (iii) The coefficient is C = 55/8 — 56 directed monogamy incidences modulo the one global-complement blind slot, with AGL(3,2) covariance fixing the measure; the last conditional — whether the per-pair direction tag is value-level or an address-level geometric stamp — is now discharged by two independent arguments: the record channel is the syndrome itself, and AGL(3,2) covariance forbids an address-level orientation outright. The dynamical picture has firmed up too: the local KMS scheduler is now derived from symmetric Schwarzschild microcanonical exchange; a radial freeze-shell/escape-cone map gives the Hawking M⁻² scaling; a standard Schwarzschild spin/partial-wave greybody transfer dresses the finite ladder; and the absolute flux equals the standard Hawking coefficient via the near-horizon Bogoliubov spectrum, with the (10/27)α₀ source-counting a 0.29% shortcut (species: two-helicity photon plus a computed 11.4% graviton). Prediction: Ω_Λ = 12π/55 = 0.6854 (α-free, +0.1σ, Planck branch of the Hubble tension). An earlier ≈0.31-Eddington horizon-bandwidth reading and a near-unit ringdown-echo claim are both withdrawn — the channel is a post-service record-writing channel, not a real-time entropy bottleneck or a coherent mirror; and fast scrambling is forbidden by finite-range locality (the bounded-degree, translation-invariant ℤ³ abelian-Cayley no-go), a falsifiable negative. The absolute Planck-mass scale is not settled here — it rests on the separate gravity-sector selector/billing analysis — nor is the continuum/background lift.

A consolidated, self-contained account of what dark matter could be in the finite-QEC substrate: not a new particle but crystallisation debris — defects left behind when the lattice ordered too quickly to heal. The June 2026 canon narrows the interpretation: this K04 fossil is a pinned, distinctive dark component and a falsification target, not the dominant mobile dark matter and not the carrier that completes the CMB third peak — that pressureless budget belongs to a separate R4 zero-mode / sterile-neutrino branch. It answers four questions a graduate scientist can follow without prior exposure to the programme. Taxonomy: using a standard topological argument, a defect is permanently locked only if it winds the system, so the smallest indestructible object is a one-dimensional string, not a point particle — every finite (local) defect can in principle heal, and explicit enumeration confirms it does. Mobility: the locked objects are extended and frozen, consistent with the separate result that such debris cannot be pushed by gravity — ruling it out as a free, collisionless particle gas but exactly what a frozen large-scale structure should do. Energy scale: the two defect tensions are computed exactly — a string costs w₄+4w₆ per lattice step, a frustrated domain wall 2w₄+12w₆ per cut cell — and, as a by-product, the cell crystal is hugely degenerate, so most domain walls cost nothing. Abundance: combining a Kibble–Zurek picture of defect formation with the above, the relic density takes the clean, falsifiable form ρ_dark ∼ (4/7) σ_wall/ξ(R), where ξ(R) is the correlation length set by the cooling rate; the fraction 4/7 — the share of domain walls that actually cost energy — is exact. The remaining unknowns reduce to two pre-existing open problems: the cooling law that fixes ξ(R), and the conversion of lattice energy units to physical units. Every numerical claim is reproduced by a short self-checking program.

A more accessible account

A focused companion that reads the matter–antimatter asymmetry off the code itself. Why is the observable universe made of matter when CPT-symmetric physics produces equal amounts that annihilate to radiation? Sixty years after Sakharov, no mechanism derives the measured baryon-to-photon ratio η ≈ 6×10⁻¹⁰ from first principles — grand-unified and Standard-Model electroweak baryogenesis are excluded or fine-tuned, and leptogenesis works only with free high-scale parameters. Here the magnitude follows from one parameter-free assumption: the early universe is the self-dual [8,4,4] extended Hamming code, whose boot-time QEC pruning is the physical origin of the photon bath. The asymmetry is then not a fine-tuned initial excess but an error rate — almost all matter and antimatter are corrected back into photons (the Landauer exhaust), and the surviving baryon number is the residue of logical faults that bypass the code's stabilizers undetected. The minimum-weight undetectable fault has weight equal to the code distance d = 4, giving a suppression α₀⁴; a colour-singlet selection over the 14 weight-4 logical channels contributes a 3/14 branching, so η = (3/14)α₀⁴ = 6.08×10⁻¹⁰ — a 0.9σ match to the Planck value with no free parameters once the fine-structure constant α₀ is fixed. The three Sakharov conditions map onto three intrinsic features of the substrate; the lepton-number-to-baryon-number conversion reproduces the standard sphaleron factor 28/79 on the substrate's particle content; and the absolute sign of the asymmetry remains, as in all of physics, anchored in a discrete convention — here a geometric phase of the code — rather than fully derived. Explicit about tiers: the magnitude is a genuine parameter-free prediction, the conversion is inherited standard physics, the definite non-zero net is computed, and the orientation is an irreducible geometric primitive. Every numerical claim is reproduced by self-asserting scripts.