OPH observable status

Measured quantity: the joint frequencies of classical readouts - which repair coin fired, the seam current, and the load after repair. OPH's two candidate record laws C and E predict identical frequencies for every such measurement, so no classical experiment can tell them apart; only coherent (interference) readouts can.

For all 78 load basis states the C and E instruments have the same joint law of coin, current and post-repair load; by induction through adaptive classical protocols, any classical dataset gives L_C/L_E = 1. Exact replay: 182,520 matrix-unit cases on 30 seams plus 504 adaptive histories.

Measured quantity: the coherence (fringe visibility) that survives one repair. E behaves like C plus a retained seam-parity record, which dephases the state - the difference shows up as lost interference, not in classical counts.

Exact source discrimination identifies E as C followed by a retained seam-parity measurement; forgetting the extra record does not undo its dephasing.

Measured: Pr(plus) after one native repair on a coherently prepared seam, at phase 0 and π. A falsifiable lab test of how nature records events: a coherent event reads the coherence multiplier g, which differs between record laws.

One native repair on seam (0,1) after a coherent preparation: Pr(plus) = 3/8 + Re(g e^{-iθ})/2. Phase 0: C0 0.729, C 5/8, E/T 3/8; phase π: C0 0.021, C 1/8, E/T 3/8. Requires 8,192 trials per setting and a 1/64 apparatus error budget; evaluator currently returns no_data.

Measured: the same readout with an empty and a full seam, which fixes the multiplier k. Extends the discrimination programme to the seam-total record law.

A second preparation with an empty and a full seam reads the multiplier k and separates the T record law from E.

Measured: how often the C/E choice is right over 3,927 trials with no resets and no IID assumption. Shows the C/E test survives without idealized resets or independent trials - closer to a real apparatus.

379 unread preparation attempts before each of 3,927 trials; matching probabilities 341/432 (C) vs 1343/2000 (E); exact-source wrong-choice bound 3/400. A 1% physical bound needs per-trial service error ≤ 1/1570800 (not achieved).

Measured: the oscillation of a Y readout over modular time s: its frequency log(5/4) and its amplitude. Candidate readout of an observer's own modular ('felt') time - and it differs between record laws, so it could discriminate them too.

Source-derived Palm reference with weights (5/13, 4/13, 4/13) and modular frequency log(5/4). A coherent preparation plus Y readout responds periodically: 1/2 − sin(s·log(5/4))/140 for C, 1/2 − sin(s·log(5/4))/220 for E.

Measured: whether the modular parameter, the native event count and a local clock reading advance together. Linking the observer's forward-moving modular flow to substrate repair steps is the key bridge that would promote many finite theorems (proper time, arrow of time, clock laws) to 'theorem + executed' in physical time.

Native event counts, local event-clock readouts and the modular parameter have not been identified with one another. Modular dynamics have a finite covariance defect showing event operations and modular flow cannot simply be equated.

Measured: the field-plus probability after three attempts, and the tick conversion between two observers' clocks. Equal clock rates do not mean identical readings: clock comparison carries the full count distribution, as relativistic clock comparisons should.

Two local event clocks across observers keep complete quantum field outputs. C and E share the completed clock law but predict field-plus probabilities 35/54 vs 14/27 after three native attempts. Clock conversion: mean 2 B-ticks per two A-ticks, variance 16.

Measured: how far a disturbance can be detected after each ordered repair: at most one seam. The speed-of-light theorem is not only proved but realized in running repair histories (in graph hops per event; no lab speed yet).

For a fixed seam schedule and shared coins, dependence crosses at most one seam per ordered repair event, and retained signal witnesses attain the bound in execution.

Measured: distances read from records between the twelve ports; they form an exact rank-three metric. The 3D theorem is recovered operationally: an observer reading only its records finds three dimensions. Calibrated extended space remains open.

Records reconstruct an exact unitless rank-three metric on the twelve ports; all 30 native exchange seams are its shortest shell and the field generator is the sum of exchange terms on those edges.

A certified measurement of one proposed refinement map. The map is insufficient; the observable remains to be derived by another route.

Executed adjacency check: port-ancestry maps break adjacency in 74/2,520 (level 0→1) and 280/10,080 (1→2) fine seams. This rules out the current port-ancestry coarse-graining route, not neighbouring relations or continuum spacetime in general.

Measured: detector densities predicted by repairing local histories, compared with the apparatus law (RMSE 0.288). The strongest integrated result: consensus-style history repair computes the same complete detector laws as a supplied oscillator apparatus.

The local compatibility solver executes repair for all 130 anharmonic endpoints, reproducing RMSE 0.2876427868 with max density discrepancy 1.79e-14; fair orders reproduce the chronological law, unfair orders need not close.

Measured: the coherence of an untouched reference qubit after two incident-clock ticks with record feedback. A single twelve-port carrier already supports an observer, repair, clocks and coherent records - federations are optional.

A logical qubit with untouched reference evolves through two native incident-clock ticks with record-controlled feedback; comparison bound below 7.779e-10. C and E: identical classical records, different reference coherences.

Measured: the change in what a root observer reads as the federation grows from 20 to 320 carriers. Local observers' experience is insensitive to far-away screen detail - locality survives refinement.

Federations of 20/80/320 carriers; on 15,360- and 245,760-port screens, matched radius-nine restrictions give root-observer output distance < 0.000382; incident-clock comparison < 6.656e-9.

Measured: how close a fixed-number sector gets to its stationary state, uniformly over untouched references. Thermal equilibrium is reached by repair alone; the conserved total remains an input.

Finite native equilibration prepares the stationary state within a connected fixed-number sector with error bounds uniform over untouched references.

Measured: the covariance of seam currents in the recovered 3D frame, (4N/99)·I3, and its random-walk limit. Random repair currents average into isotropic 3D diffusion - a seed of kinetic behaviour.

Seam currents mapped through the recovered rank-three frame have covariance (4N/99)·I3 and a Brownian path limit with action coefficient 99/8.

Measured: four-read field statistics on all 28,680 two-particle states, including feedback reversal. Effective field descriptions in an observer's own clock units emerge from counting local repair attempts.

Counting every attempted repair at the observer region gives a positive effective transfer and controlled logarithm; complete four-read protocols on all 28,680 two-particle states of a 240-port federation; density 1/3 feedback reverses a connected statistic.

Measured: correlations at time lags not used in the fit, predicted by the reconstructed seven-dimensional transfer. An observer can reconstruct a quantum Hamiltonian-like transfer purely from its record correlations.

Exact correlations reconstruct a seven-dimensional cyclic positive transfer whose recurrence predicts unused lags.

The protected defects of the repair network carry exactly the Standard Model centre classes: quarks in 1/5 and 4/2, lepton and Higgs doublets in 3, right-handed leptons and gauge fields in 0.

Measured: the Z6 flux class of protected defects in the stored simulator runs. Exact on all 32 patterns: class k = 6Y mod 6, multiplicities (4,6,6,4,6,6), Aharonov–Bohm phase exp(2πi fk/6); all 16 reaction types of the stored runs conserve class mod 6 and every carrier is class neutral.

Most defect faces already carry a Standard Model hypercharge, but the lift is not a conserved label inside a class.

Measured: unreduced register currents on every face of every stored cut (levels 4–7). Lift mod 6 equals the stored class everywhere; 0 of 68,515,840 carrier states have nonzero total; 99.7% of defect faces hold a 6Y value of a Standard Model multiplet.

The generation register's phase θ = 2/9 is a read count; at that phase the charged-lepton ratios follow with Koide Q = 2/3 and no measured mass input.

Measured: phase per unit clock of the weak round on the sixty-address carrier, 10⁴ to 2×10⁶ rounds. Limit 2/9 + 9×10⁻¹⁴; closed form N·atan(P sin(1/N)/(1−P+P cos(1/N))), P = 2/9.

This is the e << μ << τ hierarchy: two dimensionless ratios follow without a measured lepton-mass ratio as input. It is conditionally completed, not a closed physical theorem: the declared register and mass carrier are premises; pair creation, kick source, partner rule, phase-round count and absolute scale remain open.

On the declared generation register, Koide balance Q = 2/3 and the read-count phase θ = 2/9 together fix both independent mass ratios: m_μ/m_e = 206.770316 and m_τ/m_e = 3477.4728. The executed weak-round limit is θ = 2/9 + 9×10⁻¹⁴. Anchoring only the electron mass gives m_μ = 105.659414 MeV and m_τ = 1776.985 MeV. The comparison is not blind.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃, Q = +2/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Quark-mass status: open. The current certified inputs do not distinguish a two-parameter family of spectra; this limits those inputs, not the possibility of deriving quark masses. The rejected shape and register-Clebsch candidates rule out only those candidate routes. A Yukawa source equation, physical family attachment, or new selector could still determine the masses.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the up quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = −2/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the up quark by that conjugation; mass status as for the up quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃, Q = −1/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Quark-mass status: open. The current certified inputs do not distinguish a two-parameter family of spectra; this limits those inputs, not the possibility of deriving quark masses. The rejected shape and register-Clebsch candidates rule out only those candidate routes. A Yukawa source equation, physical family attachment, or new selector could still determine the masses.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the down quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the down quark by that conjugation; mass status as for the down quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃, Q = −1/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Quark-mass status: open. The current certified inputs do not distinguish a two-parameter family of spectra; this limits those inputs, not the possibility of deriving quark masses. The rejected shape and register-Clebsch candidates rule out only those candidate routes. A Yukawa source equation, physical family attachment, or new selector could still determine the masses.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the strange quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the strange quark by that conjugation; mass status as for the strange quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃, Q = +2/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Quark-mass status: open. The current certified inputs do not distinguish a two-parameter family of spectra; this limits those inputs, not the possibility of deriving quark masses. The rejected shape and register-Clebsch candidates rule out only those candidate routes. A Yukawa source equation, physical family attachment, or new selector could still determine the masses.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the charm quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = −2/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the charm quark by that conjugation; mass status as for the charm quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃, Q = −1/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Quark-mass status: open. The current certified inputs do not distinguish a two-parameter family of spectra; this limits those inputs, not the possibility of deriving quark masses. The rejected shape and register-Clebsch candidates rule out only those candidate routes. A Yukawa source equation, physical family attachment, or new selector could still determine the masses.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the bottom quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the bottom quark by that conjugation; mass status as for the bottom quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ d_R (3,1)₋₁/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃, Q = +2/3, defect classes 1 (left) and 4 (right) (= 6Y mod 6). Top mass: conditional SM two-loop criticality coordinate (λ = 0 and β_λ = 0 at the log-midpoint anchor E* e^(−π) P^(−1/6)); the boundary-scale selection theorem is open and the candidate was identified after the implied scale was computed.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the top quark: the complement of all five bits of the code pattern, which conjugates every charge (Q = −2/3) and maps class k to 6 − k (classes 5 and 2). Same mass as the top quark by that conjugation; mass status as for the top quark.

Quantum numbers Q_L (3,2)₁/₆ ⊕ u_R (3,1)₂/₃ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Colour triplet: a colour-charged class, confined by the Wilson-plaquette seam cost. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁, Q = −1, defect classes 3 (left, shared with the Higgs doublet) and 0 (right) (= 6Y mod 6). Charged-lepton status: conditional. The declared generation register compresses to a balanced circulant (Koide Q = 2/3); its exclusive read count fixes the phase θ = 2/9, executed to 2/9 + 9×10⁻¹⁴ over up to 2×10⁶ rounds. Ratios follow with no measured mass as input (comparison not blind); the absolute scale F and the pair-creation, kick and round-count rules are open. The electron is the anchor: its absolute mass sets the scale.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the electron: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1) and maps class k to 6 − k (classes 3 and 0 (class 3 is its own inverse)). Same mass as the electron by that conjugation; mass status as for the electron.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁, Q = −1, defect classes 3 (left, shared with the Higgs doublet) and 0 (right) (= 6Y mod 6). Charged-lepton status: conditional. The declared generation register compresses to a balanced circulant (Koide Q = 2/3); its exclusive read count fixes the phase θ = 2/9, executed to 2/9 + 9×10⁻¹⁴ over up to 2×10⁶ rounds. Ratios follow with no measured mass as input (comparison not blind); the absolute scale F and the pair-creation, kick and round-count rules are open.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the muon: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1) and maps class k to 6 − k (classes 3 and 0 (class 3 is its own inverse)). Same mass as the muon by that conjugation; mass status as for the muon.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁, Q = −1, defect classes 3 (left, shared with the Higgs doublet) and 0 (right) (= 6Y mod 6). Charged-lepton status: conditional. The declared generation register compresses to a balanced circulant (Koide Q = 2/3); its exclusive read count fixes the phase θ = 2/9, executed to 2/9 + 9×10⁻¹⁴ over up to 2×10⁶ rounds. Ratios follow with no measured mass as input (comparison not blind); the absolute scale F and the pair-creation, kick and round-count rules are open. A separate frozen tau window (FZ-10) is registered.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the tau lepton: the complement of all five bits of the code pattern, which conjugates every charge (Q = +1) and maps class k to 6 − k (classes 3 and 0 (class 3 is its own inverse)). Same mass as the tau lepton by that conjugation; mass status as for the tau lepton.

Quantum numbers L (1,2)₋₁/₂ ⊕ e_R (1,1)₋₁ are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ (left-handed), Q = 0, defect class 3 (shared with the Higgs doublet) (= 6Y mod 6). Neutrino-mass status: open. Majorana vs Dirac and the absolute-scale mechanism are unselected; the only target-informed mixing candidate failed the NuFIT test. A physical neutrino identity needs a separate attachment.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the electron neutrino: the complement of all five bits of the code pattern, which conjugates every charge (Q = 0) and maps class k to 6 − k (class 3 (own inverse; this does not make it Majorana)). Same mass as the electron neutrino by that conjugation; mass status as for the electron neutrino.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ (left-handed), Q = 0, defect class 3 (shared with the Higgs doublet) (= 6Y mod 6). Neutrino-mass status: open. Majorana vs Dirac and the absolute-scale mechanism are unselected; the only target-informed mixing candidate failed the NuFIT test. A physical neutrino identity needs a separate attachment.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the muon neutrino: the complement of all five bits of the code pattern, which conjugates every charge (Q = 0) and maps class k to 6 − k (class 3 (own inverse; this does not make it Majorana)). Same mass as the muon neutrino by that conjugation; mass status as for the muon neutrino.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

A fermionic quantum on a carrier port: pattern L (1,2)₋₁/₂ (left-handed), Q = 0, defect class 3 (shared with the Higgs doublet) (= 6Y mod 6). Neutrino-mass status: open. Majorana vs Dirac and the absolute-scale mechanism are unselected; the only target-informed mixing candidate failed the NuFIT test. A physical neutrino identity needs a separate attachment.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Antiparticle of the tau neutrino: the complement of all five bits of the code pattern, which conjugates every charge (Q = 0) and maps class k to 6 − k (class 3 (own inverse; this does not make it Majorana)). Same mass as the tau neutrino by that conjugation; mass status as for the tau neutrino.

Quantum numbers L (1,2)₋₁/₂ (left-handed) are read off the five-level code C³ ⊕ C² (exact on all 32 patterns; class rule replayed on the stored runs). Exact B − L is conserved by the declared operations, which exclude Majorana pairing in that sector. The class carries neither the generation nor the rest mass, so the name is a candidate label until a mass readout separates the copies.

Gauge singlet pattern of the code, class 0. Whether it is a physical particle (and so whether neutrinos are Dirac) is not selected by OPH yet.

The 32-pattern code also contains the gauge-neutral pattern (1,1)₀ in class 0, completing the 16 of one chirality half. It lies outside the selected 15 Weyl states of one generation.

Massless on the declared unbroken Maxwell branch: the classical transverse mode has zero hard quadratic mass. Not yet an OPH quantum particle with a positive massless pole (conditional postdiction). Own antiparticle.

Gauge field of the unbroken electromagnetic direction, class 0. The free seam-current photon Hamiltonian is Lean-lifted on the twelve-port complex.

Massless carrier mode on the declared perturbative Yang–Mills branch; confined in the executed colour lattice (linear static potential, first-order deconfinement at β_c = 5.6925 matching the published value). Self-conjugate as an octet.

Port phases on the five-level code generate S(U(3)×U(2)); its su(3) part gives eight gluons, class 0, carried by colour currents between the three colour levels.

Tree chart coordinate 80.330 GeV from the declared chain (v = 246.60 GeV); not a physical pole comparison - the renormalized-vev, threshold and complex-pole map is incomplete. Antiparticle: W⁻.

Weak current s2→s1 on the weak levels; mass from the declared electroweak coupling chain and the strict source-audit branch.

Antiparticle of the W⁺: same chart mass coordinate, opposite charge.

Weak current s1→s2; the conjugate of the W⁺.

Chart coordinate 91.119 GeV (strict branch, zero-selector law; tree value of the declared chain 91.588); not a physical pole comparison. Own antiparticle.

Neutral weak direction orthogonal to the photon; the photon/Z coupling dictionary on the committed charge columns is machine-checked algebra.

Mass: conditional SM two-loop criticality coordinate 125.77 GeV at the log-midpoint anchor; on the fit-free m_t→m_H curve the measured top gives 124.73 GeV (−0.32%). Boundary-scale selection open. Own antiparticle.

The Higgs register toggles the weak levels (H⁺, H⁰); the Higgs doublet shares class 3 with the lepton doublet. One Higgs doublet is an exposed premise (selection row 6).

Massless on the declared Einstein–Hilbert branch (zero hard quadratic mass). Not an observed particle and not a completed quantum-gravity derivation (conditional postdiction).

Transverse mode of the declared pure-Einstein action on the recovered geometry.

Stability: the forced product gauge algebra excludes the minimal-GUT X/Y channel; general proton stability is not claimed.

Under the stated premises (spin doublet, Gauss law, antisymmetric occupation) a baryon is three quanta on a carrier. Nucleon mass from the conditional Λ_QCD times an external numerical ratio: 0.944 GeV [0.838, 1.057]. Quenched colour lattice on OPH links gives m_N/m_ρ = 1.45 ± 0.13 (PDG 1.211).

Antiparticle of the proton; same conditional nucleon mass; X/Y-channel exclusion applies equally.

Three antiquarks on a carrier: the complement pattern of the proton. Mass as for the proton by conjugation.

Conditional nucleon mass 0.944 GeV; the neutron–proton splitting is not derivable while the u and d masses are unselected.

Under the stated premises (spin doublet, Gauss law, antisymmetric occupation) a baryon is three quanta on a carrier. Same conditional nucleon-mass route as the proton; the n–p mass difference needs the light-quark masses, which are not yet derived.

Antiparticle of the neutron; mass as for the neutron.

Complement pattern of the neutron.

Open (T0): no pion-mass route until the light-quark masses are selected; then the same external-ratio route extends.

Quark–antiquark colour singlets. The chiral-sector masses need the light-quark Yukawa selectors.

Open (T0): requires light-quark selectors and nonperturbative ratios per channel.

Complete spectral and detector records must decide whether a candidate is an elementary channel, composite, boundary excitation or resonance.

Probabilities must be consistent across observers sharing effects; a finite Busch-Gleason theorem then leaves only the trace rule.

Every nonnegative normalized valuation additive on coexisting effects is the trace against a unique density operator, in every finite dimension, without continuity axioms.

An observer who already knows the answer must not be disturbed by asking again; that consistency picks the projection postulate.

The effect table alone does not fix the post-measurement update, but invariance on outcome-certain states selects the Lueders map.

Quantum correlations are exactly as strong as commuting observer records allow, no stronger.

CHSH correlations on commuting record subalgebras are bounded by 2 sqrt 2, attained on a declared entangled witness; record-diagonal states stay at 2.

OPH is a quantum theory of records, not a hidden-variable theory; the replay confirms it is consistent with observed Bell violations.

Replaying the Hensen et al. 2015 loophole-free records gives S = 2.42250, rejecting the local classical reading of the diagonal branch.

Public records can be copied, private quantum states cannot - the distinction between public and private is built in.

Theorem: an ancilla-free isometry that copies two sharp states from a common blank forces their overlap to be 0 or 1. On the record side, the projectors of any finite partition span a commutative star algebra that is exactly equivalent to functions on the active labels - public records are classical and copyable, quantum states in general are not.

Non-commuting questions cannot be jointly sharp for any observer; the inequality follows directly from the finite event algebra.

A finite density state and two Hermitian observables obey the Robertson inequality with exact saturation controls.

Charge sectors that no observer can coherently superpose appear as superselection rules of the record algebra.

Block pinching equals the uniform average over signed block reflections; partition-relative superselection readouts are characterised exactly.

Why quantum amplitudes are complex: OPH points to a phase that observers must track, but the source derivation is owed.

Real closures are excluded by finite route-specific obstructions, which locate an algebraic commutator phase lift; a source-selected complex phase instrument is not yet constructed.

Unitary time evolution is the reversible part of repair; the generator itself must come from the source.

A Schroedinger frame flow and Stone-converse theorems give unitary evolution from a supplied self-adjoint generator.

Measurement is not outside physics: an observer is another subsystem doing repair, and the process is simulated end to end.

Flux, charged matter and a scalar field on one register with complete instruments and feedback; certified nonzero infinite-occupation response.

Classicality is publicness: information copied redundantly to many observers becomes an objective record.

Public records arise from local repair; record majorization and two-scale public repair make classical facts stable.

Overlap consistency forbids an observer from steering another's statistics without a record carrying the influence.

For OPH's concrete local repair, a repair word of length n has an n-step closed-neighbourhood dependency bound: changing a record outside that grown region cannot affect the readout inside it. On a finite bipartite split, local operations on one factor leave the other factor's statistics unchanged. Realized by the executable model's causality checks.

A genuine prospective test of OPH's executable observer against a laboratory instrument.

A coherent event reads the record law's coherence multiplier g; law C predicts 5/8 and 1/8, law E predicts 3/8, with a complete-count rejection rule fixed before data.

Spin is a property of how ports are oriented; minimal coupling follows from the port-charge structure.

Pauli minimal coupling squares exactly; a declared Pauli-Y effect and static Born table reproduce spin-1/2 statistics.

Why half-integer spins are fermions: OPH has a finite Spin fixture but no source theorem yet.

Spin-exchange selection is delimited at the boundary; a source derivation of fermionic exchange signs remains owed.

The executable observer reproduces real lab oscillator data under a supplied apparatus model.

Executable readout RMSE 0.066 on 100 withheld points; driven anharmonic RMSE 0.056 over 707 means (McGarry et al. data).

Six antipodal axes of the icosahedron project to exactly three independent directions: space is 3D because the observer cell is icosahedral.

The normalized twelve-port repair response has an intrinsic rank-three Gram quotient; the Z6 load lattice and D6 seam image embed densely into one 3D Euclidean completion.

One record-ordering direction (time) plus three response directions (space) produce Minkowski signature.

The real time axis plus the rank-three source quotient give Lorentz inertia (1,3) with the S2 null boundary; authenticated logs embed by exact order embeddings.

Changing observer is a conformal map of their celestial sphere - that is exactly a Lorentz transformation.

The orientation-preserving conformal group of the observer's celestial sphere, Conf+(S2), is SO+(3,1). Lean proves the Pauli-coordinate module R x R^3 maps onto 2x2 Hermitian matrices with determinant equal to the Lorentz form (+---); future null rays are points of S2 and future unit timelike directions form H3. Localizing physical record tokens in that H3 chart is conditional on calibrated modular cap responses.

Information can only jump one patch boundary per repair step; that maximum rate is the speed of light.

Influence crosses at most one seam per ordered native repair event, and retained witnesses attain that bound, giving a light cone. Separately, the seam field is stable exactly when h^2 (3 + sqrt5) < 4; at or beyond that step an explicit zero-current solution has unbounded electric energy. Realized in the executable model.

Cause precedes effect because records are produced in an order that every observer agrees on.

The causal relation of the Hermitian Lorentz module (nonnegative Lorentz square and time component) is a partial order, and the finite causal observer nets embed into it. Record order alone supplies only order data: a three-tick readout and its cubic regrading are not affinely related, so a metric clock needs an extra calibration rank.

Time is counted, not assumed: the number of events in a causal diamond scales like its 4-volume.

Record counts in source-record diamonds recover proper-time ratios through a unique fourth-root readout. The proper-length functional is invariant under midpoint refinement, and index accrual vs proper-time accrual of an internal clock are compared exactly. Identifying record counts with physical proper time is one of the open bridges.

A clock is just a repeated record; comparing clocks is comparing record counts.

Local event clocks with stopped instruments; clock conversion keeps the whole count distribution; frequencies recovered from record covariances.

A naive mapping of native clocks to lab clocks fails, constraining how OPH time must attach to physical time.

Native incident-count clocks compared with King et al. Ar13+/Yb+ ratio blocks: the stated direct attachments are rejected (bounds below 1e-104).

The smooth continuum is the long-time limit of discrete repair, like a heat equation emerging from random walks.

One repair history gives a regular strongly local Dirichlet form of spectral dimension two, Gaussian density laws and finite-speed waves cos(t sqrt A).

The fundamental screen is two-dimensional; bulk dimensions are reconstructed holographically.

The screen Dirichlet form has spectral dimension two, as required for a two-dimensional holographic screen. Conditional on the source DAG carrying the screen scalar, collar release, precision and radial receipts, OPH also obtains an exact gamma-ratio screen covariance used by the cosmology branch.

Icosahedral symmetry is so round that no direction is preferred until l = 6.

For the positive-cosine carrier class, anisotropic ranks one through five vanish; the first allowed anisotropy is at angular rank six.

If spacetime is woven from icosahedral cells, a tiny rank-six anisotropy in high-energy propagation is unavoidable.

On the primitive twelve-port propagation branch, the port orbit is the only intrinsic directional support and forces equal port coefficients, giving the dispersion omega^2 = (1/2a^2) sum_i [1 - cos(a k.u_i)]. Icosahedral symmetry kills all anisotropy at angular ranks 1-5; the first allowed term is l = 6 with B6/B0 in [-16/135, 16/75] and D6/D0 = (12/5) B6/B0. Frozen as FZ-11/FZ-12: a resolved rank-1..5 term or B6/B0 outside the band excludes the whole carrier class.

The carrier must not split light polarisations; the null is registered but not yet frozen.

FZ-09 is registered as resource_deferred: OPH intends a frozen stance on vacuum birefringence, but no target, tolerance or decision rule has been stamped yet. Until then this is owed, not predicted.

Rest energy and momentum combine Lorentz-covariantly because they are counted on the same H3 velocity space.

Scaling a future unit-timelike frame vector by a declared mass gives the exact kinematic packet: Lorentz square m^2, E^2 = m^2 + |p|^2, E >= m. The boost-shear map transports the three-dimensional completion carrier onto each rest space isometrically. Two independent selection routes fix the inertial coefficient as m + E.

Energy is the modular-energy ledger of the cap first law; mass is the rest frequency of an internal clock. E = mc^2 should then say that a system's internal clock rate is its inertia.

Partially derived. The kinematic half (E^2 = m^2 + p^2) is a finite theorem, and a conditional precursor shows the internal clock's rest frequency equals the declared mass and internal modular energy adds to inertia. The registry is explicit that this does not yet derive the identity: binding modular energy to calibrated physical energy is open.

Flux through nested shells in three dimensions dilutes as 1/r^2 - a direct consequence of 3D space.

On the three-dimensional completion carrier ball volume scales as r^3 and shell content as 4 pi r^2, so any conserved spherically symmetric flux falls as 1/r^2. A layered discrete Gauss law is exact on finite graphs given the shell-cardinality, equidistribution and steady-sourcing premises PR-29..PR-31. The inverse-square law is a consequence of three dimensions plus flux conservation.

Classical mechanics emerges as the stationary path of repair histories; the boost clause remains a premise.

Polynomial boost selection: four clauses select exactly the committed mode-extremal Lagrangian; boost covariance is a declared candidate axiom.

Forces are what change the transport of a charged record along its worldline.

For a charge hopping along a seam-step worldline with fixed potentials, the exact one-step action difference gives a discrete Lorentz-force balance on the thirty-seam complex, and inside the timelike (rest-diluted) class it reads as rate of change of momentum. Exact finite statements; continuum attachment is conditional.

Translation symmetry of repair means total momentum of composite systems transforms covariantly.

In the declared slope family of composite momentum maps, every member has time component m + E at the standard frame, and the family transforms covariantly under the Lorentz module. Momentum conservation follows from the finite conservation/Ward precursor; physical attachment is conditional.

Noether's theorem in record form: every symmetry of the consensus process carries a conserved record.

On the twelve-port, thirty-seam incidence graph, any update of the form q' - q = source + boundary(current) obeys regional load change = source - outward flux; internal seams cancel, and zero total source conserves total load. This is the finite precursor of Noether currents and Ward identities.

Distance is the time light-like records take to go and come back, counted.

Along a seam-step worldline with unit tau per step, the clocked index counts complete units of accumulated proper length; it is monotone and increments by at most one per step. Proper length is thus a count of clock events, not a background metric quantity.

Repair erases disagreements but never creates them back: time's arrow is the direction of consensus.

Reference-preserving stochastic repair contracts relative entropy to the reference, so the direction in which records accumulate is monotone. This sits inside the conditional four-law package; Lean keeps repair order, record order, modular parameter, clock readout and proper time as eight distinct types, with all 56 implicit coercions rejected.

Equilibrium between patches is shared modular temperature on their common collar.

Native repair alone drives the system to equilibrium (executed in the model). The collar modular surface fixes the thermal reference, with modular Hamiltonian K = lambda . constraints; it does not by itself pin an inverse temperature, which needs the declared clock-and-energy calibration row.

Energy is the modular generator of repair; it adds over independent patches.

The modular energy ledger is exactly additive over product references, and the Gibbs reference-energy identification reads it against the screen field energy. This gives the first law inside the conditional four-law package on one finite regulator stage; it is not yet a source-realized theorem of A1-A3.

Consensus only removes disagreement, so information-theoretic entropy relative to equilibrium decreases monotonically.

Reference-preserving stochastic repair contracts relative entropy, so generalized entropy relative to the equilibrium reference never decreases under repair. Part of the conditional four-law package with five typed source and physical receipts.

Reaching zero temperature would require infinite repair resources.

Included in the conditional four-law package. The source-realization audit on 1,028 observers and 31,744 transitions checked all fifteen coordinate maps of the committed packet fields; realization from source is still open.

Records are physical; forgetting one is a physical act with a price.

Erasing one bit of record costs at least kT ln 2, inside the conditional four-law package. In OPH this is natural: records are the physical content of the world, so destroying one has an entropic price.

Time-reversed repair histories are exponentially suppressed by entropy production.

Crooks- and Jarzynski-type fluctuation relations hold in the conditional four-law package for repair trajectories against the reference state.

Macroscopic transport coefficients are correlation integrals of repair currents.

For a finite reversible stochastic kernel, L = I - K has a nonnegative Dirichlet form, and a Poisson solve on centred currents gives a symmetric positive-semidefinite Green-Kubo diffusion matrix. Finite theorem; physical transport coefficients need attachment.

Work measurements alone cannot fix the underlying repair law; this rules out that identification route, not work or heat themselves.

For pair-mean repair, total load is conserved and Q = sum x_i^2/2 drops by (x_i - x_j)^2/4 at each repaired seam. A cumulative-loss record preserves Q + B but is provably not identifiable with heat: work and heat need extra structure.

Gravity is entanglement equilibrium: the requirement that generalized entropy is balanced on every small null cap forces Einstein's equation (Jacobson-style, but from observer overlap).

Tensor completion of a realized null balance under Ward conservation, Bianchi identity and one scale identification gives G_ab + Lambda g_ab = 8 pi G T_ab.

No scale breaks the diffeomorphism-like rechartings of the screen, so the graviton has no mass.

On its declared branch the spin-two response carries no hard mass parameter, so the graviton is massless as a structural statement. It is conditional on the compact-gauge/transport branch and the Einstein-equation route; no independent graviton-mass bound is derived.

Entropy counts records crossing the boundary - so it scales with area, not volume.

Collar decomposition with edge term sum p log d; sparse crossing-read functional Gamma-converges to perimeter.

Information is never lost because it is always held in someone's records on the screen.

Information is not lost but stored as public records at the horizon. Conditional on stable whole-fibre record closure and horizon-record saturation, the de Sitter branch gives Lambda l*^2 = 3 pi / N*; collar recovery bounds the conditional mutual information exponentially in collar width, so interior data is recoverable from boundary records. Physical attachment is conditional.

A published retraction - OPH keeps kills as prominent as confirmations.

FZ-06: the historical alpha = 4 ringdown row is void/misattributed; the integer-k Kerr comb template remains build-stage (FZ-14).

A finite-capacity screen forbids time-advance shocks in de Sitter space.

With fixed total screen capacity M, an observer occupying c_obs of it changes the maximal generalized entropy by exactly log(1 - c_obs/M) < 0. On the pure de Sitter horizon shock equation mu^2 = d - 2, independent of Lambda. Conditional on the horizon-area dictionary and an inhabited Einstein branch, this fixes the sign of the de Sitter time advance (negative shock).

The number of facts the universe can hold equals its horizon area in Planck units - stated, not yet derived.

The official closure equation is N = log M_0(U_N), with M_0 a multiplicative code size of correctable public records. Identifying that capacity with horizon area is undischarged; terminal normal forms and local checkpoint marginals cannot determine capacity because different global couplings give different correctable capacities. Only that readout route is ruled out.

Matter's energy is read off as the response of records to deformations of a small patch.

Finite null tomography is exact: nine generic null directions reconstruct a symmetric trace-free rank-two tensor up to the trace ambiguity. Upgrading this to a local physical stress-energy tensor sourcing the Einstein equation is conditional on the null-net and modular premises.

Light-sheets carry the entropy bookkeeping that later produces Einstein's equation.

On the producer branch the null blow-up net uses one common GNS space. MaxEnt states and Cauchy control alone do not prove standardness; a uniform cofinal cyclicity receipt is required for every half-line used. With it, the null nets support light-sheet entropy statements; without it the step is open.

In OPH both inertia and gravity read the same record-level energy ledger, so their equality should be structural rather than a coincidence.

Not yet a stated OPH result. The route: the same modular-energy ledger that supplies inertia (internal clock rest frequency) is what the Einstein composition consumes as source energy via the Gibbs reference-energy identification. Showing these are one quantity on the physical branch would give inertial = gravitational mass.

A fixed screen capacity gives a mechanism for the puzzling negative de Sitter shock (time advance); the gravitational attachment remains a premise.

Exact: pure de Sitter has μ² = d − 2 = λ₁(S^{d−2}), independent of Λ; the finite-sector entropy maximum and its gradient fix the capacity-transfer direction. Conditional: identifying screen capacity transfer with a horizon shock gives the time-advance sign of Chen–Stanford–Tang–Yang. The repair generator excludes dimension-changing shocks.

Gravity counts all records, including ones that never couple to light. Galaxy-scale deviations follow from collar saturation of the screen.

Dark matter is classified as non-luminous modular charge of the screen; geometry responds to total modular charge, so 'missing mass' is a gravity deviation, not a new particle.

Deep in the galaxy, saturated collars make gravity fall like 1/r, giving flat rotation curves (MOND-like phenomenology).

OPH reads the dark-matter effect as a gravity deviation from collar record defects, not new particles. With degree-one radial scale covariance and quadrature composition of independent per-source defects, the unique deep law is g = sqrt(g_bar a0), giving flat rotation curves and v^4 = G M_b a0. a0 itself is fitted, not derived.

a0 is tied to the cosmic capacity (Hubble scale), explaining the coincidence a0 ~ cH0.

a0 sets where the deep-regime law takes over. It is not source-derived: FZ-01 freezes it (with three other cosmology targets, 2026-07-17) against future releases, while SPARC fits are labeled postdictions. A source derivation of a0 is owed.

OPH should predict how tight the radial acceleration relation is; not yet frozen.

FZ-07 is resource_deferred: the per-cut variance model implies a specific scatter law for the RAR/BTFR, but no target and tolerance are stamped yet. The SPARC matched-observable diagnostic is a labeled postdiction excluding bulge-dominated galaxies.

Lensing must see the same total modular charge as dynamics.

If the gravity deviation is a record-defect effect, it must also lens light like the inferred dark matter does. A dedicated CI suite tracks lensing by non-luminous charge; attaching it to cluster and galaxy lensing data remains open.

If the screen's capacity is fixed, vacuum energy per record is constant - no evolving dark energy.

Fixed record capacity gives (w0, wa) = (−1, 0) exactly (Lean FixedCapacityWLaw), frozen as FZ-13 (2026-10-04, stamped, upgrade pending). Against official DESI DR2 chains: BAO+CMB 2.61σ, +PantheonPlus 2.60σ (tension), +Union3 3.38σ, +DESY5 3.93σ (exceeds 3σ, diagnostic). Seen data.

OPH's fixed-capacity branch predicts no evolution; DESI DR2-type hints would test it.

FZ-08 is resource_deferred: OPH has not yet frozen a stance on DESI's evolving-dark-energy hint. Postdiction comparisons with DESI DR2 (2.6-3.9 sigma against w = -1) are recorded separately as retrospective.

Lambda is tiny because the universe's record capacity N is huge: Lambda ~ 1/N.

OPH ties Lambda to total record capacity: Lambda l*^2 = 3 pi / N. Two executed capacity candidates give N = 3.2921e122 and 3.3001e122 against the measured 3.3129e122 (inverse Lambda in Planck units), within about 0.6% and 0.4%. Equality requires a typed bridge proving that construction-side and readback-side expressions read one invariant; that bridge is open.

The number of public records is the single big number of OPH; its closure law is owed.

Closure demands the capacity equation N = log M_0(U_N). On the conditional electroweak bridge the reserve candidate is N_0 = pi exp(6 pi / (P alpha_U)). Which candidate is selected requires a one-zero law that is open (selection row 15, bridges BR-1..BR-6).

Why are the seeds of galaxies equally strong on every scale? In OPH the screen fixes it: the only fluctuation spectrum compatible with the native screen dynamics is the scale-invariant one, with no inflaton field or tuned potential put in by hand.

Two results. (1) Any sky field read as a bounded image of the screen's native long-average field must have l(l+1)C_l bounded above and below: the min-max comparison allows precision growth l^(2+theta) only for theta = 0. (2) If a homogeneous isotropic bulk field restricts to spheres of unboundedly many radii with C_l = 2 pi A/[l(l+1)], overlapping radii force one coefficient A, so the bulk covariance is logarithmic and the 3D power spectrum is P(k) = 2 pi^2 A / k^3. The small red tilt (n_s = 1 - P/48) needs an extra ingredient beyond this covariance and is a separate frozen row.

Primordial fluctuations come from the full-collar density P/24 of the screen; the pixel constant P fixes the tilt.

FZ-01/FZ-15 frozen: edge-center branch n_s = 0.96602. ACT P-ACT-LB posterior mean 0.97426 puts it in lower-tail tension (retrospective).

Homogeneous expansion is record density diluting uniformly as capacity is shared.

On the golden source-record family, the read law is invariant under layer-dependent rescaling, which gives an exact spatially flat expanding background. Given the Einstein equation with G = l*^2 and Lambda l*^2 = 3 pi / N*, standard photon-baryon Boltzmann transport follows; those premises are supplied, not derived.

Icosahedral imprint on large-angle CMB, if the screen symmetry survives to the sky.

If the screen carries icosahedral symmetry, the sky's angular modes branch under A5: no invariant for l = 1..5 and the first nonconstant A5-invariant at l = 6. Frozen as FZ-02 (2026-07-26); the WMAP ILC A5 search at l >= 6 gave p = 0.64, and the frame-lock clause awaits issue #643.

Which vacua are observer-consistent, rather than a landscape of arbitrary vacua.

On a finite regulator the normal-form map is a retraction, so settlement fixes every law supported on normal forms: consensus selects no physical probability law over vacua. OPH therefore cannot derive a vacuum measure from settlement alone and does not rely on an anthropic ensemble.

Galaxies grow from capacity fluctuations under total modular charge.

The cosmology programme compiles linear structure formation through the conditional FLRW/Boltzmann branch with declared likelihood contracts. Comparisons with large-scale-structure data are not yet run; the row is owed.

H0 is a capacity-scale quantity; until the clock attaches, OPH cannot give its SI value.

OPH emits dimensionless ratios; H0 in km/s/Mpc needs a calibrated physical clock and the imported SI anchors (cesium frequency, c, h). No source-emitted H0 exists, so OPH currently takes no side in the Hubble tension.

There is no 'before' because time is record order inside the closed universe.

Closure fixes structure without an external initial time. Executed so far: abundance freeze-out on a closed cell and exact particle/antiparticle class balance (see Cosmology rows) — both explicitly without expansion, temperature or particle dictionary. A physical early-universe history (thermal epochs, BBN, relic densities, baryon asymmetry) is owed.

A pure power-law primordial spectrum: the screen source has one dilation, so the tilt itself does not run.

Exact zero running from the declared source dilation cocycle and a homogeneous radial source family (exact power law). Planck 2018: −0.0045 ± 0.0067 (+0.67σ); ACT DR6 P-ACT-LB: 0.0062 ± 0.0052 (−1.19σ). Both consistent. Seen data: the repository's cosmology comparison table promotes nothing and every row was compared after the data was public.

No inflaton, so no primordial tensor background; LiteBIRD could exclude it only by detecting r.

Linear tensor evolution on the declared background with zero initial tensor amplitude and no forcing gives r = 0 exactly. Bounds: r < 0.032 (Planck PR4 + BK18 + BAO), r < 0.036 (BK18). Consistent, but upper limits cannot separate exact zero from small slow-roll signals. Tensor freeze FZ-16 is proposed, not adopted.

One release clock for every species means no isocurvature mode.

Rank-one single-clock normal form with one common release clock: purely adiabatic perturbations. Planck 2018 bounds 100 β_iso < 2.5–3.9 (95% CL). Consistent; zero is the shared baseline, so agreement supports nothing.

Maximum-entropy release is Gaussian; the observable value still needs the nonlinear transfer.

MaxEnt covariance theorem gives a Gaussian release: f_NL = 0 at the source. The order-one nonlinear transfer is not computed. Planck: local −0.9 ± 5.1, equilateral −26 ± 47, orthogonal −38 ± 24, all consistent; shared baseline.

Flatness comes from the record geometry rather than inflationary stretching; a confirmed nonzero Ω_K would refute the branch.

Vanishing area-normalized small-loop holonomy plus the clock-slice flat FLRW identification gives Ω_K = 0 exactly. Planck alone 1.63σ, Planck+BAO −0.37σ (consistent); DESI DR2 BAO + CMB 0.0023 ± 0.0011 gives −2.09σ (tension). Flatness is identified, not selected.

Cosmic expansion is how densely records are written, read off by counting — no external clock.

On the golden source-record family the scale factor enters only as count weight a⁴ per comoving cell and conformal tick; the count clock converges to proper-time ratios, and redshift is the fourth root of a record-count ratio for congruent comoving windows. Lean-checked on the declared population.

Horizon-style entropy ∝ area emerges as counting of reads across a surface.

Unordered read pairs crossing a surface per layer converge to (π/4) n² a⁴ per unit area; with n² a⁴ = 1/(π l_P²) this is the area law. A declared one-nat-per-read count on a supplied 3D population — distinct from native regional entropy, which has no boundary-seam coefficient.

Candidate branch with no inflaton; the horizon problem is not yet solved inside OPH.

Synchronization does inflation's jobs: record-density expansion is exact on a supplied population; the tilt n_s = 1 − P/48 is conditional on a declared generator density; flatness is identified, not selected; horizon coherence is not supplied; under a bounded form-congruent identification the native density field forces zero tilt.

Acoustic peaks would come out of standard physics once OPH supplies the source and photons.

On a branch that supplies geometry, photon convergence, vertex and collision premises, transport is the standard Ma–Bertschinger system plus two OPH interfaces (repair-exchange rate and collar stress) that vanish on the standard branch. The executable model supplies no photon sector yet.

The deep-law shape is conditional, but its scale is still fitted.

Dictionary a₀ = G n² c is exact, but the value is not derived; every listed a₀ is a fit. SPARC full-RAR 0.95–1.45×10⁻¹⁰ m/s² (by mass-to-light), published RAR 1.20×10⁻¹⁰, deep-regime 0.84–0.92×10⁻¹⁰. a₀/(cH₀) ≈ 0.13–0.22.

Requires the neutrino mass sector, which is still open.

No corpus value. DESI DR2 BAO + CMB: Σm_ν < 0.064 eV (95% CL). Not evaluable.

Would require deriving the particle content's thermal history, not just the particle list.

No corpus value. Planck + BAO 2.99 ± 0.17; ACT DR6 P-ACT-LB 2.86 ± 0.13. Not evaluable: the executable model has no thermal history or species dictionary.

A discrete ringdown comb would be a distinctive OPH signature if frozen and tested.

Registered pending owner freeze; no comparison contract and no event likelihood evaluated yet. Target: post-anchoring gravitational-wave events.

A genuine executed freeze-out law — but epochs count native events, with no expansion, temperature or particle dictionary, so it is NOT a relic abundance, nucleosynthesis or freeze-out temperature.

Exact rational population law on a declared 3-port closed cell (1,296 states, 7,776 attempt records, native repair + register): defects freeze out with limiting occupied face share exactly 1007/13824 = 0.07284; relaxation ≤ (1/25)^⌊n/32⌋; Lyapunov E = 5Q + 2R nonincreasing. No parameter fitted to an abundance.

The executable model by itself produces no net matter–antimatter excess; a baryon asymmetry needs an extra source and dictionary.

The native repair law has an exact conjugation symmetry; all 2,592 local branches checked and paired histories executed on the closed federation. An unbiased symmetric ensemble has zero mean signed class imbalance at every time (generic Lean theorem). Individual histories fluctuate.

Why there is matter at all remains open in OPH.

Not derived. Executed class counts are exactly C-symmetric and do not identify baryon number; physical baryogenesis needs a source, dictionary and asymmetry mechanism with complete records. Dimension-six B-violating operators are admitted but uncoefficiented.

The dark sector's shape is conditional; its cosmic amount is not derived.

No source value. Dark matter is modelled as modular charge on unrecovered collars with inverse-volume dilution, but the abundance link (stress, lensing, expansion on one process) is unsupplied.

Helium and deuterium fractions are a downstream target, not a current OPH output.

No route yet: needs a thermal history, physical clock, expansion rate and nuclear sector on the same process. The executed abundance epochs explicitly do not establish nucleosynthesis.

Requires the physical photon and scale joins.

Not derived: the executable model supplies no photon sector, physical scale or thermal preparation of the photon bath.

The proton is stable against minimal-GUT decay because the icosahedral gauge algebra has no leptoquark generator.

The forced gauge adjoint (8,1,0)+(1,3,0)+(1,1,0) contains no (3,2,-5/6) X/Y generator, so minimal-GUT proton decay is absent. An exact dimension-six census on the one-generation table admits QQQL, QQUE, DUQL and DUUE; coefficients are not derived, so general proton stability and the baryon asymmetry remain open.

Anomaly cancellation plus chirality on the icosahedral exterior algebra leaves exactly the SM generation.

Exhaustive scan of all 1024 subsets of the 10-component exterior algebra selects one charge-conjugate pair of rank-15 chiral anomaly-free projectors: Q, u^c, d^c, L, e^c.

Inconsistent quantum gauge theories are excluded because observers must agree on gauge-invariant records.

The selected Lambda^2 + Lambda^4 package cancels all five gauge and mixed anomalies and is singled out by an exhaustive scan. At fixed finite stage a gauge-invariant chiral measure exists exactly when the Ginsparg-Wilson determinant line admits a nowhere-zero equivariant section.

Oriented A5 action keeps handedness, so nature distinguishes left from right.

Only chiral rank-15 masks survive the exhaustive scan: the selected generation is left-right asymmetric, so the weak force couples to left-handed doublets. Chirality is an arithmetic property of the declared generation table.

The same rank three that gives 3D space is the candidate for three families - suggestive, not proven.

Intrinsic-CP and weak-sector premises restrict the count to the window 3 <= N_g <= 5; A5, anomaly cancellation and the target-free matter reduct alone select nothing inside it. On a strengthened screen interface the exact Laplacian band costs 5 - sqrt5 < 6 < 5 + sqrt5 pick the rank-three band uniquely, and tensoring with the 15-state table gives a conditional rank-45 candidate. Physical matter-pole, continuum Spin/locality and seam-selection attachments are open (selection row 14, issue #736).

The fermion mass pattern needs a source flavour law that is not yet constructed.

Source-only Yukawa coefficients are not emitted. With the current certified inputs, independent rescaling of the up- and down-sector log-spreads preserves representations, anomalies, hypercharges and one-Higgs structure, leaving two moduli unidentifiable. This limits the current inputs, not all possible Yukawa derivations.

All SM pieces fit into one structural action on the carrier; coefficient sourcing is open.

Declared flat classical action assembles gauge, Grassmann-Weyl, Higgs and symbolic Yukawa terms with Ward controls.

Finite systems cannot produce genuine S-matrices; the continuum limit is required.

In any Hausdorff group, convergence of g^n forces g = identity. So a nonidentity unitary update at fixed cutoff has no ordinary large-time limit: scattering theory needs refinement or interaction-picture structure, not a naive limit.

Interacting fields are mathematically well defined on the carrier.

First-order trajectory convergence for the real quartic-wave sector; unique self-adjoint closure of the declared Hamiltonian.

The vacuum is the repair-stable state; its fidelity under refinement is controlled.

For the finite scalar Hamiltonian, exact Gaussian formulas give particle production, excess energy and vacuum overlap of kick/drift programs at every step. A polynomial symplectic update can preserve the oscillator vacuum only when the spectrum is small; root counting rules out a general vacuum-preserving polynomial integrator.

Massless chiral fermions arise as the spectral limit of charged hopping.

A unitary three-axis Pauli walk on the 3-torus (q divisible by 4) has continuum Weyl speed c/3 with explicit band error, and its Bloch matrix has exactly eight zero-energy cones, four of each chirality. Charged Weyl fermions emerge as a spectral limit; doubling is explicit.

The 1+3+3'+5 decomposition of the icosahedral carrier only admits these compact factors: the Standard Model gauge group is the symmetry of the observer cell.

Complete compact port response (A1) and endogenous overlap transport (A2) force the abstract Lie type u(1)+su(2)+su(3) on twelve ports.

The six antipodal axes become the Z6 that ties colour, isospin and hypercharge quantization together.

The common central kernel on every declared tensor is Z6, giving maximal faithful image (SU(3)xSU(2)xU(1))/Z6.

Charges are quantized because the gauge group is a quotient by a finite centre.

On the trace-balanced carrier C^3 + C^2 with hypercharges -1/3 and 1/2, Lambda^2 + Lambda^4 gives exactly one 15-state chiral generation with hypercharges 1/6, -2/3, 1/3, -1/2, 1. The common Z6 kernel makes charges quantized in thirds and fixes the global group (SU(3)xSU(2)xU(1))/Z6.

Unbroken U(1)em survives electroweak breaking, so its gauge boson stays massless.

The unbroken U(1)_em direction carries no hard mass parameter on the declared branch, so the photon is massless structurally. Its Maxwell dynamics is a finite theorem; masslessness as a physical bound is conditional.

SU(3) from the 3 and 3' sectors is unbroken; the gap makes coloured states non-propagating.

SU(3) from the 3 and 3' sectors is unbroken and gluons are massless on their declared branch. Confinement is tied to the Yang-Mills gap, which OPH identifies with the limiting repair gap; that identification is conditional.

Repair has a minimal nonzero rate; in the continuum that becomes a positive mass gap.

The continuum gap is identified with the limiting repair gap under named finite-rate, transfer and reconstruction certificates.

Electromagnetism is the curvature of port transport around icosahedral faces.

Unique minimal-energy Coulomb solution, local twenty-face curvature action gauge-invariant for conserved seam currents; Whitney-form continuum Maxwell dynamics.

Static field energy minimisation in 3D gives 1/r^2.

On the thirty-seam, twelve-port table the vertex Laplacian has an explicit rational Green matrix with L G = 1 - (1/12) J and constant kernel. Every neutral source has a unique minimal-energy Coulomb solution; continuum 1/r follows with the inverse-square shell theorem.

Charge is a record that can move but never disappear.

For a nonzero step h, hopping load and current satisfy the scaled continuity equation pointwise at every port and step, and so do finite families of charges. A face-local discrete Poynting law gives the matching conserved energy current.

Light is quantised oscillation of face curvature; modes are harmonic oscillators.

The source-free transverse sector of the 13-vertex, 42-edge cone with Lean-checked positive Whitney mass forms gives a finite free radiative Hilbert space. Carrier-mode oscillators cos(n theta) v solve the discrete field equation exactly when 0 <= h^2 lambda <= 4 - photons as quantized carrier modes.

The relative strengths of gauge forces are constrained by icosahedral invariance.

Ad-invariance leaves one kinetic coefficient per simple factor (u(1), su(2), su(3)); in the F and G families the three weights reduce to two, with sqrt5 golden weights. Absolute normalisations need the coupling bridge.

A raw icosahedral bracket isn't a Lie algebra yet; a repair rule must select the compact family.

The cyclic bracket of 20 oriented faces fails Jacobi in exactly 240 of 2640 coordinates; the B14 repair rule is open.

OPH predicts the SM group directly, not as the remnant of SU(5).

The forced adjoint (8,1,0)+(1,3,0)+(1,1,0) contains no mixed (3,2,-5/6) generator, so there is no SU(5)-type X/Y boson and no minimal grand unification. The Standard Model gauge algebra appears directly, not as a broken GUT.

The Higgs mechanism is a screen-level composition; its physical action is still owed.

Electroweak breaking composition on the screen with neutral- and charged-current dictionaries; broken-phase action undischarged.

The electroweak scale is linked to the screen via a common load carrier.

The exterior Standard Model witness has exactly four weak-doublet copies per generation (Q and L; Q counts three colours), giving additive weak load 4P under the normalized load law. A unique abstract order-unit isomorphism links the screen line and the weak centre line; its physical naturality identity is quarantined.

The hierarchy problem is reframed: the EW scale is fixed by screen load, not fine-tuned.

Weak multiplicity 4 and the abstract order-unit map are closed. The hierarchy v << M_Planck would follow from mapping the common load to capacity N ~ 10^122; those physical maps are open. The finite-domain signed-seam gap is strictly positive (>= 24^-8661) but dimensionless.

Follows from gauge kinetic ratios once source attachment is supplied.

W and Z values in OPH are running chart coordinates (W 80.330, Z 91.119) with candidate value-law coordinates, not physical poles. A strict one-loop pole map exists at fixed parameters, but sin^2 theta_W as a physical pole quantity is not independently evaluable yet.

All couplings descend from the single pixel constant P.

alpha_3(mZ; P) enters the fine-structure closure map through the quark screening factor 1 - N_c alpha_3/pi. A physical alpha endpoint needs target-independent map selection, a same-quantity bridge and same-scheme hadronic transport; alpha_s itself is not independently emitted.

Renormalization is coarse-graining of records; couplings run because observers resolve fewer records at long distance.

Under LC1-LC3 a positive quadratic expansion of local latency forces an isotropic infinitesimal clock, and refinement bounds influence by the resulting cone (RG as local clock reduction). A resource bound requires at least d^m alternatives for lossless decoding of m records. QCD-style asymptotic freedom is the target; the beta function is not derived.

Gauge fields are felt through loop phases - the record-level Aharonov-Bohm effect.

For group-valued labels on finite paths, the transport ratio of two paths with common endpoints equals the holonomy of the closed loop, and every unitary character turns this into an exact relative phase - the finite form of Aharonov-Bohm. No physical interference readout is attached yet.

One geometric number of the icosahedral screen sets all dimensionless couplings.

The single screen-grain constant P ~ 1.63097 links the golden ratio, pi and the fine-structure constant; it feeds tilt, couplings and masses.

Alpha is a self-consistency fixed point of the screen: alpha determines P which determines alpha. Residual 0.000339 is the open hadronic term.

Interval-certified screen-grain closure fixed points 136.994835 (root) and 137.035660 (with gauge width) vs CODATA 137.035999.

Running from mZ to zero momentum requires hadronic vacuum polarisation not yet source-derived.

Endpoint 136.38275 vs CODATA 137.036 (compare-only); retrospective accounting interval [0.6199, 0.6506] contains the reference deficit.

A pure-number gap of the screen spectrum underlies the scale hierarchy.

On the frozen 8662-node local domain, the sign-twisted incidence operator has full rank, so H = D*D is positive definite with lambda_min >= 24^-8661: a strictly positive dimensionless gap. A 24-stage register alone fixes no physical frequency, because uniform rescaling preserves it; the physical mass scale needs a calibrated clock.

The icosahedron's golden ratio is imprinted in coupling constants.

phi is native to the icosahedral carrier. The face normal operator's golden sector splits into two Galois-conjugate pieces (eigenvalues 3 +- sqrt5), each irreducible by Burnside. phi enters the pixel constant P, the sqrt5 gauge-kinetic weights and the golden source quadrature.

The Higgs sits at the edge of vacuum stability: its quartic and its running vanish at a screen-derived boundary scale.

Adopted conditional branch: SM two-loop criticality (λ = 0, β_λ = 0) at the log-midpoint anchor E* e^(−π) P^(−1/6) gives m_H = 125.77 GeV; on the fit-free m_t→m_H curve the measured top gives 124.73 GeV (−0.32%). The anchor was identified after the implied scale was computed; boundary-scale selection is open and a three-loop packet will discriminate. The earlier 125.207 GeV value was a target-anchored calibration surface and carries no predictive content.

Top Yukawa near one: the top saturates the criticality boundary together with the Higgs quartic.

Same conditional criticality branch as the Higgs: m_t(pole) = 172.63 GeV. The double-criticality family across candidate boundary scales spans 169.4–175.9 GeV at two loops; boundary selection theorem open.

W mass from the electroweak load map; a strict one-loop pole map isolates the complex pole.

Particle-zoo paper: target-free running-chart coordinate 80.330 GeV; candidate value-law coordinate 80.3770000154 GeV; postdiction-ledger chart 80.373315 GeV [80.369, 80.377]. All are chart outputs flagged NOT_EVALUABLE as a physical pole comparison. Reference: PDG 2026 fixture 80.3625 +- 0.0077 GeV.

Z mass from the same electroweak chart as W.

Particle-zoo paper: target-free running-chart coordinate 91.119 GeV; candidate value-law coordinate 91.1879780779 GeV; postdiction-ledger chart 91.193124 GeV [91.188, 91.198]. Chart outputs, NOT_EVALUABLE as a physical pole comparison. Reference: PDG 2026 fixture 91.1879 +- 0.0020 GeV.

The three charged leptons' square-root masses are eigenvalues of a face circulant on the carrier; Koide's mysterious 2/3 is the balanced point.

For a positive-chamber C3 circulant, Q = 1/3 + (2/3)(|b|/a)^2, so Q = 2/3 iff |b|/a = 1/sqrt 2, independent of phase.

Koide balance turns two lepton masses into a sharp prediction for the third; improved tau measurements test it directly.

FZ-10: under balanced-circulant premise, measured e and mu fix m_tau in [1776.968991, 1776.969063] MeV, 0.43 sigma from PDG 1776.93 +- 0.09.

Lepton rest masses are rest phases per tick of a three-state generation register; the absolute scale needs a calibrated clock.

New generation-register route: the phase θ = 2/9 fixes the lepton mass ratios with no measured input; the electron is the anchor that sets the absolute scale, whose factor F is not yet given by the source. The older MCPR triple (≈ −84 ppm common offset) is retained as a target-informed T2 lane.

The muon is the k = 2 eigenvalue of the balanced generation circulant at the read-count phase 2/9.

At θ = 2/9 (executed limit 2/9 + 9×10⁻¹⁴) the register's rest rates give m_μ/m_e = 206.770316 vs CODATA 206.7682827(46): +9.83 ppm, no parameter or round-count adjustment, no measured mass input. Not blind; the residual equals a phase shift of −1.75×10⁻⁷ whose constant is open.

The absolute lepton scale needs a source-emitted bridge; a value outside [0.6199, 0.6506] would refute the decomposition.

Anchor-gap 0.6379 closes the lane on measured masses; +0.0070 to the on-shell deficit is the unfixed scheme term (owner #736).

The current certified inputs do not determine the six absolute quark masses; this does not rule out a future Yukawa source equation, physical family attachment, or new selector. The rejected register-Clebsch candidate is only one failed route.

The current certified source inputs leave a two-parameter spread unresolved, so no absolute quark mass is emitted. This is conditional non-identifiability of those inputs, not an impossibility theorem for deriving quark masses.

This rejects only the cross-sector register-Clebsch candidate relation, not quark-mass derivation in general.

The register-Clebsch route gives ms/md = 22.97 vs FLAG 19.94/20.36; all six channel assignments are rejected by the conservative gate. The channel receipt only shows compatibility (one invariant line per allowed channel, none for the forbidden one), not mass identification.

Only the direct real-axis candidate is ruled out; quark mixing still requires a complex phase source not yet derived.

The 31 icosahedral residual axes have minimum nonzero angle 20.905 deg (sine 0.3568), so the direct real-3D axis equality candidate for |V_us| is rejected. sqrt(md/ms) = 0.2086 is explicitly not claimed as a derived Cabibbo angle. Other routes to CKM remain open.

CP violation would come from the same phase that makes quantum amplitudes complex.

No source-derived CKM or PMNS phase exists. A CP phase needs a complex lift of the real finite structures, which is open; the rejected Cabibbo candidate shows only that the proposed real-axis route does not suffice.

The template continuation fails; the finite OPH construction is untouched.

A target-informed weighted-cycle PMNS candidate was tested against NuFIT 6.1 and rejected (Delta chi^2 20.12 or 18.44 vs threshold 11.83). FZ-03 on neutrino ordering and mixing is registered but pending freeze.

Ordering stance from the frozen likelihood once registered.

FZ-03 is registered_pending_freeze: OPH intends a frozen normal-vs-inverted ordering statement, but the target and decision rule are not yet stamped.

Neutrino masses await the source flavour law.

Absolute neutrino masses have no source attachment; any numbers are compare-only. Owed alongside the PMNS route.

Dimensional transmutation of the source strong coupling gives the hadronic scale.

The inherited conditional coupling (α_s(m_Z) = 0.1183) gives Λ^(3)_MS̄ = 0.340 GeV in [0.325, 0.355] over sampled threshold corners; Λ^(5) = 0.214 GeV. Source colour action and matching not certified.

Most visible mass is QCD binding energy: Lambda_QCD times a lattice ratio.

Conditional Λ_QCD × external numerical ratio: 0.9436 GeV in [0.838, 1.057] (+0.56%); no certified full uncertainty enclosure. Independently, quenched lattice QCD on OPH seam links gives m_N/m_ρ = 1.45 ± 0.13 (PDG 1.211), without a GeV scale.

Mesons and baryons will follow once source QCD parameters are emitted.

The QCD solver is compiled, but invocation is gated until source-side parameters (coupling, quark masses) are emitted. Hadron masses beyond the nucleon conditional are owed.

Mass is a frequency of an internal clock; turning frequencies into GeV needs one calibrated clock, which OPH has not yet derived from records.

OPH emits dimensionless ratios. The finite local domain gives a strictly positive dimensionless signed-seam gap (>= 24^-8661), but a 24-stage register fixes no physical frequency because uniform rescaling preserves it. A mass in GeV needs a calibrated physical clock - the open record-clock = proper-time bridge.

Supports the programmed implementation; standard QM predicts the circuits, so no OPH-vs-QM discrimination.

Blinded record-gated controller passes frozen primary nulls on development and held-out QPUs; some legacy summaries have mixed outcomes / incomplete custody.

The executable observer pipeline reproduces real trapped-ion readout data under a supplied apparatus model.

21 calibration probes fix two preparation parameters; 100 reserved complex probes give per-spin-mean RMSE 0.06647 (analytic variant 0.07639).

Predicts unseen time-evolved data; controls show the anharmonic + dephasing model is needed. No native C/E likelihood is evaluated.

50 zero-duration probes calibrate; 707 positive-duration means predicted with binary-probability RMSE 0.05558 (no fit to those means). Controls: harmonic 0.2856, no-dephasing 0.1206, frozen 0.3474 (per-spin-mean).

Transfer to a changed potential works approximately; material trajectory discrepancies remain.

Five preparations, 125 derived position estimates: RMSE 0.28764 (position-estimator units), reproduced by the primitive runtime; cosine-Hamiltonian comparator 0.31768.

Model-independent quantum consistency checks reveal residuals no oscillator action could remove.

Two-order Gram positivity requires correcting at least one deposited complex mean by ≥ 0.02439 or 0.03129 (coordinate extents 4/5); probability-RMSE floor 0.03419.

Excludes treating this output as the complete endpoint with zero missing correction - not an OPH-wide rejection.

Native attachment uses 1/α = 136.994835177 vs CODATA 137.035999177: a 300.39 ppm deficit; enclosure misses the 5σ interval.

Rejects collective regional event-count clocks as direct optical-clock readouts.

Against all 11,782,056 ordered pairs of 3,433 regional event sets, conservative bounds below 1e-121 (36Ar) and 1e-22 (40Ar).

Atomic clock frequencies are not simply native modular gaps with one common scale.

All nine assignments of the native three-mode transfer gaps with one scale miss R40 and R36 by > 0.057.

Shows the observer CMB pipeline is consistent with Planck spectra, though not an independent native prediction.

Planck TT/TE/EE standardized-residual RMS ≈ 1.0136 / 1.0198 / 1.0194 on 2471/1967/1967 multipoles; amplitude, tilt, background and transfer imported.

No icosahedral imprint found in WMAP at that sensitivity - a documented exposure.

Preregistered A5 search at l ≥ 6 with null family-wide p = 0.64; its data are excluded from FZ-11/FZ-12 verdicts.

DESI's evolving-dark-energy hint is in tension with OPH's fixed-capacity branch; adjudication governed by FZ-13.

Gaussian diagnostics for (w0, wa) = (−1, 0) range 2.60–3.93 standardized units across overlapping DESI DR2 combinations.

Galaxy dynamics broadly follow the deep law, but a0 is fitted, not derived.

Deep-regime acceleration and BTFR comparisons fit a0 and expose tension under declared weighting and mass-to-light choices.

A template neutrino continuation fails its declared gate.

Δχ² = 20.12 or 18.44 vs threshold 11.83: candidate rejected in both atmospheric treatments.

A retrospective strain on the conditional primordial branch; FZ-15 remains the prospective test.

Edge-center n_s = 0.966021 sits at posterior mass 3114/508985 of the P-ACT-LB chains (mean 0.97426 ± 0.00338): lower-tail tension.

The declared coupling chain reproduces a crossover, not a first-order transition, at the Standard Model temperature.

Lattice Monte Carlo of the 3D SU(2)+Higgs theory at the declared chain's couplings (dimensional reduction imported). T_c = 161.13 ± 0.13 (lattice) ± 1.6 GeV vs 159.5 ± 1.5 GeV (SM lattice), +0.74σ; first-order endpoint at m_H = 72.5 ± 0.7 GeV vs 72(2). Not blind.

Confinement, the first-order deconfinement transition and hadron binding appear on OPH's own seam links.

Seam cost on a colour holonomy = Wilson plaquette action. Measured at N_t = 4: β_c = 5.69248(71) vs 5.6925(2); first order with three Z3 sectors; T_c/√σ = 0.614(18) vs 0.598(3); linear static potential; quenched m_N/m_ρ = 1.45 ± 0.13 vs 1.211. Binding melts above the transition. Not blind; no GeV scale.

Declared forms that fit; derivation open. The chain is a compact target for a source derivation, not a result.

Five declared forms at P = 1.6309721: 1/α_U = 24.3166; v = 246.60 GeV (246.22); α_s(m_Z) = 0.11834 (0.1180); sin²θ_W = 0.23074 (0.23122); 1/α_em(m_Z) = 128.308 (127.95); 1/α(0) = 136.995 (137.036). The count 4 in v's exponent is the plaquette cost of one weak-centre flux quantum (derived); the rest is declared.

OPH answer: the universe is a self-referential fixed point, R(D(U)) ≅ U - it contains observers who recover its specification and realize it, so it needs no outside cause or first premise. Existence is self-realization rather than something granted from outside.

The essay 'Why does anything exist' develops existence as inhabited closure: a world whose parts record its architecture, recover it from the records and realize it through their activity. Fixed-point constraints show how relations can fix their members together with no first term; a finite realization lemma separates a description from a causal realization. The ontological step, intrinsic realization (a complete inhabited causal structure is actual through its own dependencies), is stated as a hypothesis, kept separate from what the mathematics proves.

OPH answer: observers are primitive, not late products of matter. Qualia are the qualitative character of an observer's enacted self-reading, and spacetime is the public reconstruction from relations among such observers - so experience is the starting point, not an add-on.

The essay 'Why do qualia exist' separates three commitments: there is an experiencing unit, its self-reading changes its continuation, and that difference is carried by its lived content. Under those premises a conditional theorem shows an observer with n distinct response classes must have at least n distinct qualitative contents. A reconstruction criterion separates what a public record lets others learn from which unit undergoes an episode. Distinguished from Russellian monism and integrated information theory; the identity it rests on is stated so the hard-problem objection applies at one identifiable point.

OPH answer: the laws are the ones a self-reading universe must have to be consistently recovered by its own observers - no anthropic multiverse and no external lawgiver. Constants are fixed by closure and screen capacity; which ones are already derived is tracked row by row in this table.

Synthesis paper, section 'Closure' and 'No outside': a structure with no outside has no place from which a postulate could be imposed, so the carrier, observer algebra, repair law and two closure coordinates are justified by being recovered by observers, running, and reproducing measurements. The same rule forbids assuming anything not recovered: state selection minimises relative entropy (A3), and endogeneity (A2) forces u(1)+su(2)+su(3). Finite results give the closure condition exact content: the packet-quotient closure theorem, and the record-closure equation N = log M0(U_N), which is posed but not yet identified.

Oscillating strings could be one way to describe edge modes of the screen, but no string vacuum is currently selected by OPH.

Owed. String theory is treated as an effective OPH edge language, and this programme remains open. One specific candidate, a Bouchard-Donagi heterotic row, was tested against OPH gates and retracted by a fail-closed moduli-locking gate; that retraction rules out that row only, not the edge-language route.

If observers are primitive, a consistent universe must contain the observers that read it - closure without an outside.

Speculative extensions: observers as self-reading patches, and a closure hypothesis in which the universe reads itself into existence.

The self-consistency of observers reading each other is the only selection principle; no anthropic multiverse is needed.

The synthesis paper's closure hypothesis: no external time, no outside observer; constants are what closure fixes and observation reads off.

Fields are effective descriptions of what observers jointly measure, not fundamental.

Of seven structural QFT targets, two carry theorem-shaped finite surrogates. The inductive-limit C*-seminorm on the consensus-tower colimit is built with its exact kernel, and selected finite density states descend to a GNS expectation. Continuum relativistic QFT is the declared target, not yet derived.

OPH distinguishes theorem, execution and physical comparison; the bridges are the main owed work.

20 undischarged physical identifications (e.g. record clock = proper time, repair generator = Yang-Mills Hamiltonian).

Gravity is the geometry observers must agree on to keep records consistent; GR should be its effective field theory.

Research goal: recover GR as the long-wavelength description of record consensus. Finite pieces exist (Lorentz module, null tomography, Einstein equation up to Lambda on the conditional branch, massless graviton structurally); the continuum attachment, null-net standardness and local stress upgrade are open.