Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Universalraum
The published foundation in this area
14 authored claim references lead into the original ledger and paper sections. This source record remains available even where no separate reviewed research packet is attached.
Universalraum keeps two directions separate: operationally complete TFPT as a common parent, and derive TFPT readouts from a deeper shared source. Future equivalence is defined relative to an explicit menu of interventions and records.
Starting structure in the Atlas orientation
Formal future-equivalence criteria, finite filters and parents, and counterexamples to premature correlation removal are available.
Which connection is sought
The goal is either operational completion of TFPT or a deeper source process that generates TFPT readouts; both require states, interventions, events, and records.
How it connects
Universalraum→TFPT asks for the deeper source; TFPT→Universalraum asks for complete common implementation. Readout matches answer neither direction automatically.
Only the named unchanged CAR/QWZ representation with the same time. No TFPT no-go; choosing a state removes no added zero vector.
Read the exact result, assumptions and evidence
Result
All four hits add the same half-integer Cartan sectors and second K-zero vector. The already known integer-Cartan/ground-space obstruction therefore excludes equivalence to the unchanged source; positive algebraic extension remains possible.
Required assumptions
Fixed CAR source and adjoined half sector
Ordered eight-channel cocycle, s=(1/2)^8, Q, quarter phase and K_alpha=N+|p|²/2+delta_alpha.p are supplied; alpha=1/4,3/4. Parity equivalence is in the global operator envelope without a separately marked physical X. Neither source nor extension is derived from P1/P2.
Unchanged specified CAR/QWZ source
Compare the known quarter-CAR source or full mass=1, ny=8 QWZ operator with the identical Hilbert representation, Cartan action and physical time. Preserve its previously proved unique ground state and spectral gap. This does not compare all P1/P2 realizations.
Fixed phases and corresponding invariant starts; real time retains conjugation/time reversal. No assertion about all P1/P2 sources.
Read the exact result, assumptions and evidence
Result
C and K may separately break; A=CK preserves H for all fixed link phases and T_p→T_−p. Invariant starts retain equal Euclidean opposite-charge returns, including quarter phases/flux.
Required assumptions
Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Fixed link phases and A-invariant start
Arbitrary fixed unitary link phases in the same hopping, real original Hdiag/cocycle and initial density invariant under A=C times complex conjugation. Positive Euclidean T return responses are considered; no general real-time equality is assumed.
Fixed nonzero chiral quarter twist
The comparison target is the stipulated Kδ Fock space with original nonzero quarter twist, normalized ±Bp primary states, fixed charge marking and the same positive time. Equality of all these responses is required.
Only the fixed marked response identification at these starts and the same time.
Read the exact result, assumptions and evidence
Result
The native ratio is one; the fixed quarter twist gives exp(−2tδ·Bp), which differs from one on at least one original basis direction.
Required assumptions
Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Charge-conjugation-invariant start
The initial density is invariant under linear C:n→−n, including full and C0 Gibbs starts of unchanged H. Compare actual adjoint-paired, opposite marked T responses at the same time.
Fixed nonzero chiral quarter twist
The comparison target is the stipulated Kδ Fock space with original nonzero quarter twist, normalized ±Bp primary states, fixed charge marking and the same positive time. Equality of all these responses is required.