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.
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.
Balanced W remain within the sector; T insertion/removal responses require Cp. No derived physical measuring instrument.
Read the exact result, assumptions and evidence
Result
η·Qtot is zero on C0. T_p enters Cp; full propagation yields ratio exp(−2tη·p). For v=Bp, conditionally η=Bᵀδ. Only the odd factor is matched.
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.
Chemical comparison with charged intermediate sectors
Additionally supplied Hη=H+η·Qtot, C-invariant initial density in C0 and full propagation after onsite T moves C0 into Cp. η is comparison input, not a derived seam parameter.
Unchanged finite source and specified invariant start; different states or operator dictionaries are not excluded.
Read the exact result, assumptions and evidence
Result
Original C T_p C=T_−p, T_p*=(-1)^e(p)T_−p and C H C=H. At an invariant start all C-conjugate bounded words agree.
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.
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.
Construction applies only with complete coherent K values and stated domain conditions; K from the original TFPT source has not been derived.
Read the exact result, assumptions and evidence
Result
Given a positive Gram kernel K with normalized reference, compatible composition/adjunction, and null-stable continuation, quotienting by null vectors and completing constructs H_K and the well-defined word action. Cyclic realizations of the same complete K values are unitarily equivalent on the common word domain; for unbounded operators, closures and self-adjointness remain additional requirements.
Required assumptions
Positive word kernel with null stability
The GNS/Gram reconstruction requires a Hermitian positive kernel K, normalized reference, declared composition and adjunction, and stability of null relations under every allowed continuation; these are conditions on a supplied K source, not TFPT axioms proved from bare future answers.
Applies exactly relative to the declared experiment alphabet and complete answer functional; no absolute ontology or physical TFPT source claim.
Read the exact result, assumptions and evidence
Result
For a fixed experiment alphabet and complete answer functional r, u~v exactly when r(uw)=r(vw) for every allowed continuation w. The quotient is the minimal distinguishable process state relative to those answers; by itself it yields neither complex amplitudes, the Born rule, continuous time, a metric, nor E8.
Required assumptions
Declared complete answer functional
A fixed set of allowed experiments and the answer functional r for every finite experiment sequence are additional operational inputs; they define the future quotient only relative to that experiment alphabet.