Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Interlocking clocks
The published foundation in this area
23 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.
TFPT uses several distinct algebraic clocks and transfers: Coxeter period 30, phase automorphisms, an order-12 compiler action, and separate relaxation factors. Their mathematical periods do not by themselves define physical duration.
Starting structure in the Atlas orientation
Known structures include finite actions: Coxeter number 30, μ4 on phase data, an order-12 compiler action, and separate relaxation rates.
Which connection is sought
The open work is a common source derivation, event interpretation, and a parent realizing one time rule for matter, boundary, and instruments.
How it connects
Clock actions organize E8/code readouts and event sequences; algebraic orders are neither measured seconds nor proofs of dynamics.
Audit of the cited proof only; not a general impossibility theorem for P1/P2 or a revocation of declared unit winding.
Read the exact result, assumptions and evidence
Result
The original argument first states that uniqueness needs classification of the minimal stratum, then asserts it without that classification. Well-ordering N4 yields a minimal value, not a unique operator fiber. Nonzero spectral flow alone also does not prove attainability of one.
Required assumptions
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact field-type comparison in the same given source. No universal exclusion of E8 or future source/sector extensions.
Read the exact result, assumptions and evidence
Result
Each of the four candidates acts on the eight original complex fields with two copies of every quarter phase. Their neutral bilinears form A3+4A1 with twenty roots and rank seven, rather than D5+A3 with fifty-two roots. The latter uses the stipulated spinor completion. The new marking changes neither K nor the known ground-state comparison and supplies no event instrument.
Required assumptions
Fully normalized time/charge family in the given E8 completion
The given chiral quarter source, its eightfold pushforward and stipulated even E8 completion supply K_alpha and the full additive U1 generator Q. Only characters in the real span of their torus vectors modulo E8 are searched; no P5 is supplied as a search variable or target projector. Physical identification of this completion and of a composed marking is not assumed.
Stipulated E8 quarter-fold dictionary
The existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed.
Given chiral source in both quarter domains
D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources.
Given chiral source, fold, full normalized charge and stipulated E8 completion. Algebraic construction and Lean lattice theorem; no physical selection of W or source from P1/P2.
Read the exact result, assumptions and evidence
Result
Full lattice saturation reduces the continuous source torus to sixteen four-torsion characters, twelve primitive and exactly four D5+A3 markings. P5 is reconstructed from neutral root moments; a control without M or a target projector finds the same four. W=exp(4πiK)exp(-iπαQ/2) realizes one while preserving quarter time; sheet transport gives W Zq. Compensation was previously known; complete classification and control are added here.
Required assumptions
Fully normalized time/charge family in the given E8 completion
The given chiral quarter source, its eightfold pushforward and stipulated even E8 completion supply K_alpha and the full additive U1 generator Q. Only characters in the real span of their torus vectors modulo E8 are searched; no P5 is supplied as a search variable or target projector. Physical identification of this completion and of a composed marking is not assumed.
Stipulated E8 quarter-fold dictionary
The existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed.
Given chiral source in both quarter domains
D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources.
Global charge transports in the stipulated even completion; not local vertex insertions, an ordinary-local odd CAR/E8 inclusion or event dynamics.
Read the exact result, assumptions and evidence
Result
On the even D8 Fock sector W4=Us Rc holds with the actual ordered CAR/E8 cocycle, Klein signs, all oscillators and current central term; Rc preserves Q,K and the quarter transition. The E8 extension and lift convention are explicitly given.
Required assumptions
Stipulated even E8 completion with actual Klein signs
Assume the E8 extension of the even D8 CAR sector constructed in seam-joint-ward-state, with original ordered cocycle, retained quarter transition and explicit P-lift convention. An ordinary-local inclusion of odd CAR fields is not assumed.
Given source, grade and J>0; the two-time kernel is neither a physical measuring instrument nor a universal three-dimensional memory realization.
Read the exact result, assumptions and evidence
Result
Original grade and transport generate M4(C(S1)) with integer carry. Full H couples grade and carry. The GNS projection has K(t)=B*exp(itLQ)B with rank K(0)=3; its minimal temporal realization may be infinite-dimensional. No external memory is appended.
Required assumptions
Declared native charge/scalar source
Fixed finite periodic spatial lattice source of rounds20–26 with original G, cocycle, neutral Z8 charges, scalar field and H=Hdiag+Hhop; a,m,beta>0 and original couplings are supplied. Nontrivial memory requires J>0. The original grade k is additionally retained, without presuming its selection from P1/P2.
Finite spatial volume and original neutral scalar/charge source; no spatial continuum or P1/P2 selection claim.
Read the exact result, assumptions and evidence
Result
The original H is positive self-adjoint and has a faithful Gibbs state for every prescribed beta. The actual transfer reconstructs Hδ=−log Qδ/δ; removing the temporal regulator makes its unitary dynamics converge to the same H. Spatial lattice, couplings and beta remain declared inputs.
Required assumptions
Declared native charge/scalar source
Fixed finite periodic spatial lattice source of rounds20–26 with original G, cocycle, neutral Z8 charges, scalar field and H=Hdiag+Hhop; a,m,beta>0 and original couplings are supplied. Nontrivial memory requires J>0. The original grade k is additionally retained, without presuming its selection from P1/P2.
Applies to the cited operational seed category and its collar completion; it does not claim that no other original selector exists.
Read the exact result, assumptions and evidence
Result
The original definition already assumes (A_loc, tau_t, Theta, omega, [u_Sigma], D_coll); its collar-completion theorem derives B_Sigma and spectral data from them, but does not select those inputs.
Required assumptions
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.