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.
Exact conditional classification of the particle LR block of the given representation, not a complete real-triple classification or P1/P2-derived coupling. Already encoded3+2 structure is not newly selected.
Read the exact result, assumptions and evidence
Result
For M=diag(Yup,Ydown), every particle LR one-form obeys q_a(Mr_b−q_bM)=q_a(r_b−q_b)M. The factor is quaternionic and b=eR spans all qM. Including the seed yields M(H)=HM with H=[[φ1,φ2],[-barφ2,barφ1]]. The four Yukawa matrices and color/weak modules remain inputs; D_F=0 gives no finite fluctuation. The linear identity was checked exactly against unchanged existing code with a complete coefficient basis, without choosing physical couplings.
Required assumptions
Given finite SM representation with symbolic Yukawa inputs
Use only the existing v252/v254 representation with C⊕H⊕M3, already supplied color/weak modules and four symbolic complex3×3 Yukawa blocks. No physical values are chosen or fitted. Classify the particle LR one-form block; no proof of the full real96-dimensional fluctuation with antiparticles, JAJ and Majorana sector is claimed.
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.
Concrete algebraic/smooth enlargement, not the entire bounded-operator algebra. Does not exclude an independently derived noncommutative local field algebra.
Read the exact result, assumptions and evidence
Result
P0=C−UCU* and Emn=U^m P0 U^(−n) supply all finite matrix units. The represented generated algebra has scalar commutant and center. Since I is a one-form, every element a=aU*[B,U] is a one-form. The enlargement permits arbitrary finite-rank matrix perturbations but selects neither a Higgs coupling nor3+2 and cannot silently replace the original local algebra with smooth center.
Required assumptions
Explicitly additional nonlocal Cauchy enlargement
On the Fourier basis en,n∈Z, U is the bilateral shift and C projects onto n≥0. Consider the algebraic or explicitly smooth *-algebra with controlled bounded commutators generated by U,U*,C. No identification with B(l²), automatic domain statement for its norm completion or original local field algebra is assumed.
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.
Complete one-form/one-particle holonomy theorem only for this explicit coordinate algebra. No P1/P2 no-go, identification with the full physical net, fixed Fock-vacuum equivalence or anomaly cancellation. Real completion depends on actual J and sign.
Read the exact result, assumptions and evidence
Result
From [Bα,Mb]=−iMb′ and U*[Bα,U]=I one obtains exactly Ω¹_B(C∞(S¹))={Mv}. Selfadjoint perturbations are real smooth v. With mean vbar, Bα,v=e^(−iλ)Bα+vbar e^(iλ), λ′=v−vbar; the same quarter holonomy requires vbar∈Z. Fluctuation preserves the represented algebra and line module and thus creates no new SU2 fundamental or3+2 selection in this realization.
Required assumptions
Local coordinate algebra of the conditional quarter source
Given the conditional scalar circle realization H=L²(S¹), Dom B=H¹_per, Bα=−i∂θ+α with α=1/4 or3/4. The local algebra investigated here is explicitly smooth multiplication C∞(S¹) on this line, not a complete physical field-insertion algebra already derived from 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 zero-jet identifiability test on the given free source path. No no-go for a complete Φ-dependent functional or later original selector; no general interacting Yukawa theorem.
Read the exact result, assumptions and evidence
Result
The existing direct Grassmann path yields the same complete unnormalized source polynomial and Z0=69649/65536 for both supplied extensions at Φ=0. The mixed derivative is zero or offdiagonal -65536/69649; -K0(∂Φ K^-1)K0 reconstructs the supplied derivative K′. A joint source derivation therefore still needs the actual original field dependence and correctly equivariantly typed coupling.
Required assumptions
Given free quarter-source background without a selected Higgs derivative
The existing two-mode source path has K0=diag(17/16,4097/4096) and a fixed Berezin measure. Compare only completely coincident fermionic source polynomials at Φ=0 and explicitly supplied extensions K0 or K0+Φσx. These are diagnostic extensions, not two claimed P1/P2-admissible worlds or a comparison of complete Φ-dependent functionals.
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.
Excludes only the local invariant-theoretic inference under the stated polynomial interpretation. No P1/P2 countermodel or refutation of additionally justified global minimality or actual branch-tensor support; no new Lean build.
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Result
For V=C5,W=C2, (V⊗W)⊗Λ4V⊗W→detV⊗detW is a nonzero S(U5×U2)-invariant tensor with even fermion degrees2/4. Centers and U1 charge force positive invariant total degrees(5m,2m); thus the tensor is primitive at carrier degree7. It refutes the local inference that r≥4 must factor in the invariant ring. The stronger Lean premise E≃(Λ²E)* remains valid and needs its own source derivation.
Required assumptions
Covariant invariant-ring primitiveness at variable carrier rank
For the local inference test: V=C^b, W=C², G=S(U(V)×U(W)), both fermion legs in Λeven(V⊕W). Primitiveness excludes invariant factors of smaller positive carrier degree in the covariant polynomial invariant ring. No global minimum over different sources/ranks or independently selected special tensor support is assumed.
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.
Audit of the specified archived origin chain and elementary bundle controls; no refutation of an actually supplied equivariant bosonic operator, P2 postulate, or conditional Lean theorem.
Read the exact result, assumptions and evidence
Result
The archived determinant argument uses X=-2P3+3P2 and an explicitly rank-two weak block before the later rank-two conclusion. H0(O(1))=C² alone determines neither rank E+ nor its operator kernel; the same determinant line occurs at different ranks and different h0. The Lean Higgs theorem explicitly assumes its linear identification with binary forms.
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.
Literal source interface of the archived definition; not a refutation of the algebraic 3+2 statement for a supplied P2 carrier. Likewise (2G−I)|Ran(G)=I: full boundary data alone do not create an internal marking.
Read the exact result, assumptions and evidence
Result
Pprim=C Pgap implies Ran(Pprim)⊂Ran(C). Thus (2C−I)|H_car=I for a carrier embedded there, and E_−=0. Every isometric pullback W into Ran(C) also yields W*(2C−I)W=I. The later 3+2 polarization does not follow this way. The general lemma CQ=Q ⇒ (2C−I)Q=Q is kernel-checked. A different carrier factor needs an explicit different map.
Required assumptions
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.
Literal carrier embedding after positive compression
Read the archived phrase H_car after primitive admissibility compression literally as a subspace of Ran(Pprim)⊂Ran(C), then define internal polarization as (2C−I)|H_car. A different coefficient-factor interpretation instead requires its own embedding and internal involution.
Correction of the general geometric identification in the archived source, not rejection of P1/P2 or all seam realizations. A nonlocal R:=2C−I can be defined but thereby has no demonstrated geometric origin.
Read the exact result, assumptions and evidence
Result
The original source identifies R_tau=2P_C−I from reflection regularity. A compact product-Dirac counterexample with B=diag(A_1/4,−A_1/4) and local R=σx disproves that general inference: the deck lift on the two fixed boundary faces changes G, whereas 2G−I commutes with G. The principal-symbol comparison confirms the type distinction. R_alg=J_n(2C−I) is a reconstructed, generally nonlocal involution; its algebraic quarter turn does not derive charged quarter holonomy.
Required assumptions
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.
Local geometric lift on a Dirac boundary
The claimed geometric deck reflection acts at the fixed boundary through a local bundle lift over the same base reflection. Compare an ordinary positive-dimensional Dirac boundary with orthogonal Calderon projection; a nonlocal operator subsequently defined as 2P_C−I is not a pre-established geometric action.
Audit of this definition, not a disproof of all other selection theorems. Its electromagnetic alpha is not automatically the quarter-phase parameter in the CAR energy test.
Read the exact result, assumptions and evidence
Result
The definition fixes d*_disc and P_adm first. Its barrier is zero for B≅B_min and infinity otherwise. M therefore optimizes continuous xi on the already selected branch; this definition neither classifies B_min nor derives the least charge-one excitation rule.
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.
Global variational theorem in a given scalar CAR source; no change to B and no finite-search proof. General unitary vacuum symmetries may yield the same minimal state energy. The least-excitation selection rule and origin of fields, state and time are not derived from P1/P2.
Read the exact result, assumptions and evidence
Result
With B_alpha and the reference sea fixed, every unimodular H1 symbol u=exp(i phi) of winding one has E(R_u Omega)=alpha+½⟨(phi prime−1)²⟩. The unique scalar-multiplier minimum is u=exp(i chi)z. Both b_(1/4) and z²/b_(1/4) have excess 1/15. The produced state changes, not the reference sea.
Required assumptions
Fixed scalar Hardy model with quarter time
H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.
Charged CAR algebra and original negative sea
Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise.
Complete analytic theorem in the supplied scalar Hardy class. Leakage excludes only the pure-isometry route, not general physical sources. Not a P1 classification.
Read the exact result, assumptions and evidence
Result
Every continuous scalar unimodular winding-one symbol with isometric Hardy compression is a single Blaschke factor modulo phase. With B_alpha fixed, only the centered factor z has constant shift covariance. The strictly oriented control z²/b_(1/4) has leakage 15/4096.
Required assumptions
Fixed scalar Hardy model with quarter time
H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.
Conditional analytic reconstruction on a common core; Lean verifies the algebraic identity and mode recurrence, not physical derivation of inputs. One channel is not the five-slot P2 carrier; no event law.
Read the exact result, assumptions and evidence
Result
Under the operator hypotheses, Wold supplies a complete mode basis U^n w and B=N+alpha. With the CAR/sea premise, R c_n R*=c_(n+1), R*QR=Q+1 and R*H_alpha R=H_alpha+Q+alpha. R Omega is a new charge-one state; exp(2pi iH_alpha)=exp(2pi ialpha Q) retains the quarter phase.
Required assumptions
Hypotheses of joint operator reconstruction
For this conditional theorem: orthogonal projection C, unitary U, (1−C)UC=0, index(CUC)=−1, pure isometry and minimal unitary dilation. Actual selfadjoint B satisfies U*BU=B+1 and Bw=alpha w on a common invariant core, alpha=1/4 or 3/4. These conditions are not presumed derived from P1/P2.
Charged CAR algebra and original negative sea
Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise.