Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Historical: common source, state and event selection
Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?
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.
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.
The reviewed decision record says which approach can be reused, which failed in its scope and what a new attempt would have to change.
Insufficient for the goal
Polynomial degree as a physical source selector
The cited original seed definition assumes A_loc, tau_t, Theta, omega, [u_Sigma], and D_coll as data and shows only their collar completion. This cited evidence supplies no rule selecting the common physical source from a polynomial degree.
Consequence: Provide an explicit original-source rule mapping degree to source selection before assessing the strategy as a selector.
Order-four markings from given time and full charge
The whole family is completed by lattice saturation and exact classification, including an original-frame control.
Consequence: New knowledge requires a justified change to the original source operator or its field/sector map; further phases of the same family are already covered.
Use the downstream master functional as an original selector
The allowed source is already named in the zero/infinity barrier. A minimum on that restricted branch does not prove this upstream selection.
Consequence: Supply a selection rule computable from original data without a presumed B_min and prove its relation to the actual field/state/time operator.
Identify geometric deck lift with boundary polarization
The general implication from reflection regularity is disproved by a compact Dirac counterexample; carrier restrictions built on it need their actual operator map established again.
Consequence: Keep geometric lift, normal Clifford action and Calderon polarization distinct. For dynamics retain the full two-face relation and use the already verified inverse reader.
Determine the common original clock lift and event menu
Supply the actual common4/5/20 continuation of the existing coherent clock polynomial and the original-source event menu; jointly check normalization, erasure, products and full source time. Determine the complete4/5 generators or their currently free data from it.
Builds on: Reconstruct the actual common native operator object; Classify native rates and coherent residual channels
Resolved in scope
Reconstruct original mark and test native clock continuation
Consistently connect actual positive polar transport, unchanged four-clock and original decoder; test product lifts and the same native polynomial continuation on a decisive input.
Builds on: Reconstruct the actual common native operator object
Classify polar fibre and test existing native selection mechanisms
Completely classify actual clock-compatible marking fibre, characterize the original polar rule canonically and test existing moment parent/geometric product transport against the target operation.
Builds on: Reconstruct original mark and test native clock continuation
Retain actual original off-code states and compute feedback without fitted coupling or executed projection; decide whether same family admits closed five-dimensional linear continuation.
Builds on: Test full source-return code closure and erasure Ward terms
Derive actually original canonical geometric source histories including higher modes on4/5/20 and first forced erasure correction/native sector action without coupling choice; determine whether this class selects marked clock.
Builds on: Derive full source feedback and necessary memory
Check full local Cartan insertion and ordered product
Decide on actual original current field whether pure native erasure is local; derive regular carry and full local response and test stated ordered Cartan-Weyl class without fitted algebra.
Builds on: Derive original all-mode conformal/erasure bridge
Derive unmarked native simplex from local quartic product
Reconstruct a separately used native structure from full local product without its target coordinates; literal comparison only afterwards, physical selection separate.
Builds on: Determine full local source hull and unfiltered returns
Test original seam/state/event data on full field tensors
Determine actual event/state response on fulloriginalfieldtensors and whether given normalization/sectoraction yieldsoriginalpolar/P2 withoutnewselectionrule.
Builds on: Derive unmarked native simplex from local quartic product
Derive original P1 gap-scale term and test direct native spectral bridge
Evaluate explicit original source function without profile/measurement fitting and test smallest actually source-fixed3+2 bridge on full outputs. Keep physical overall selection separately open.
Builds on: Derive full original current/field products and original seam grading
The complete original boundary graph can determine B and, under CAR identification, the state jointly. The source must supply this graph, fiber comparison and scale. This replaces separate spectral/state searches; physical marking additionally needs the original local operator algebra. ReviewedKMSlocalcorrection:globalrotationmovesintervals,localTakesakitimedependsonrestrictedstate;deriveitsstate/netcomparisonfirst.
Original historical attempts linked to this question
These are original research records. Their reported verdicts are distinct from the reviewed results above.
e series source reconstruction 20261024
Reconstruct the canonical local E8 field completion from the already established marked D5+A3/C4 compiler glue; determine which original source and dynamics implications are actually proved.
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.
Does the actual original seam representative derive a local mixed spinor weight-one current through quarter-twist fusion, and does the pasted scalar pair response identify that field?
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.
Which marking and response memory follow from the original charge source, and can the derived four-grade factor close under the same Hamiltonian and actual clocks?
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.
Does the existing signed neutral scalar/charge source generate a common time, state and ordered response law, and what information must an exact marked readout retain?
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.
Does the proposed eightfold fold/multi-interval completion derive physical quotient locality and an E8 field extension from the same source while preserving the quarter phase, state and time?
Recorded verdict: EXCLUDED_IN_UNCHANGED_SOURCE
Historical inventory; not independently reviewed by this export.
Which full charged crossed-defect extensions of the fixed ordered CAR source preserve its marking, W4 composition and supplied time law, and which obligations remain for a joint source/state/event derivation?
Recorded verdict: PARTIAL
Historical inventory; not independently reviewed by this export.
Does the original source derive time, state and the internal 3+2 carrier together, or do the proposed Higgs/Yukawa repairs assume the missing field map?
Recorded verdict: PARTIAL_SOURCE_DERIVATION_NOT_CLOSED
Historical inventory; not independently reviewed by this export.
Can one D8-containing even-unimodular extension preserve the source charge/clock class, determinant-only packet response, unchanged fold time, and original vacuum requirement at once?
Recorded verdict: EXCLUDED_MARKED_FOLD_COMPLETION
Historical inventory; not independently reviewed by this export.
Which order-four markings are generated by the retained source time and full charge, and do they supply a physical common source without an inserted P5?
Recorded verdict: COMPLETE_INTERNAL_CHARACTER_CLASSIFICATION_PHYSICAL_SOURCE_OPEN
Historical inventory; not independently reviewed by this export.
Does the actual P1/P2 seam determine a common field, state and time map with the quarter phase retained, and what exact operator conditions permit reconstruction?
Recorded verdict: CONDITIONAL_SOURCE_RECONSTRUCTION_NO_P1_DERIVATION
Historical inventory; not independently reviewed by this export.