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Research snapshot 2026-11-03 · 783 active ledger claims · 784 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.

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Every one of the 783 active ledger IDs is included. All 788 ledger rows, including superseded rows, remain in the download. The reviewed research corpus contains 785 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.

The scientific findings include 587 established scoped results, 63 conditional results and 134 scoped exclusions. These labels describe the recorded finding. They do not upgrade its parent physical goal or overwrite the original ledger.

Sources were matched to their recorded hashes and line ranges at this snapshot. Bounded text excerpts make sources available even when a source is not in the earlier public release. Any omitted administrative lines are explicitly marked. This is source coverage, not a new execution of Python, Lean or Wolfram proofs.

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1567 matching records · page 72 of 79

Excluded in the stated class

Original bilocal current and natural Hodge amplitude decide two concrete Petersen candidates

finding:petersen-source-current-and-hodge-candidates-fail-physical-identification

Original bilocal current a_r* a_s changes at most one occupied index and has zero matrix element on all30 directed Petersen edges of disjoint two-words. New natural candidate C_v=*(v wedge .),v=(1,...,1),matches disjointness support exactly,but C_v³=5C_v and chi=lambda^4(lambda²-5)^3. Six of twelve pentagons have negative flux;diagonal phase gauge or orientation does not yield A_Pet. This concerns linear operator equality. Born readout of squared moduli is a distinct specifically tested route and is not excluded merely by this sign result. Existing quartic fields and two-boundary state do not define marked Lambda²C5 compression with weights,compensating charge and time.

Scope: Only direct bilinear candidate and linear Hodge gauge identification excluded. C_v is not defined as physical operator in v474. No general exclusion of quantum probabilities,quartics,original source or E8. Existing Bell Petersen population process retained,not reinterpreted as source dictionary despite incompatible Sym²C4/Lambda²C5 representations.

Required premises and original source excerpts
  • Specified Petersen shells and full finite family recursion

    v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time.

    premise:specified-petersen-shell-and-full-family-finite-recursions
  • Original quarter CAR source with fixed fold and current dictionary

    The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.

    premise:original-quarter-car-fold-current-subalgebra
  • 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.

    premise:typed-source-structures

Established within the stated premises

Original eight-clock marks A7 and neutral E7 zero-root mode

finding:a7-clock-direction-identifies-neutral-e7-zero-root

With rho_A7=(7,5,3,1,-1,-3,-5,-7)/2 and q=(1,...,1),exactly delta=-rho_A7/8+(2a-1)q/16 and H8=8L0-rho_A7.a0+(2a-1)Q/2. p*=(++++----)/2=omega4(A7) has norm²2,Q0,rho.p*=8 and is unique neutral E8 root of H8 grade0. The126 neutral roots form E7(q/2),exactly56 A7 roots plus70 Lambda^4C8 weights. All240 roots and reflection closure checked exactly.

Scope: New joint interpretation of existing clock shift and already known charge census. No rediscovery of old ground doublet or D8/E8 Coxeter grading claim. Q is source U1,not automatically electromagnetic charge. p* is an E7 root,not E7 singlet. No time generator changed.

Required premises and original source excerpts
  • Four D8 source modules with fixed affine time

    Mathematical parent of the four D8*/D8 modules 0,v,s,c with eight identical Heisenberg oscillators, source charge chart p and N≥0. H=8(N+|p|²/2+delta.p),delta_j=(j+a)/8−1/2,0<a<1,Q=sum p_j. Original quarter cases are a1/4,3/4. Conformal L0, individual Cartan charges and totalQ remain distinct. This mathematical completion does not assume a physical P1 realization of the Ramond space or a local field map.

    premise:four-d8-sectors-with-fixed-affine-source-time
  • 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.

    premise:typed-source-structures

Established within the stated premises

Oriented sewing continuation and genuine reversal satisfy distinct exact compositions

finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal

alpha01=T,genuine reversal T^-1,continued positive quarter alpha10=beta0 T^-1. Hence alpha10 alpha01=beta0 and alpha01 alpha10=beta1,whereas forward/reverse yields1. Normalized central cocycle omega(1,1)=beta describes nonsplit1->C4->C8->C2 over mu4,with correct adjoint and defect-line dualization. Positive local spin quarter lift squares to+i independently of lift sign,matching marked q norm factor. Literal unextended D4 reflection s²=1 cannot map to alpha²=beta.

Scope: Marked spin transport and existing two-object vertex functor. Full open P1 amplitude functor,its determinant line and identification of U_Gamma with normal spin transport remain to derive. No identification of group orders or two-object set with physical spacetime.

Required premises and original source excerpts
  • Marked oriented quarter spin and two-object vertex transport

    Positively oriented marked quarter turn z->iz of normal two-plane with Spin(2) lift a=+/-exp(i pi/4),a²=i; existing genus2 source (C,S0,Dq,Q) and selected beta; existing lattice vertex objects F0,F1,unitary T:F0->F1 and beta1=T beta0 T^-1. Continued oriented quarter step and geometric reversal remain distinct arrows. An open P1 amplitude functor is not assumed.

    premise:marked-oriented-quarter-spin-and-two-object-vertex-transport
  • 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.

    premise:typed-source-structures

Excluded in the stated class

Natural single-face compression of Calderon projector is not Perron projector

finding:calderon-single-face-compression-is-not-perron-projector

For Pi=[[I-C,X],[X,C]],Pi is rank3 orthogonal projector on six-space. Natural single-face compression C has eigenvalues{1/2,4/13,1/10},hence rank3,not a projector and not rank1 Perron projector. I-C also has full rank. Seven rational checks establish counterexample to The reviewed proposed identification in natural finite comparison. Two actual The reviewed Opus4.8 consultations retained with corrections;The reviewed retracted five false time/state/grading claims of first round.

Scope: Exclusion of precisely specified single-face inclusion;not every source-derived invariant shell inclusion. Same formula2P-I or minus sign identifies neither spaces nor actions. The reviewed responses remain external proposals;no automatic proof acceptance or source-time change.

Required premises and original source excerpts
  • Natural single-face inclusion in the given family Calderon graph

    Given positive invertible M of v486/v487 family recursion;C=M²(I+M²)^-1,X=M(I+M²)^-1 and Pi=[[I-C,X],[X,C]] on doubled six-space. Tested inclusions are the two coordinate faces. No geometric P1 shell space or its embedding is thereby derived.

    premise:natural-single-face-inclusion-in-given-family-calderon-graph
  • Specified Petersen shells and full finite family recursion

    v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time.

    premise:specified-petersen-shell-and-full-family-finite-recursions
  • 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.

    premise:typed-source-structures

Non-scientific attribution omitted from public display.

Established within the stated premises

Hodge Born magnitudes and filtered Petersen jump block agree exactly

finding:hodge-born-magnitudes-and-filtered-petersen-jump-match

Entrywise |C_ef|²=A_Pet[e,f]. For x=cos(sqrt5 t),U(t)=exp(-itC) has exact population values p_diag=(2+3x)²/25,p_edge=(1-x²)/5,p_nonedge=(1-x)²/25. Thus no full U(t) population is pure Petersen transition. At t*=(pi/2+k pi)/sqrt5,added edge filter yields existing subnormalized jump block A_Pet/5 with probability3/5. Reject is4/25 at input plus1/25 at each of six nonneighbors,not old stay block2I/5. Conditioning on change gives A_Pet/3 in short-time limit. C/sqrt3 is not Kraus;C/sqrt5 has rank6 projector effect rather than3I/5 and superoperator rank36 versus actual J20 rank40. Six actual J20 phase matrices gauge to -A_Pet,not C.

Scope: New exact Born-magnitude bridge and conditional population matching. No equality of full instruments or P1 derivation of measurement basis,time,acceptance or reset rule. Linear sign obstruction explicitly does not imply general exclusion of quantum-probability derivation.

Required premises and original source excerpts
  • Oriented five-slot Hodge candidate with explicit basis readout

    Ordered orthonormal basis e0,...,e4,its volume form and v=sum e_i. On Lambda²C5 consider new mathematical candidate C=*(v wedge .). Conditional Born test explicitly sets two-words as measurement basis,U(t)=exp(-itC) as generator ansatz and input-label-dependent disjointness filter. These readout data and choice of C are not derived physical P1 rule.

    premise:oriented-five-slot-hodge-candidate-with-explicit-basis-readout
  • Specified Petersen shells and full finite family recursion

    v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time.

    premise:specified-petersen-shell-and-full-family-finite-recursions
  • 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.

    premise:typed-source-structures

Established within the stated premises

Five complement amplitudes give full Petersen quantum channel and SU5 response sectors

finding:five-complement-amplitudes-form-full-petersen-quantum-channel

C_m²=P_m of rank6,sum P_m=3I10. Phi=(1/3)sum Ad(C_m) is CPTP,unital,HS selfadjoint;population exactly A_Pet/3 without time or filter,Choi rank5 with eigenvalue2^5,superoperator rank100. Correct covariance connects10 and10bar. Actual24 is dGamma(sl5),Phi(dGamma A)=-(2/3)dGamma(A)^T. On End10=1+24+75,Phi²=Pi1+4/9 Pi24+1/9 Pi75,so Phi^6 spectrum1^1,(64/729)^24,(1/729)^75. Actual radial restriction on Petersen shells1,3,6 yields previously transported P. As specified channel,Phi has unique stationary density I10/10.

Scope: Previously excluded single coherent sum C_v remains excluded as Kraus normalization;five events change premise. Fermionic reduction channel is known mathematics;new result is concrete TFPT source/record/rate connection. Same three values identify neither all100 quantum directions with3D family space nor physical time or initial state.

Required premises and original source excerpts
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Specified Petersen shells and full finite family recursion

    v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time.

    premise:specified-petersen-shell-and-full-family-finite-recursions
  • 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.

    premise:typed-source-structures

Established within the stated premises

Original twenty events factor into Hodge outputs and conditional four-phase record

finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record

For each of6 marks,old20 jump events group into5 blocks of4 with Hodge effectP_m/3 and same basis movement. Exactly R_l=D_l C_m onP_m;relative to baselineD0,H_l=D_lD0* form projective K4 with3 characters each multiplicity2. Psi_m=(1/4)sum Ad(H_lD0) after Phi_m. New/old Choi ranks peroutcome1/3,total5/15;superoperator ranks100/40. All60 ordered intersecting-duad coherences permark distinguish channels. No common10-label diagonal gauge for all5 baselines:complete finite test0 solutions permark.

Scope: Outcome-dependent phase averaging before forgetting m,not one phase channel after coarsening. K4 is actual tested projective four-group,not automatically cyclic C4 clock. Proof in fixed event-label chart,without physical Bell10/Lambda²5 or SU5/native group identification. Classically merging20 outcomes does not restore lost coherences.

Required premises and original source excerpts
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Specified old J20 instrument in fixed six-mark duad chart

    Actual twenty jump events U_l(I-D_l) per mark from compiler-correlated-event-clock-20260919/source_channel.py;J20 effect3I/5,normalized jump channel Psi=(5/3)J20. Retain common duad labels of ten basis states. Comparison chart does not provide linear SU5/native group identification of Bell10=Sym²C4 with Lambda²C5 or already selected P1 apparatus.

    premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart
  • 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.

    premise:typed-source-structures

Established within the stated premises

Actual mixed E8 current response is full Clifford channel with retained carry

finding:actual-e8-mixed-current-response-is-full-clifford-channel

In D5+A3 frame:60 g2=(10,6) root brackets g1=(16,4)->g3=(16bar,4bar),gain15I64. All112 D8 root actions/3584 sign equations and all960 nonzero g2 columns match CAR in joint cocycle chart. Normalized response factors Q5 tensor Q3 with Q5=(1/5)sum(a rho a*+a* rho a),Q3 analog1/3. Reduced carrier theorem also holds for correlated input. Lambda² sends3/5 toLambda³ (Petersen A/5 after duality) and2/5 toLambda¹ as genuine carry. Full Fock population isQ5 cube,antipodal quotient already known Clebsch16 of v810.

Scope: No raw bitbasis partial trace:product phase gauge absent there;full group action must transport. No unconditional A/3 onLambda² and no old stay2I/5. Internal Clifford action on bosonic weight-one current states does not supply spacetime fermion fields. Actual P1 event/time selection from this reader remains open.

Required premises and original source excerpts
  • Given full E8 current source with fixed carrier SU5

    Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved.

    premise:given-full-e8-current-source-with-fixed-carrier-su5
  • Specified inclusive current response with invariant metric

    For an explicitly specified irreducible insertion sector and input/output modules,let B_a be actual current brackets in Killing-orthonormal basis. If sum B_a*B_a=kI,E(rho)=sum B_a rho B_a*/k denotes mathematical inclusive response with unread insertion index. Reduced response uses tensor chart transported by group action. This defines tested reader,not asserted selection of physically executed P1 instrument or original time.

    premise:specified-inclusive-current-response-with-invariant-metric
  • 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.

    premise:typed-source-structures

Established within the stated premises

Centralizer of given carrier SU5 supplies direct E8 Petersen quantum response

finding:carrier-su5-centralizer-gives-direct-e8-petersen-response

Fixed carrier A4 inside D5 has exactly20 centralizer roots in same E8 with derived A4 Cartan matrix. Four50 sectors give (5,10),(10,5bar),(10bar,5),(5bar,10bar). Actual bracket(5,10) tensor(10,5bar)->(10bar,5) has50 rank12 Kraus B_mab=C_m tensor A_ab. One joint cocycle chart satisfies600 bracket edges plus1500 neutral A4+A4 action edges,including fixed dual Hodge signs. Gain12I50,normalized response Phi_Petersen tensor WH5,WH5=(Tr sigma I-sigma^T)/4. For all correlated inputs,reduced carrier response is Phi,without3/5 conditioning. All600 original P2 X charges satisfy qout+qenv=qin with dual target and qenv=-X_m.

Scope: Closes algebraic origin of full Hodge/Petersen channel as mathematical inclusive response of same given E8 source. New50s are not old64s;family5 restricts to oldA3=4+1,not new physical generation count. Joint tensor chart instead of raw coordinate trace. Z5 center not automatically original C5/Galois/Coxeter/physical clock. P1 selection of exactly these50 insertions,their record,state and time iteration is not proved by bracket alone.

Required premises and original source excerpts
  • Given full E8 current source with fixed carrier SU5

    Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved.

    premise:given-full-e8-current-source-with-fixed-carrier-su5
  • Specified inclusive current response with invariant metric

    For an explicitly specified irreducible insertion sector and input/output modules,let B_a be actual current brackets in Killing-orthonormal basis. If sum B_a*B_a=kI,E(rho)=sum B_a rho B_a*/k denotes mathematical inclusive response with unread insertion index. Reduced response uses tensor chart transported by group action. This defines tested reader,not asserted selection of physically executed P1 instrument or original time.

    premise:specified-inclusive-current-response-with-invariant-metric
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • 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.

    premise:typed-source-structures

Established within the stated premises

Full SU5 covariance and Petersen support fix complete quantum response

finding:su5-covariance-and-petersen-support-fix-complete-quantum-response

Actual dual Choi representation splits multiplicity-free5+45+50 with explicit projectors. All25 gl5 actions,Casimirs24/5,64/5,84/5,and one highest-weight line per sector checked. All covariant CPTP Choi are sum p_d(10/d)P_d. Zero stay forces p50=0,zero intersect p45=0,hence T=Phi including phases. Within exact covariant class,total stay/intersect leaks s,o give p50=5s,p45=3o/2-9s/2 and exact diamond distance3o+s. SM plus actual carrier wedge fivecycle would generate full SU5.

Scope: Conditional complete channel classification at fixed carrier,not proof that P1 supplies full SU5 event covariance. General commutant method is known primary literature;concrete rigidity checked here. No physical time inferred from channel powers.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Specified full SU5 covariant channel with Petersen support

    H=Lambda²C5 in given oriented unitary duad basis,target dual H. T is CPTP and T(R rho R*)=barR T(rho)barR* for R=Lambda²U,U in SU5. Basis transitions to same or intersecting duads vanish. This is explicitly a mathematical conditional premise,not assumed physical P1 event covariance.

    premise:specified-conjugate-su5-covariant-petersen-channel

Established within the stated premises

Neutral joint process witness separates old events and Hodge response

finding:neutral-pair-witness-separates-old-events-and-hodge-response

P5=sum|C_m>><<C_m|/6 is rank5 and full SU5/SM invariant. Normalized Choi pPhi=1,pPsi=1/5 for all6 actual old marks. All single-leg marginals equalI10/10,joint neutral commutant restrictions differ. Old SU5 twirl weights exactly(1/5,2/5,2/5);twirl creates stay2/25,intersect38/75 rather than pure Petersen support and does not restore Phi.

Scope: In specified duad comparison. Bell10=Sym²C4 is not thereby SU5 module Lambda²C5;no physical P1 Choi preparation or admitted P5 measurement established. Image membership and reference separate.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Specified old J20 instrument in fixed six-mark duad chart

    Actual twenty jump events U_l(I-D_l) per mark from compiler-correlated-event-clock-20260919/source_channel.py;J20 effect3I/5,normalized jump channel Psi=(5/3)J20. Retain common duad labels of ten basis states. Comparison chart does not provide linear SU5/native group identification of Bell10=Sym²C4 with Lambda²C5 or already selected P1 apparatus.

    premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart
  • Specified full SU5 covariant channel with Petersen support

    H=Lambda²C5 in given oriented unitary duad basis,target dual H. T is CPTP and T(R rho R*)=barR T(rho)barR* for R=Lambda²U,U in SU5. Basis transitions to same or intersecting duads vanish. This is explicitly a mathematical conditional premise,not assumed physical P1 event covariance.

    premise:specified-conjugate-su5-covariant-petersen-channel

Established within the stated premises

Original degree clock is not slot cycle of same source

finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source

Original U5=exp(2pi iX/5) equals zeta5^3 I5 onV and zeta5 I10 onLambda²V. Its adjoint action generates no additional SU5 directions. Pure central phase lifts with same projective image do not change this. Actual slot cycle moves3+2 mark;nakedS5 differs from markedC_fin withAutC6. On actual50-root E8 insertion sector,W5 preserves roots/fixes familyA4 but Δh8=+1 on40,-4 on10;witnesses e1-e8→e2-e8 have grades1→2,independent of lift phase. Finite H8 kernel is not invariant under this slotcycle.

Scope: Only these explicit U5,W5 and given H8 insertion;no exclusion of noncentral monodromy,resolved C12/C48 or full TFPT. H8 not identified with physical OS time.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Fixed three plus two mark and typed original degree clock

    V=C5,P rank3 color projector,G_P=S(U3xU2),X=(-2,-2,-2,3,3),original U5=exp(2pi iX/5). Literal slot cycle c=(01234) is distinct and moves P. Covariant transport over Gr(3,5) concerns different marks,not full SU5 covariance within one fixed marked instrument. Continuous marks are not six old outer event marks or135 D8 frames.

    premise:fixed-three-plus-two-mark-and-typed-original-degree-clock
  • Given full E8 current source with fixed carrier SU5

    Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved.

    premise:given-full-e8-current-source-with-fixed-carrier-su5

Excluded in the stated class

Full mark transport and equal spectra do not select Hodge channel

finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel

For rank3P,U(P)=-I onCC,+I onCW/WW. T_P=Phi o AdU(P) is full SU5 covariant family overGr(3,5) with dual output,G_P covariant,same population/Choi rank5,but P5 value4/15. S_P=AdbarU(P) o Phi o AdU(P) likewise natural family;in adapted real chart real symmetric Kraus,unital,HS selfadjoint,same5 effects,Petersen population,full spectrum,unique fixedI10/10,but P5 value7/15. Powers similar,not identical. U(P) violates exterior-square phase relation,not carrier torus gauge. Full family covariance plus all listed criteria therefore insufficient.

Scope: Counterexample to selection rules in fixed dictionary;not asserted full E8 bracket automorphism,actual OS reflection,or classification of all merely SM covariant instruments. Does not prove fundamental gap is one-dimensional.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Fixed three plus two mark and typed original degree clock

    V=C5,P rank3 color projector,G_P=S(U3xU2),X=(-2,-2,-2,3,3),original U5=exp(2pi iX/5). Literal slot cycle c=(01234) is distinct and moves P. Covariant transport over Gr(3,5) concerns different marks,not full SU5 covariance within one fixed marked instrument. Continuous marks are not six old outer event marks or135 D8 frames.

    premise:fixed-three-plus-two-mark-and-typed-original-degree-clock

Established within the stated premises

Given two-boundary state does not determine selected epsilon event law

finding:original-pair-source-fixes-state-but-not-selected-epsilon-process

After typed embedding of dual two-hole legs,P5 on fixed sectors is even eight-field word;total contragredient P2 pair charge neutral,individual matrix units only particle-number neutral. Existing bilocal/vertex/GNS theorems transport word if actual local source map given. FullP_A fixes state/word expectations,not input-reference/Choi preparation or Kraus record. In givenE8_1 module,compact50-current Gram delta canonical(raw cocycle26+/24-),gain12 forces inclusiveTP normalization1/12. Using this reader as P1 event operation does not follow from Gram.

Scope: No new free field choice or reopening resolved source bridges. Specific local,time/reflection-compatible P1 embedding of A4+A4 sector and operational epsilon sewing identity remain required source derivation.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Given full E8 current source with fixed carrier SU5

    Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved.

    premise:given-full-e8-current-source-with-fixed-carrier-su5
  • Specified inclusive current response with invariant metric

    For an explicitly specified irreducible insertion sector and input/output modules,let B_a be actual current brackets in Killing-orthonormal basis. If sum B_a*B_a=kI,E(rho)=sum B_a rho B_a*/k denotes mathematical inclusive response with unread insertion index. Reduced response uses tensor chart transported by group action. This defines tested reader,not asserted selection of physically executed P1 instrument or original time.

    premise:specified-inclusive-current-response-with-invariant-metric
  • Original admissibility and graded-source interfaces

    v42 defines P_adm through primitive seam/Cauchy,gap,color and determinant conditions; v31 closure assumes an RP CAR kernel without identifying it with the old circle. v42 exp(W_k[J]) is a formal parent integral; spectral action, positive geometric marginal and full graded source are not equated. The separate eta term of the master functional is retained. Seek an original local image, not global Hilbert equivalence.

    premise:original-admissibility-and-graded-source-interfaces

Established within the stated premises

Single positive process saturation fixes full Hodge channel without SU5 premise

finding:single-positive-process-saturation-selects-full-hodge-channel

For arbitrary CPTP T:End10→End10bar,T=Phi iffTr(P5 J_T/10)=1. Positivity forces Choi support inP5,henceJ=VKV*,K≥0. Actual25 identities C_m*C_n=delta_mnI-dGamma(E_nm) giveTP Choi partialtrace A(K)=trK I-dGamma(K^T)=I. Coefficientrank25,unique rational solutionK=I5/3,henceJ=2P5. Full100directions/phases/Petersen population follow without assumed group or population rule. Shorter concrete source target isTr((I-P5)J_source)=0 with actualTP insertion.

Scope: Complete mathematical selector for unread channel,not derivation of process saturation fromP1. Actual source amplitude/input-reference required;P_A state purity no substitute. No unique observed instrument/pointer register or full physicalTFPT established.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index
  • Specified CPTP source process with positive P5 saturation

    In fixed dual H=Lambda²C5 dictionary,T is a CPTP channel with Choi J_T,trace10. Require Tr(P5 J_T/10)=1 for rank5 projector from epsilon amplitudes. Sufficient conditional contract,not already proved P1 premise or arbitrary P_A state expectation. No assumed fullSU5 covariance,Petersen population or observed Kraus register.

    premise:specified-cptp-source-process-with-p5-saturation

Established within the stated premises

Old five-slot wedge table is the exact E8 Hodge coefficient

finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient

Old architecture and v880/v888 already contain Lambda²E×Lambda²E→Lambda4E with all15 doily lines. Canonical volume character chi(m)=(-1)^m exactly gives epsilon(m,i,j,k,l)=chi(m)epsilon(i,j,k,l). All30 directed coefficients and sum C_m* C_m=3I match the checked A4×A4 E8 current bracket. Carrier tensor was not invented by later SU5 covariance.

Scope: Algebraic provenance closed. Original text explicitly leaves physical quadratic one-step exhaustion open. Read P1 net does not specify a concrete charged E8 insertion or inclusive50-current contraction; reflection and abstract Z4 Q-system do not automatically supply them.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index

Established within the stated premises

Native Pauli F20 and cyclotomic four match metrically with quarter lift

finding:native-pauli-f20-metric-and-quarter-bridge

Actual v783 words yield C_p=-i(I⊗H)CNOT(S⊗I)(H⊗I),G_p=(Y⊗Z)CNOT(I⊗S)(S⊗I),C_p^5=G_p^4=I and G_p C_p G_p^-1=C_p². Complete Pauli16×mu8 search at fixed C_p yields exactly four mu4-equivalent G corrections. Explicit four-intertwiner T to v419 satisfies both generator equations and T†T=2(5I-J),with dimension-one intertwiner space. G_p has conformal symplectic multiplier i; existing mu8 lift zeta8^-1G_p is symplectic order8. Quarter character makes Sym²4 and Lambda²Perm5 isomorphic F20 modules. Merely imposing F20 leaves ten-dimensional commutant M2(C)+C+C,dimension6.

Scope: Earlier reasoning was too narrow in conflating old noncentral v419 clock with separate scalar hypercharge U5. Available carrier subgroup and metric representation are now explicit. Original physical subgroup selection,full field dictionary and channel equality do not follow. Choi ranks15 and5 remain different.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Original Pauli and v419 F20 source words

    Use frozen v783 two-qubit Clifford generators, existing Pauli16 and central mu8, and actual cyclotomic v419 C5,G matrices. A constructed source-word F20 subgroup is available; its physical seam selection is not assumed.

    premise:original-native-pauli-and-v419-f20-source-words

Conditional result

Two actual coherent events herald Hodge at optimal1/25

finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five

In each fixed source-derived duad chart,the Hodge5 Kraus space intersects marked20 jump span in2D (15+5−18) and unmarked60 span in2D (55+5−58);hence no pPhi CP subchannel for p>0 after one step. Two-step products A=[vec(U2U1)] have rank100. Exactly V†(AA†)^-1V has three1/48 and two1/64 diagonal entries in these charts. CP order S/3600≥pVV†/3 gives exact pmax=1/25. Minimal coherent record contraction has three1 and two3/4 row-Gram eigenvalues and input-independent success map(1/25)Phi.

Scope: Changed premise grants coherent history access and active selection. Filter and Hodge target are chosen after a duad chart,not derived fromP1.1/25 is proved for these charts,not automatically for any subsequent metric F20/Spin5 transport. Classically read event labels are insufficient;no physical event-rate or vacuum proof.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Two actual events with coherent record access

    Compose the actual unmarked sixty-event source twice, preserving phases. Additionally grant coherent access to all 3600 ordered histories and an active heralded record contraction after fixing a Hodge dictionary. This resource and selection are not derived P1 dynamics.

    premise:two-actual-source-events-with-coherent-record-access
  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

    premise:given-five-slot-exterior-source-with-retained-complement-index

Established within the stated premises

Original color center removes the only extra H8 ground state

finding:original-color-center-removes-only-extra-h8-ground-state

Former second zero charge p*=(+,+,+,+,−,−,−,−)/2 maps under fixed Weyl M to e1+e4 in actual(3,2)_(1/6) carrier frame. It is neutral only under transported sourceU1,has colortriality1. Original P_sing=(1+Zc+Zc²)/3 kills it and retainsOmega;[H8,P_sing]=0 as Cartan actions. Full lattice classification gives full kernel{Omega,p*},center-neutral kernel C Omega. Exact H8 gaps3/2 foralpha1/4 and2 for3/4. Global nonroot bound from||delta||²85/128 proves completeness of240-root census for these gaps.

Scope: Precise scope correction to former double-ground obstruction:it remains on full gradedE8 field net but disappears on later center-neutral observable sector. P_sing is center-neutrality,not fullSU3 Haar projection. No established P1/OS identification or4D massgap.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Stipulated E8 H8 module with original color-center selector

    Retain stipulated E8 lattice extension with H8=8K_alpha,alpha=1/4 or3/4,actual rational Weyl dictionary M and original marked color center on first three carrier slots. Apply its P_sing after the carrier theorem. No intertwiner to the primitive P1/OS space is assumed.

    premise:stipulated-e8-h8-with-original-color-center-selector

Conditional result

Marked symplectic functor fixes native Hodge Kraus space

finding:marked-symplectic-functor-fixes-native-hodge-kraus-space

At fixed actual nativeF20 word pair and +i quarter orientation,the compatible alternating formOmega is unique up toscalar. W5=(Lambda²V/<Omega^-1>)⊗chi^-1 has positive metric,orthogonalq and compact real structureq conjugation. Canonical Spin5 map S→SOmega→L_S→L_Sq^-1 hasdet8,F†F=inducedSym²metric andHom_sp4 dimension1. It replaces merelyF20 U2×U1² ten-freedom by one phase line. OnW_R,K={x→*(w∧x)} is basis-independent5D,HS Gram6I andsumC†C=3I. ThusF defines a specific native Hodge candidate.

Scope: Full continuousSp4 naturality is mathematical property of category generated by markedOmega;v783 proves no such physical source symmetry. Original source must still select nativeF20 wordpair and quarter orientation. Source-conjugate wordpairs yield conjugateKraus spaces,distinct candidates in fixedBellchart. F20-labelled five-slot chart still has dimension-two Hom. No physical channel execution theorem.

Required premises and original source excerpts
  • 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.

    premise:typed-source-structures
  • Original Pauli and v419 F20 source words

    Use frozen v783 two-qubit Clifford generators, existing Pauli16 and central mu8, and actual cyclotomic v419 C5,G matrices. A constructed source-word F20 subgroup is available; its physical seam selection is not assumed.

    premise:original-native-pauli-and-v419-f20-source-words

Open questions preserve their achieved subresults

Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.

Future quotient and positive GNS reconstruction

What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?

  • Resolved in scope: Future quotient from complete rRead result
  • Resolved in scope: Conditional GNS reconstruction from supplied KRead result
  • open: Select complete K from the original source
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?

Seam connection and family action

Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?

  • Resolved in scope: Separate classes from actual transportRead result
  • open: Derive the common connection from the original source
Physical time and complete transfer

Do the original reflection/projector structures determine the full physical time generator and required field transfer?

  • Resolved in scope: Reuse the sign-projector counterexampleRead result
  • Resolved in scope: Reuse conditional full-transfer reconstructionRead result
  • open: Identify the physical complete TFPT transfer
  • Resolved in scope: Reuse complete collar reconstructionRead result
  • Resolved in scope: Classify homogeneous GKLS embedding of the shared register familyRead result
  • Resolved in scope: Decide every homogeneous GKSL logarithm of the fixed M4 channelRead result
Flavor ratio and absolute amplitude scale

Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?

  • Resolved in scope: Reuse the derived flavor ratioRead result
  • open: Determine the absolute holonomy amplitude
Alpha: derived terms, unique root and physical EM identification

Where do the factors and closed alpha equation come from, which provenance steps are proved, and which precise physical EM identification remains open?

  • Resolved in scope: Separate root calculation from source selectionRead result
  • open: Derive the actual EM functional variation and Thomson identification
  • Resolved in scope: Establish the unique global positive rootRead result
Geometric flow and gravity normalization

Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?

  • Resolved in scope: Record scope of fixed original functionalRead result
  • open: Derive geometric modular response and area coefficient
Clocks and complete neutral source response

Which complete quadratic response can the actual clock images reconstruct?

  • Resolved in scope: Reconstruct all neutral quadratic matrix directionsRead result
  • open: Derive physically admissible probe access
Clock action on charge, time and quarter transition

How does the actual Gaussian J act on the complete marked source?

  • Resolved in scope: Construct original J lift with complete time/charge actionRead result
  • open: Derive physical meaning of the frame orbit
Which responses distinguish charged time action?

Which data separate sources with identical complete neutral vacuum response?

  • Resolved in scope: Determine twist blindness completelyRead result
  • Resolved in scope: Reconstruct twist from charged responsesRead result
  • open: Derive actual charged source probes
Which seam action distinguishes native opposite charges?

Can existing native charge fields produce the quarter-twist time response of the seam?

  • Resolved in scope: Check native fields and response discriminatorRead result
  • open: Derive actual marked seam/state action
Constructive seam search: operators, state and source compatibility

What does the complete phase search decide, and which additional state information prevents a false source solution?

  • Resolved in scope: Finite search closed, actual winding and parity equivalenceRead result
  • Resolved in scope: Positive finite-word state extensionRead result
  • Resolved in scope: E8 current group conditionally determines the P signRead result
  • Resolved in scope: The same shift functional hides distinct ground statesRead result
  • Resolved in scope: No phase hit realizes the unchanged sourceRead result
Which partner actually belongs to the original seam?

Which charge, state type and time action belong to the root partner and original sheet pairing?

  • Resolved in scope: Concrete pair operator; source neutrality is not hypercharge neutralityRead result
  • Resolved in scope: Fixed quarter time splits the color/weak multipletRead result
  • Resolved in scope: Explicit conjugation for the existing sheet pairingRead result
  • Resolved in scope: Actual partner map between quarter domainsRead result
  • Resolved in scope: Bilinear sheet pairing is not Hermitian kernel selectionRead result
  • Resolved in scope: Actual quarter conjugation transports the supplied markingRead result
  • Resolved in scope: No time-stabilizing orthogonal repair of the fixed markingRead result
  • Resolved in scope: Spinor16 is a state sector, not a 16-real one-particle fieldRead result
Automated construction of operator maps and sources

Which tools generate operator maps, learn counterexamples, and can search for the full positive source?

  • Resolved in scope: Calibrate new search without supplying the target mapRead result
  • open: Synthesize a joint field, marking and transfer dictionary
  • open: Search for the positive common source kernel itself
  • Resolved in scope: Automatically construct, certify and distinguish finite kernelsRead result
  • Resolved in scope: Repair search conditions against source types and collar controlsRead result
  • Resolved in scope: Reconstruct multi-field sewing of the canonically identified boundary sourceRead result
  • Resolved in scope: Retain absolute reference amplitude in searchRead result
  • Resolved in scope: Integrate supplied free source including boundary response and scalarRead result
  • Resolved in scope: Convert the full finite CAR kernel into a link functionalRead result
  • Resolved in scope: Close original recursive word reconstruction with memoryRead resultRead result
  • Resolved in scope: Retain whole original caller through scale and readoutRead resultRead result
  • Resolved in scope: Execute actual shared Higgs source with full matter words and local RPRead resultRead result
  • Resolved in scope: Reduce whole constant original Higgs spectral fiberRead result
  • open: Resolve original geometric Higgs residue sign and field map
  • Resolved in scope: Evaluate local original Higgs heat identification and whole finite consumerRead resultRead result
  • Resolved in scope: Execute whole variable bound Higgs reference and original scale mapRead resultRead result
  • Resolved in scope: Execute whole inner Higgs scale/source and normal kernel transportRead resultRead result
  • Resolved in scope: Execute given whole superconnection and normal spectral readerRead resultRead result
  • Resolved in scope: Determine own-admissibility and whole total-chiral spectral readersRead resultRead result
  • Resolved in scope: Derive whole scale-energy map,normal profile and relative flowRead resultRead result
  • Resolved in scope: Execute original Green energy producer and mixed scale readoutRead resultRead result
  • Resolved in scope: Match current action argument and common Higgs/gravity weightsRead resultRead result
  • Resolved in scope: Execute whole original curvature consumers and Higgs radial sourceRead resultRead resultRead result
  • Resolved in scope: Execute original whole four-ghost source and geometric type testRead resultRead result
  • Resolved in scope: Execute original moving normal kernel derivative and whole source responseRead result
  • Resolved in scope: Decide fixed original O1 source and normal operator placementRead result
  • Resolved in scope: Compare whole Higgs mixture and covariance reader on invariant four-field witnessRead result
  • Resolved in scope: Test exact bounded cutoff on whole ordinary Higgs volumeRead result
  • Resolved in scope: Test whole original circle joint mode and IR Higgs normalizationRead result
  • Resolved in scope: Test original O1 mode covariance against whole Higgs-law classRead result
  • open: Reconstruct original localization from the whole process
  • Resolved in scope: Test bare native-code word compression against actual localityRead result
  • Resolved in scope: Decide original geometric local-time class and execute actual interval readerRead resultRead result
  • Resolved in scope: Execute actual regional two-face partner and supported charged wordRead resultRead result
  • Resolved in scope: Execute original color marginal, modular field law and complete class readerRead resultRead resultRead result
  • Resolved in scope: Reconstruct common Higgs law from whole original quarter source towerRead resultRead resultRead result
  • Resolved in scope: Execute original record action on Doily and ordered whole source responseRead resultRead resultRead resultRead result
  • Resolved in scope: Locally implement original record process and test unchanged exterior sourceRead resultRead resultRead result
  • Resolved in scope: Execute original elliptic insertion,whole source and causal responseRead resultRead resultRead result
  • Resolved in scope: Evaluate actual joint Higgs and color group sourceRead resultRead result
  • Resolved in scope: Execute whole original graph color reader with typed original center selectorRead resultRead result
  • Resolved in scope: Execute original color fixed source and first inherited grading testRead resultRead result
  • Resolved in scope: Execute actual original color-spinor CAR four-word and complete spin-sector sewingRead resultRead result
  • Resolved in scope: Decide actual color admissibility of density operations and coordinate regionsRead resultRead result
  • Resolved in scope: Execute actual whole seam-operation class and two-face responseRead resultRead result
  • Resolved in scope: Execute entire original C6 word expansion with source amplitudeRead resultRead result
  • Resolved in scope: Execute original collective Higgs force source and entire mean dualRead resultRead resultRead result
  • Resolved in scope: Execute original all-mode force with actual time and whole sourceRead resultRead result
  • Resolved in scope: Execute original local space/time force source and causal liftRead resultRead result
Origin reverse selection, field dictionary and original P1 kernel

What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?

Observable reality: minimal conditions and counterworlds

Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?

Formal carrier core: unbounded Pascal uniqueness and finite glue

Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?

  • Resolved in scope: Classify the unbounded Pascal proofRead result
  • Resolved in scope: Classify the formal finite glue scopeRead result
Active mathematical program: marked seam monodromies and lattice lifts

Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.

  • Resolved in scope: Define marked seam category and factor formulaRead result
  • Resolved in scope: Completely classify quarter-clock four-puncture liftsRead result
  • Resolved in scope: Determine central class and all subgroup restrictionsRead result
  • Resolved in scope: Determine full G0 cocycle and classRead result
  • Resolved in scope: Determine native4/5/6local cohomologyRead result
  • Resolved in scope: Classify unrestricted G31 reflection monodromiesRead resultRead result
  • Resolved in scope: Determine lift class beyond G0Read result
  • open: Classify additional reflection/clock equivariance and mapping-class quotients
  • Resolved in scope: Equivariant lifting and divisibility by eightRead result
  • Resolved in scope: All62clock obstructions and central transport variantsRead result
  • Resolved in scope: Actual group comparison and central pushout exclusionRead result
  • Resolved in scope: Complete invariants and explicit collisionsRead result
  • Resolved in scope: Compare E6 and E7 slices with the actual quarter clockRead resultRead resultRead resultRead result
  • Resolved in scope: Classify original character-valued G31monodromy liftsRead resultRead result
  • Resolved in scope: Determine E7-pair action on all original lattice fieldsRead result
  • Resolved in scope: Completely connect E6/E7 cuts to the original compilerRead result
  • Resolved in scope: Compare common covers and actual clock carriersRead result
  • Resolved in scope: Prove shared representation consequence for48,4/3 and5/4Read result
  • Resolved in scope: Completely decide joint compiler-field-cover constructionRead resultRead resultRead resultRead result
  • Resolved in scope: Reconstruct canonical local compiler field source from C4Read resultRead result
  • Resolved in scope: Eliminate redundant sector and multiplicity assumptionsRead result
  • Resolved in scope: Classify native equivariant markingsRead result
  • Resolved in scope: Classify pure quarter clock mapping class quotientRead result
  • Resolved in scope: Determine complete cut algebra and lossless tetrahedron transformRead resultRead resultRead resultRead result
  • Resolved in scope: Completely compare scalar glue and actual native compiler classRead resultRead resultRead resultRead result
Common clock sectors, quartic geometry and operational reconstruction

Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?

Automatic joint origin hypotheses and source responses

Which simple joint rules connect the existing P1 source chain,double cover,information and compiler,and which whole candidate classes can be decided automatically using actual source consequences?

  • Resolved in scope: Decide even-matter word class and check actual AI operator expressionsRead resultRead result
Existing TFPT derivations and correction of repeated gap diagnoses

Which common source/reconstruction chain already exists in the old original papers, and which purported global gaps arose from reducing P1 or choosing an optional CAR route?

Complete physical Hamiltonian source with Gauss sector and thermal word limit

Which whole source is constructed on the original local Hamiltonian route, how do physical constraints and thermal words follow, and how is its actual IR response distinguished from the original covariant geometric source branch?

Original TFPT source versus DET16 mirror vertex

Does the same original TFPT source produce the concrete DET16 generator and whole responses,or is a computable parent supplied as extra input?

Whole original source and canonical vacuum attachment

Which vacuum joins are already in the whole original source,and how do H ground source and R104 field/Gauss source join completely without second state choice or parent change?

Craig chiral measure and the original whole TFPT source

Which concrete operator and Berezin measure map preserves the original TFPT source when connecting Craig overlap measure?

  • open: Compare original4D fermion Hessian and measure line with Craig
Cyclic quantum universe and original Genesis connection

Does original TFPT dynamics yield the exact cyclic quantum return in the September/October press lead and a geometric Genesis transition?

  • open: Test periodicity and Genesis response on the same whole source
Physical constants as joint constraints on the TFPT source

Which independent constants constrain the original common source, and can one relative heat product supply gravity and vacuum energy together?

  • open: Evaluate original volume, curvature and gauge responses together