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The original technical record remains available here. For explanations, reviewed conclusions and the history of research questions, start with the knowledge atlas.

Research snapshot 2026-11-02 · 783 active ledger claims · 710 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.

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What does this inventory cover?

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 All 788 ledger rows, including superseded rows, remain in the download.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 711 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.

The scientific findings include 519 established scoped results, 63 conditional results and 128 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.

Atlas revision 2c1b559b738e5740ecfad8e6 · snapshot SHA256 68c2fe33ce86d45a99a8c21b1e731e40749d0accb3ae69be53d198cd7ebcb48e

107 matching records · page 6 of 6

Established within the stated premises

New feedback closes compatibility without a circular origin claim

finding:new-clock-feedback-origin-input-audit

The loop E8/J→ovoidH5→Pascal/glue→E8 already assumes E8,J and rank4. On C:y³=x⁴−1 the actual Prym clock gives SNF(I−J)=(1,1,2,2), four instead of16 classes; polarization(1,2) is degenerate mod2. V784/V796 exclusions and external bridges remain scoped.

Scope: Input audit of this route and curve; no universal P1 impossibility theorem or stale wrappers as evidence.

Required premises and original source excerpts
  • 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.

    premise:declared-p1-p2

Established within the stated premises

Marked glue square is the E8 fermionization character

finding:marked-glue-square-is-the-e8-fermionization-character

The marked Z4 glue character squared fixes grades0+2 with52+60=112 D8 roots and negates grades1+3 with64+64=128 spinor roots. At lattice level K union(K+2g)=D8. Thus the non-anomalous E8 to D8 Z2 action of standard fermionization is already in the original marked glue.

Scope: Exact charged-root action in the marked compiler frame. Does not identify geometric deck involution,CAR parity or gauging of a physical source.

Required premises and original source excerpts
  • Fixed marked glue and actual source D8 frame

    Retain marked K=D5+A3 in E8 with E8/K=Z4, original O frame and existing M of the one-channel CAR fold. The actual even source frame is D8_F=M(D8_CAR); no fitted new Weyl rotation. Cartans,time vector d=Mdelta,cocycles and field words transport together.

    premise:fixed-marked-glue-and-retained-source-d8-frame

Established within the stated premises

Split joint carrier admits a parallel representative of the whole native C12 clock

finding:global-split-joint-carrier-admits-parallel-native-c12-clock

For every natural m and given block U3xU2 connection,sigma0 from b=(1,1,1,0,0,0,0,1)/3 acts on W_m exactly as LambdaEven(diag(omega I3,I2)) tensor diag(omega,omega2,omega2,omega). It centralizes every transition and the entire induced connection. With central glue quarter kappa,c0=kappa sigma0 gives global parallel automorphisms with c0^9=kappa,c0^4=sigma0 and the complete native C12 character. The old complete torus Weyl theorem gives full inner VOA conjugacy including the common clock tuple. Exactly12 of243 thirds in the fixed toral centralizer match:two color orientations times six A3 vector weights.

Scope: Conditional mathematical closure for a GIVEN split connection,not selected from P1. Original marked chat is not automatically parallel on unchanged A_E;conjugator must transport connection and all marks or preserve them. An extra nonabelian family connection needs its own commutator,potential and closed domain their own invariance. Vertical bundle action identifies no base transport,time,CAR,state or EM response. Twelve counts marked torus points before further quotients,not physical sources. The2+2 action supplies no dictionary to original SU3 flavor on H1.

Required premises and original source excerpts
  • Existing natural joint lift with given split connection

    Assume a GIVEN unitary E=E3+E2 and GIVEN block U3xU2 connection A_E. Use only the natural iota_m with sum m=-2 completely classified on22September and their derived connection A_Wm=rho_LambdaEven(A_E)+M_m tr A_E. This does not select A_E from P1;an independent nonabelian family connection is not silently assumed.

    premise:natural-joint-spin-family-lift-with-given-split-connection
  • Fixed glue quarter and toral thirds centralizing the carrier split

    Fix the standard E8 Cartan,five plus three chart,three color and two weak indices and four family axes. Kappa=exp(2pi i v0),v0=(1/2^5,0^3). Study every sigma=exp(2pi i b/3),b in E8/3E8,centralizing the given U3xU2,and c=kappa sigma. This is a specified toral class of vertical bundle automorphisms,not an assumption about physical time or original base transport.

    premise:fixed-kappa-toral-third-centralizing-split-carrier
  • Full unitary E8 field conjugacy with transported marks

    Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.

    premise:full-unitary-e8-field-conjugacy-with-transported-marks
  • 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

Global Cartan choice is not an original scalar-source obligation

finding:global-cartan-choice-is-optional-for-original-scalar-source-fields

Original boundary data do not demand an everywhere smooth whole Cartan four. Normal geometry and flavor quotient have the same boundary-kernel origin;this supplies no actual base or bundle map. The class2 theorem remains an exclusion of the stronger Cartan choice. Any K-invariant classical polynomial value already glues across associated bundle transitions;an operator completion requires its own test. Current physical priority is corrected accordingly.

Scope: Source correction and elementary associated-bundle consequence. Does not contradict the preceding scoped Cartan theorem or identify Calderon reflection with elliptic deck.

Required premises and original source excerpts
  • Native Cartan four in whole conjugated source

    Given original Cartan h_C,H+=ker(J-i),and whole native clock chat with chat^9=Jhat,chat^4=sigmahat. Existing inner conjugacy transports the entire tuple and Cartan to kappa. H+ is not identified with SU4 family factor. In current W_m orientation,+i64 is its dual branch. No preferred conjugator is selected.

    premise:native-cartan-four-in-full-clock-conjugate-source
  • 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

Charged source quarter recovers inverse internal glue character

finding:charged-source-quarter-recovers-inverse-internal-glue

For actual given fold holonomy g_alpha=exp(2pi i Mmu_alpha.H), entire E8 lattice module satisfies g_alpha²=exp(2pi i alpha Qsource/4) Cint^-1. With c0=M(j/4)=(-1,0,2,-1,0,3/2,-1/2,-1/2) and v=(0^5,1/2^3), c0+v=(-1,0,2,-1,0,2,0,0) belongs toD8 subsetE8=E8*. Inverse is essential: C0 differs from Cint on all128 halfroots. For either quarter, U5 residue3 plus eigenvalue-1 of g_alpha² exp(-2pi i alpha Qsource/4) selects exactly creation30. Omitting charge factor leaves raw Ward-phase spaces of1 or11 directions, each with only one creation root.

Scope: Exact joint character identity on same marked source, no fitted extra clock or discarded charged phase. Lattice proof extends beyond complete240-root check. Closes this internal clock comparison; identifies neither affine winding, NS/R transition nor OS time. Actual local P1 use of filter remains part of Xi.

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 local E8_1 vacuum representation and explicit cocycle

    Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.

    premise:local-e8-current-response-realization
  • Given E8 fold with retained source charge and P2 grading

    Use the same explicit Weyl matrix M from v16-operator-pullback-20261014/fold-results.json, mu_alpha=(j+alpha q)/8 with q=(1)^8 and alpha=1/4 or3/4, Qsource=(Mq).H, and original P2 Cartan charge X=(-2,-2,-2,3,3,0,0,0). Given D5+A3 target frame and compact E8 current representation. Do not assume raw local P1 spinor-field map, executed spectral filter, new physical time or changed source phase.

    premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading

Established within the stated premises

Puncture meridians carry one glue class and residue duality does not select a metric

finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric

H1=Z4/Z1 and H^1=ker sum have a canonical index-four quotient Z4 through the marked counting construction. In the normalized realization meridians mi=ei−1/4·1 are A3* weights and their differences are A3 roots. m0 literally equals original v983 OMEGA_F and with the supplied D5 spinor gives its actual LAM. All four mi have the same discriminant class. Corner C4 acts trivially on A3*/A3, so its mark permutation is not glue-class translation. The four-by-four delta residue pairing on puncture loops in Architecture section011:32–45 conflicts with their zero sum; correct readers use zero-sum residues or I−J/4. This dual pairing alone selects no positive metric.

Scope: Integral marked topology and supplied original charge dictionary; no new selection of four punctures, physical clock or blanket exclusion of a different sector-changing field map. Metric normalization follows only under the separate joint-completion theorem. Original paper and ledger unchanged.

Required premises and original source excerpts
  • Given spinor-meridian extension with integral selfdual charge pairing

    Fixed additive L=(D5+A3)+Z((1/2)^5,m0), m0=e0−1/4·1 from four oriented puncture meridians, actual product W(D5)×C4 action, positive real symmetric invariant form and integral unimodular total charge pairing. Root lengths, carrier scale, orthogonality and evenness are not additional premises. These common completion data are not a physical source derived from P1.

    premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing

Established within the stated premises

Joint integral selfdual charge closure selects the entire invariant metric

finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric

On the fixed original additive spinor-meridian glue lattice the entire positive real W(D5)×C4 invariant metric has three parameters x,a,b: carrier xI5 and family a(P−vvT)+bvvT, P=I−J/4,v=(1,−1,1,−1)/2. W(D5) removes mixed blocks without assumed orthogonality. Integral root pairings force x,b,a+b and hence x,a,b to be positive integers. The original index four gives detL=x^5 a^2 b. Unimodularity forces exactly x=a=b=1. Carrier scale, orthogonality, root lengths and evenness are no longer extra premises in this class. An explicit A3→D3 map identifies the completed lattice with D8 union D8+(1/2)^8; evenness follows. The theorem covers the entire class analytically rather than by sampling. Thirty exact checks pass normally and with −OO; two independent analytic and full invariant-space reviews.

Scope: Conditional rigidity of charge completion. Fixed additive glue lattice, actual product symmetries, real charge metric and integral unimodular total pairing remain joint inputs. Does not derive their physical origin from P1, select a quarter source/state/time, or close3+1D or F1. Derived in this session with no claim of global mathematical novelty. E8 is not an additional premise of metric selection.

Required premises and original source excerpts
  • Given spinor-meridian extension with integral selfdual charge pairing

    Fixed additive L=(D5+A3)+Z((1/2)^5,m0), m0=e0−1/4·1 from four oriented puncture meridians, actual product W(D5)×C4 action, positive real symmetric invariant form and integral unimodular total charge pairing. Root lengths, carrier scale, orthogonality and evenness are not additional premises. These common completion data are not a physical source derived from P1.

    premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing

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 response search with original-source decision

Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?