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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 · 706 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 All 788 ledger rows, including superseded rows, remain in the download.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 707 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.

The scientific findings include 515 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 4d8fcdb3587f8e4cc0898e5c · snapshot SHA256 7c23438352ba021cef5aa0999c31e5c242fbc6ed12b172e4d35fb6a68f65dbb4

5 matching records · page 1 of 1

Original ledger status

GATE.METRIC.06

GATE.METRIC.06

CARRIER INDEX LEMMA [L] - the Gate-A theorem gets an equivalent index-theoretic form (sharper as a target): by Kawahigashi-Longo-Mueger (mu_A=[B:A]^2 mu_B; lattice nets mu=|discriminant|=det Cartan) the carrier inclusion has Jones index [(E8)_1:(D5)_1x(A3)_1]=sqrt(16/1)=4=|mu_4|=|Z2|^2 - the glue-group order IS the inclusion index. The extension is the mu_4 simple-current extension at level 1: adjoint branching 248=(45,1)+(1,15)+(16,4b)+(16b,4)+(10,6)=45+15+64+64+60; the three non-vacuum glue sectors are CURRENTS (h=1 exactly: 1/2+1/2, 5/8+3/8, 5/8+3/8); 1+3=4 sectors = the same Z4 glue as the lattice construction (v1). mu-additivity: an index-4 simple-current extension of the carrier has mu=16/16=1, so HOLOMORPHY FOLLOWS from the index statement - it need not be assumed. CONSEQUENCE: (H) 'seam-Calderon net holomorphic with c=8' <=> (H') 'seam net contains the carrier net with Jones index 4 as its mu_4 simple-current extension'. Why sharper: both ends of (H') are constructed objects (v77), finite index is controllable by Longo index theory, and the gap Delta_eff>0 (v76) supports finiteness. Negative control: mu(SO(16)_1)=4!=1 (v83/v87). Honest scope: the seam-side index computation is NOT done here; the boundary-net identification stays [P]/[A]

Recorded status: Lattice [L] (index arithmetic + reframing) + [P]/[A] (seam-side identification)

Dependencies, status detail and source

Canonical status: Lattice [L]: Gate A <=> index-4 mu_4 simple-current extension of the carrier net

Dependencies: GATE.METRIC.05; GATE.METRIC.04; E8.GLU.01; v77

Scripts: v89_carrier_index_lemma.py

Location: tfpt_5_redteam;tfpt_research_contracts

Original CSV, line 163

Original ledger status

CAR.QFREE.01

CAR.QFREE.01

ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise; anchors the carrier choice to the Gate-A objects): (1) MAJORANA BOOKKEEPING [I] - level-1 central charges c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 = N_fam, c(SO16)_1 = 120/15 = 8, c(E8)_1 = 248/31 = 8; the carrier net (D5)_1 x (A3)_1 = SO(10)_1 x SO(6)_1 = 10 + 6 = 16 FREE MAJORANA FERMIONS with c = 16/2 = 8; the whole extension tower carrier(mu=16) -> SO(16)_1(mu=4) -> E8_1(mu=1) carries the SAME 16 fermions, only the certified glue grows (index steps 2 x 2 = 4 = |mu_4|, GATE.METRIC.06/07). (2) WICK/PFAFFIAN [I] (exact, 10-Majorana Jordan-Wigner model): ALL 210 vacuum 4-point functions AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel - one kernel determines all correlations; quasi-freeness realised exactly. (3) THE KERNEL IS A CALDERON INVOLUTION OF RANK g [I]: M = I + iA with A integer antisymmetric, A^2 = -I; P = M/2 is a projection with rank P = 5 = g_car = c(D5)_1; eps = iA is an involution; at seam level (16 Majoranas) the rank is 8 = rank E8 - THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL (5 carrier block, 8 seam hull). (4) ONE KERNEL <=> ONE STATE [I]: the joint kernel of the five annihilators is exactly 1-dimensional - the polarization fixes the vacuum uniquely; kernel => state => (Wick) all correlations. (5) PREMISE MERGE [P] (recorded, not claimed): QBL's remaining input 'single scalar 2-point kernel' = 'the seam state is quasi-free' = the defining property of the free-fermion net the R2 gate already posits (Gate-A (H') index-4 extension, GATE.METRIC.06); QBL adds NO assumption beyond R2; upgrade contract: R2 closes => the carrier choice closes [L] along free net => one kernel => sheet-odd (CAR.PAIR.02) => self-counting tower (CAR.PAIR.01/CAR.COUNT.01) => complete transport (CAR.QTRANS.01) => carrier; gate typing [P]/[A] unchanged

Recorded status: Identity [I] (exact Pfaffian/Wick + polarization theorems + bookkeeping) + Physical [P] (premise merge)

Dependencies, status detail and source

Canonical status: Identity: one quasi-free kernel determines the whole net (rank = c); QBL input = R2 premise; upgrade contract R2 => carrier [L]

Dependencies: CAR.PAIR.02; CAR.COUNT.01; CAR.QTRANS.01; ARCH.QUAD.01 (QBL); GATE.METRIC.03-07 (Gate A); CAR.LADDER.01

Scripts: v113_quasifree_kernel.py

Location: tfpt_1; tfpt_research_contracts

Original CSV, line 197

Original ledger status

SYNTH.INVENTORY.02

SYNTH.INVENTORY.02

RESIDUAL INVENTORY UPDATED (post v110-v122; supersedes the CONTENTS of SYNTH.INVENTORY.01 while keeping its cardinality): (1) thirteen new ledger rows machine-pinned (CAR.PAIR.02, CAR.QTRANS.01, CAR.COUNT.01, CAR.QFREE.01, GATE.UWALL.06-09, FLAV.H2.02-05, ARCH.TRIAD.01). (2) R2 CARRIES THREE LOADS: the single index-4 boundary-net statement closes, when proven, the metric gate (GATE.METRIC.06), the carrier choice (CAR.QFREE.01 upgrade contract) and the QBL programme (ARCH.QUAD.01) - one theorem, three doors. (3) UPDATED RESIDUAL TABLE, exactly FIVE structural classes: R1 seam quantum clock (produce the bend log_{3/2}3 at coupling ~1/3pi) [P]; R2 index-4 seam net (3 loads) [P]/[A]; R3 seam determinant => EH [A]; R4' SELECTOR ESTABLISHMENT (derive n = (5,-9,6) + the diamond determinants from the parabolic geometry; replaces the DISCHARGED 'H2 dictionary' class) [A]/[P]; R5 parabolic realisation of Q (GATE.QGEO; carries P1) [P] - plus the two irreducibles (v_geo, pi) and the frozen data surfaces; a sixth structural class would FAIL the script. (4) THE FLAVOR SIDE HAS NO OPEN ANALYSIS CLASS OF ITS OWN: H2 values exact (FLAV.H2.02), addresses pinned (FLAV.H2.04), margins theorems (FLAV.H2.05); residue = five frozen selector integers. Ledger-bookkeeping module, Python-only by nature

Recorded status: Identity [I] (machine bookkeeping + typing contract)

Dependencies, status detail and source

Canonical status: Inventory: five classes re-pinned (R1 clock; R2 index-4 net with 3 loads; R3 EH; R4' selectors; R5 Q); flavor side discharged; sixth class fails the script

Dependencies: SYNTH.INVENTORY.01; GATE.METRIC.06; CAR.QFREE.01; ARCH.QUAD.01; FLAV.H2.05; HOR.CLOCK.02; GATE.QGEO

Scripts: v123_inventory_update.py

Location: origin_theory; introduction

Original CSV, line 207

Original ledger status

GATE.METRIC.08

GATE.METRIC.08

THE GLUE Q-SYSTEM (the index-4 mu4 extension exists as an explicit Longo Q-system; the R2 gate sharpens from 'find a Q-system' to 'match the constructed one'): (1) Q-SYSTEM AXIOMS [I] on A = C[Z4] (the glue group algebra; multiplication delta_a x delta_b -> delta_{a+b}, unit delta_0): associativity, unit law, FROBENIUS (m x 1)(1 x m*) = m* m = (1 x m)(m* x 1), and SPECIALNESS m m* = |Z4| id all hold exactly => a special C* Frobenius algebra = a Longo Q-system with dim theta = 4: JONES INDEX [B:A] = 4 = |mu_4| - exactly the GATE.METRIC.06 Carrier Index Lemma value; KLM bookkeeping mu_carrier = 16 = 4^2 x mu_E8 re-verified. (2) LOCALITY = ISOTROPY [I] (GATE.METRIC.07 re-derived in Q-system language): on the Lagrangian glue <(1,1)> the discriminant form q = (5x^2+3y^2)/8 gives q(k(1,1)) = k^2 = (0,1,4,9), all integers - the Q-system braiding obstruction vanishes (local/bosonic extension); the two Lagrangian glues = the sheet pair are the only maximal isotropic choices. (3) THE HALFWAY SUB-Q-SYSTEM [I]: {0,2} < Z4 closes multiplicatively => the unique intermediate Q-system C[Z2] = the SO(16)_1 step of the tower (GATE.METRIC.07/CAR.QFREE.01), index factorisation 4 = 2 x 2. (4) R2 SHARPENED [P] (recorded, not claimed): the gate's algebraic object now EXISTS explicitly; what remains is the operator-algebraic IDENTIFICATION 'the seam-Calderon inclusion of the 16-Majorana net realises THIS Q-system' - matching two constructed objects, not a search; the three loads (metric + carrier + QBL, SYNTH.INVENTORY.02) hang on this one identification; gate typing [P]/[A] unchanged [2026-08-03 LIII: the index side is now MEASURED on the CAR ladder (v726, 57/57, GNET.PPINDEX.01): the mu4-average expectation has optimal Pimsner-Popa constant EXACTLY 1/4 and Watatani index EXACTLY 4 via an explicit quasi-basis with FORCED weights, with mu4 DERIVED from the clock (not inserted) and the Ramond sector healed state-preservingly by the v679 Klein dressing; the remaining half of the gate is the IDENTIFICATION of this ladder Q-system with the constructed GATE.METRIC.08 object -- registered as the open contract half of GNET.RAMIFIED.01 (kills: Frobenius mismatch, index != 4 on the state-preserving ladder, dressing incompatible with the sigma descent). No status move.] [2026-08-05 LXII (v779): the finite precursor of the R2 identification is measured -- the coherent COMMUTING system of index-4 expectations along the Haar tower (restriction coherence, [E_I, E_J] = 0, joint idempotency, all exact) is the finite half of the Longo Q-system identification, and the exact dim law d_c(l) = 4^(l-1) + 2^(l-1) cos(pi c/2) makes the 4-element C[Z4] group-layer quasi-basis obstruction exactly 2^-l at every finite level (d_0 - d_2 = 2^l > 0), restored only asymptotically -- the crossed-product structure is exactly asymptotic; d_2(1) = 0 IS the l = 1 index-3 anomaly. No status move.]

Recorded status: Identity [I] (exact finite Frobenius/Q-system axioms + isotropy) + Physical [P] (identification)

Dependencies, status detail and source

Canonical status: Identity: C[Z4] is a special Frobenius algebra (Longo Q-system) of index 4 = |mu4|; locality = isotropy; halfway C[Z2] = SO(16)_1; R2 = identification of constructed objects

Dependencies: GATE.METRIC.06; GATE.METRIC.07; CAR.QFREE.01; SYNTH.INVENTORY.02 (R2)

Scripts: v125_glue_qsystem.py

Location: tfpt_research_contracts

Original CSV, line 210

Original ledger status

E8.GRADE.01

E8.GRADE.01

THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations gain their structural anchors): R2 HALF - (1) EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots, built as explicit norm-2 vectors in D5 (+) A3 + glue coordinates, decompose over the glue group Z4 as 240 = 52 + 64 + 60 + 64 (C0 = carrier roots 40+12; C1 = (16, 4bar) from norm 5/4 + 3/4; C2 = (10, 6) from 1 + 1; C3 = (16bar, 4)) - exactly the GATE.METRIC.06 branching, now as vectors. (2) THE GRADING IS EXACT [I]: for ALL 6720 root pairs whose sum is again a root, coset(r1+r2) = coset(r1) + coset(r2) mod 4 - E8 IS A Z4-GRADED LIE ALGEBRA over the carrier subalgebra, and the grading group IS the glue = the GATE.METRIC.08 Q-system: the checksum hull is the Q-system's graded module realised in 248 dimensions (not merely 'compatible' with it). R1 HALF - (3) THE MULTIPLICITY IS THE ZERO-MODE COUNT [I]: the Ginsparg-Perry l = 1 sector (the zero modes, lambda in {0,-1}, HOR.CLOCK.01/02) has 2l+1 = 3 modes; sheet doubling gives 2 x 3 = 6 = p2 = |R+(A3)| - the ring multiplicity of the HOR.CLOCK.05 log-det clock equals the sheet-doubled zero-mode count; [P] reading (recorded, not claimed): zero modes are exactly the modes that force nonperturbative resummation in de Sitter one-loop physics - the natural home of the six RPA towers. (4) RESIDUE [P]: R1 = compute the RPA determinant on the six sheet-doubled l=1 zero modes; R2 = identify the seam-Calderon inclusion with the Z4-graded structure now exhibited inside E8 itself

Recorded status: Identity [I] (explicit construction + exact grading + arithmetic) + Physical [P] (anchors)

Dependencies, status detail and source

Canonical status: Identity: E8 = Z4-graded Lie algebra over the carrier (grading = glue Q-system; 6720 pair checks); ring multiplicity 6 = sheet-doubled GP zero modes

Dependencies: GATE.METRIC.08; GATE.METRIC.06; HOR.CLOCK.05; HOR.CLOCK.01; E8.GLU.01

Scripts: v128_graded_hull.py

Location: tfpt_research_contracts; tfpt_horizon_readouts

Original CSV, line 213

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 closure for fixed inputs

Which closure equation follows for a fixed seam projector, and which inputs still need justification?

  • Resolved in scope: Separate root calculation from source selectionRead result
  • open: Derive alpha inputs and Thomson transfer
  • 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?