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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 All 788 ledger rows, including superseded rows, remain in the download.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

7 matching records · page 1 of 1

Original ledger status

AX.P1.01

AX.P1.01

c3 = 1/(8 pi) boundary seam kernel -- a DECLARED input but NOT a free knob: it reduces to the parabolic anchor a=(1,1,2) via c3 = 1/(2 e1(a) pi) = 1/(8pi) (e1(a)=4=|mu4|; ANCHOR.GEN.01/v23), and the '8' is the one-sided Gauss-Bonnet of the seam normal slice (|Z2|*2pi*chi(S^2)=8pi, chi=2; v58/v73). On the dimensionless axis the ONLY transcendental primitive is pi (ARCH.CORE.01/v53); {c3,g_car} reduce to {a, pi} SYNTHESIS NOTE (2026-08-28, v993 -- marker Axiom UNCHANGED): the mu4 average E = (1/4) sum_r Ad(u^r) is the UNIQUE trace-preserving finite conditional expectation onto the clock-fixed algebra (uniqueness needs the module property; kernel dim 36/720 without it); the arithmetic 1/(4 * 2 pi) = c3 is the v484/v813 identity (not a new derivation of P1). The equidistribution identification (modular det-line response even over the four deck sectors) stays the open [C] of v813. Axiom typing UNCHANGED.

Recorded status: Axiom (declared input; reduces to the anchor a=(1,1,2)+pi)

Dependencies, status detail and source

Canonical status: Axiom (declared) but anchor-reducible: c3=1/(2 e1(a) pi); only pi is the dimensionless primitive | 2026-08-28 v993: unique finite CE + 1/(4*2pi) arithmetic shadow; equidistribution stays [C] of v813; axiom typing UNCHANGED WAVE-5 (2026-08-29): SEAM.MMST.TYPEIII.CHARGED.01 reads P1 as theorem-conditional on seam identification + beta_angle=2pi (KLM + Longo-Tanimoto GIVEN identification); axiom typing UNCHANGED.

Dependencies: ANCHOR.GEN.01; ARCH.CORE.01; v993

Scripts: See original ledger entry

Location: tfpt_1

Original CSV, line 2

Original ledger status

AX.P2.01

AX.P2.01

g_car = 5 carrier interface (3+2) -- a DECLARED input but an OVER-DETERMINED bootstrap fixed point, not a free choice: forced three independent ways by the E8 closure (bootstrap mu^2-5mu+4=0, BOOT.01/v6), uniquely solved by the Pascal carrier condition 2^g=g^2+g+2 => g=5 (Lean-formalised, no sorry; FORM.LADDER.01), and the (g_car,N_fam)=(5,3) pair is the anchor moment data e2(a)=g_car (ARCH.CORE.01/v53; a=(1,1,2) the unique multiset with elem-symm (4,5,2)). Reduces with P1 to {a, pi}. SYNTHESIS NOTE (reduction state 2026-07-21; text consolidation, marker Axiom UNCHANGED): P1 + the four marks are [E]-anchored (v216); given the marks, g_car = 5 follows via the partition 4 = 2+1+1 plus the Deligne/Birkhoff-Grothendieck/stability typing (v491/v499, residual R1 [C]); the clock order, the Z8 tower, the deck class and the position half of the alignment bit are theorems (v506/v507/v510) -- the compiler's dimensionless inputs reduce to: four marks (derived from P1-side topology), ONE square-modulus datum (tau = i, equivalently: the clock / the CM-fixed half-period / the non-split extension class on the free seam circle / the flag-transitivity bit V4 -> D4, v512), and pi, plus the [C] identifications R1/R2 of v499. SYNTHESIS NOTE (2026-07-22, v512 -- marker UNCHANGED): the reduction state can equivalently be written 'four marks + one discrete symmetry-lift bit (flag transitivity <=> tau = i) + pi'. This describes the REDUCTION STATE; the axiom stays declared and QGEO.REALIZE.01 stays [C]/[O] [2026-08-02 XXXIX: the four-mark closure lands -- v624: under the D_{d+1}+A_{d-1} glue architecture three independent selectors (disc-group census, even-glue norm equation, Pythagorean (3,4,5)) force d = 4, with (1,1,2) the unique 3-part partition and c_3 = 1/(8 pi): the two-input presentation reduces to ONE boundary degree d = 4 plus pi, CONDITIONAL on the architecture; the axiom keeps its typing -- the residue moves to why the physical boundary realizes the minimal cyclically-glueable genus-0 divisor; see EXTREV.LATTICE.01.] SYNTHESIS NOTE (2026-08-28, v993 -- marker Axiom UNCHANGED): the architecture conditionality of v624 is lifted at the census level -- the FULL rank-8 ADE pair census with cyclic Z4 glue on BOTH factors selects (D5, A3) uniquely (D3 ≅ A3 aliases collapsed), so the D+A split is an OUTPUT of (rank 8 + cyclic Z4), not an INPUT. Cited-not-proved remain c_- = 8 and holomorphic uniqueness of (E8)_1. Axiom typing UNCHANGED. WAVE-6 (2026-08-30, v1005): relative pencil identities exact but CIRCULARITY-FLAGGED -- carrier 5 already sits in the column sums of Q_2 and C; NOT a P2 selector until Q, C, epsilon are derived from seam geometry independently. Axiom typing UNCHANGED. LATE EVENING (2026-08-30, v1014): W-bridge premise P-anch DERIVED (anchor chain: e1 = R^{-1}(1,1,2)^T uniquely via the winding/triple lock); P-dem narrowed to the character-blind determinant-response map -- same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. Axiom typing UNCHANGED. MONDAY MORNING (2026-08-31, v1015): BOTH W-bridge premises now derived at finite level -- P-anch already (v1014 winding/triple lock); P-dem DERIVED (character-blind determinant response r=(1,1,1) exactly at collar sizes 12 and 16, democracy residual 0; mutants split (1,0,0) and (5/4,1,5/4)). The axiom-core remainder is ZERO modulo the externalized MMST identification. Axiom typing UNCHANGED (the finite derivations are shadows; the continuum identification is the same external leg).

Recorded status: Axiom (declared input; over-determined bootstrap fixed point, Lean-forced)

Dependencies, status detail and source

Canonical status: Axiom (declared) but bootstrap-forced (3 ways) + Pascal-unique (Lean): g=5 is not a free knob; reduction state 2026-07-22: four marks + one discrete symmetry-lift bit (flag transitivity <=> tau = i) + pi (v491/v499/v506/v507/v510/v512), marker unchanged | 2026-08-28 v993: v624 architecture conditionality lifted at the census level (D5, A3 unique in full rank-8 ADE); axiom typing UNCHANGED | WAVE-6 (2026-08-30 v1005): pencil circularity-flagged (5 already in Q_2/C column sums); NOT a P2 selector; axiom typing UNCHANGED | AFTERNOON (2026-08-30 v1010): pencil selector rehabilitated: column sums forced by prior constructions (ladder c=2 + n=3 force Q sums (9,5,1); C's 5 inherited from R col 3 -- non-circular); W-shift conditionally unique given democratic-image + carrier-anchor-kernel (1078 -> 1); remaining obligation = seam-geometric derivation of those premises; axiom typing UNCHANGED | LATE EVENING (2026-08-30 v1014): W-bridge premise P-anch derived (anchor chain); P-dem narrowed to the character-blind determinant-response map -- same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. Axiom typing UNCHANGED. | MONDAY MORNING (2026-08-31 v1015): BOTH W-bridge premises derived at finite level (P-anch v1014; P-dem r=(1,1,1)); remainder 0 modulo MMST. Axiom typing UNCHANGED.

Dependencies: BOOT.01; ARCH.CORE.01; v491; v499; v510; v512; v993

Scripts: v1005_relative_pencil_bridges.py, v1010_simplicity_bridge_census.py, v1014_bridge_refinements.py, v1015_axiom_core_closure.py

Location: tfpt_1

Original CSV, line 3

Original ledger status

ARCH.CORE.01

ARCH.CORE.01

Compiler core - the whole integer skeleton from one pair (g_car,N_fam)=(5,3): rank E8=g+n=8 (D5(+)A3 rank split), |Z2|=g-n=2 (carrier-family), |mu4|=(g+n)/2=4; (N_fam,|mu4|,g_car)=(3,4,5) is THE Pythagorean triple. NOT decorative: grand-mass-volume exponent Delta_Y=g_car^2=25 (det M_SM~phi0^25) splits as a DIFFERENCE OF SQUARES Delta_Y=g^2=N_fam^2 + (g-n)(g+n)=N_fam^2+|Z2|*rank(E8)=9+16=dim S+, i.e. down sector=N_fam^2, up+lepton=|Z2|*rank E8=dim S+ (K-row sums (6,9,10)). ANCHOR is the Dirac square root: a=(1,1,2) is the UNIQUE 3-multiset (0..6) with elem-symm (|mu4|,g_car,|Z2|)=(4,5,2); char poly chi_a(t)=(t-1)^2(t-2)=t^3-|mu4|t^2+g_car t-|Z2| => compiler atoms ARE its char-poly coefficients. Only transcendental is pi (c3=1/(8pi), 8=rank E8; seed 1/(6pi), 6=|R+A3|). New READINGS/syntheses of v23/v37/v46/v47 atoms [I]

Recorded status: Identity [I]

Dependencies, status detail and source

Canonical status: Identity [I]

Dependencies: FLAV.MASSVOL.01; v23; v47; BND.GLUE.01

Scripts: v53_compiler_core.py

Location: tfpt_1

Original CSV, line 136

Original ledger status

HOR.NARIAI.01

HOR.NARIAI.01

THE MAXIMAL BLACK HOLE IS THE ANCHOR (carrier-in-the-bulk surface; Schwarzschild-de Sitter in seam units): (1) NARIAI = ANCHOR - at M_N = 1/(N_fam sqrt(L)) the horizon cubic is t^3-3t+2 = (t-1)^2(t+2), roots (1,1,-2) = the traceless projection of the anchor a=(1,1,2) (coefficients (-3,2) = (-N_fam,|Z2|); cf chi_a = (t-1)^2(t-2), ARCH.CORE.01). (2) the Koide 2/3 IS the Nariai entropy bound: S/horizon = S_dS/N_fam, total = (|Z2|/N_fam) S_dS, deficit S_dS/3; interpolation S_tot/S_dS = (x^2+1)/Phi_3(x), monotone, min at the merge. (3) three-sheet conservation pi sum r_i^2 = |Z2| S_dS for every M. (4) Koide-form quotient of the three roots ranges [3/8,1/2] = the two nonzero SU(4)_1 weights (pure dS -> 1/2 = delta; Nariai -> 3/8 = p2(a)/e1(a)^2). (5) mass-line double cover disc ~ (1-3m)(1+3m): branch +-1/N_fam, separation 2/3; deck = horizon swap (gravitational twin of the sheet Z2). (6) temperature lemma |kappa_b/kappa_c| = (2x+1)/(x(x+2)) > 1: evaporation flows AWAY from the merge - anchor point = repeller, democratic endpoint = attractor (same orientation as the flavor flow, FR.KOIDE.04) [audit]. (7) seam-unit mechanics: dM = c3 kappa dA, Smarr 2c3, Bekenstein 1/(4c3), P_H = c3/(1920 M^2) (=|W(D5)|, HOR.01), lifetime 5120 pi M^3 = 128 g_car M^3/c3 (128 = 2^7 = dS prefactor), Kerr A_ext = M^2/c3 (ratio 1/2 = 1/|Z2|, S_ext: 1/4 = 1/|mu4|), area quantum 4 ln3 = ln(N_fam^4) = ln(disc of the flavor cover) [P as HOR.QNM]. Six independent landings on already-load-bearing atoms, zero free parameters; lifetime/power normalisations are standard photon/geometric-optics conventions (external); carrier-in-the-bulk reading [P]; structure surface, not a measurement surface (M_N today ~1e22 M_sun)

Recorded status: Identity [I] (exact GR arithmetic on compiler atoms) + Physical [P] (bulk reading)

Dependencies, status detail and source

Canonical status: Identity: six atom landings in SdS mechanics; bulk reading [P]

Dependencies: AX.P1.01; ARCH.CORE.01 (anchor); FLAV.PENCIL.03 (cover); FR.KOIDE.04 (orientation); HOR.01; GATE.METRIC.07 (SU(4)_1 weights)

Scripts: v101_horizon_anchor.py

Location: tfpt_horizon_readouts;origin_theory;tfpt_2

Original CSV, line 184

Original ledger status

WITNESS.ECON.01

WITNESS.ECON.01

WITNESS-INDEPENDENCE / GENERATOR-ECONOMY AUDIT (2026-06-21): the STRUCTURAL anti-numerology firewall complementing the v100 phenomenological null test. [E] GENERATOR ECONOMY: 13 headline integers (|mu4|=4, g_car=5, |Z2|=2, N_fam=3, dim S+=16, rank E8=8, |R(E8)|=240, dim E8=248, |2I|=120, h(E8)=30, |W(D5)|=1920, Omega_adm=48, gap exponent 6) are all documented images of the single anchor a=(1,1,2) (e=(4,5,2), p_n=2+2^n; v23/v228), with pi the only transcendental primitive (ARCH.CORE.01) => 13 atoms / 2 free primitives = 6.5x compression made EXPLICIT; the recurring 2/3=|Z2|/N_fam and (2/3)^6 are ONE ratio, not many. [E] WITNESS INDEPENDENCE: E8, g_car and the anchor are overdetermined (>=3 structurally distinct derivations sharing only leaf inputs: v1/v15/v77+v92; v2/RR/reverse-glue), while the 5 pure-seed readouts (theta12/theta13/beta/Omega_b/lambda_C) are single-witness (multiplicity 1) = correlated, NOT 5 independent confirmations. [E] CORRELATION HONESTY: the 9 phi0-sharing scorecard observables must be scored JOINTLY (v100 fixes phi0 in MC-A), never as p^9. [E] NEG/POWER: alpha^-1's '137' is foreign to the anchor family (prime; no e_k/p_n/product) = an INDEPENDENT witness (F_U1 cubic, v3), and foreign integers stay un-generated (the map discriminates). Structural bookkeeping that quantifies the compression and correlation so neither masquerades as independent evidence; NOT a new physical claim and NOT a proof the anchor is forced (P2/v23/v228).

Recorded status: Identity/Numerical [I]/[N] (structural firewall)

Dependencies, status detail and source

Canonical status: [I]/[N] the generator-economy images + the 6.5x compression ratio + the witness-multiplicity bookkeeping + the shared-seed correlation map + the foreign-integer negative control. Makes the compression and correlation explicit; does NOT add physics and does NOT upgrade any status.

Dependencies: ANCHOR.GEN.01; REG.FREEZE.01; DATA.SCORECARD.01

Scripts: v305_witness_independence.py

Location: tfpt_5_redteam

Original CSV, line 401

Original ledger status

ARITH.CAPSTONE.01

ARITH.CAPSTONE.01

THE CAPSTONE: THE SM STRUCTURAL SECTOR IS Q(zeta30) + GALOIS mu4 x Z2, COMPLETE INPUT {a, pi, v_geo} (2026-06-21, synthesis of the v313-v317 arc). [E] ARITHMETIC SKELETON: the SM STRUCTURAL sector (3 generations, 2 CP phases, the orbit/hierarchy ordering) lives in the cyclotomic field Q(zeta30): [Q(zeta30):Q]=phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=h(E8), Galois (Z/30)^x=mu4 x Z2 (order 8) -- carrier mu4=(Z/5)^x (golden sqrt5, v313/v315), family/sheet Z2=(Z/3)^x (zeta3=CP conjugation, v316); the 3 generations = the mu3 cube-root orbit (v317), the 2 CP phases = the zeta6 family-factor data (v316). [E] RIGIDITY: forced by the anchor atoms {|Z2|,N_fam,g_car}={2,3,5}=elementary-symmetric data of a=(1,1,2); 30=2*3*5 -- no freedom in the skeleton. [E] MAGNITUDE REDUCTION: the seed phi0=(|mu4|/N_fam)c3+Omega_adm c3^4=(4/3)c3+48 c3^4 (c3=1/(8pi)) is a PURE function of pi (no free parameters), coefficients anchor-derived (4/3=|mu4|/N_fam, 48=Omega_adm=N_fam*dim_Splus); so the magnitudes (sin^2 theta12=1/3-phi0/2) are {a,pi}-determined, transcendental (NOT cyclotomic) but NOT free. [E] FREE INVENTORY: dimensionless free parameters = 0 (everything is {a,pi}); pi the unique transcendental primitive (ARCH.CORE.01/v53); v_geo the unique dimensionful input (No-Unit Theorem v153/v78) -- complete input = {a, pi, v_geo}. [O] HONEST RESIDUAL: this rigidity holds GIVEN the axioms; it does NOT prove the raw seam REALIZES the structure -- the open bedrock QGEO.SYM.01/SEAM.EQUIV.01 stays [O]. VERDICT: SM structural sector = Q(zeta30)+Galois mu4 x Z2 (rigid, anchor-forced, degree=rank E8); magnitudes = {a,pi}-transcendental (phi0); the only genuinely free datum is v_geo; dimensionless free parameters: 0.

Recorded status: Synthesis/inventory [E] (arithmetic + {a;pi} reduction) + [O] (seam realisation)

Dependencies, status detail and source

Canonical status: [E] the Q(zeta30)/Galois=mu4 x Z2 skeleton (degree=rank E8) + the anchor-rigidity + the phi0={a,pi} reduction (pure pi, anchor-derived coefficients) + the 0-dimensionless-free-parameter inventory ({a,pi,v_geo}); [O] the seam realisation. A synthesis/inventory capstone of the v313-v317 arc; does NOT close the open bedrock and does NOT add a physical readout.

Dependencies: GALOIS.FAMILY.01; GALOIS.READOUT.01; COX.COUPLE.01; ARCH.CORE.01; NOUNIT.01; v313; v314; v315; v316; v317

Scripts: v318_arithmetic_capstone.py

Location: origin_theory

Original CSV, line 415

Original ledger status

P2.PARTITION.01

P2.PARTITION.01

g_car = 5 AS A COROLLARY OF THE FOUR MARKS (2026-07-20; the partition sharpening of ARCH.CORE.01/v53): a multiset of exactly 3 POSITIVE INTEGERS summing to 4 is UNIQUE -- {1,1,2}, the unique partition of 4 into exactly 3 positive parts -- so the elementary symmetric functions e = (4,5,2) and hence g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2 - e3 = 3 are COROLLARIES, not inputs; the carrier formula closes as a fixed point ((2^(g_car-1)-1)/g_car = 3 = rank H^1 = #marks - 1). [E] NEGATIVE CONTROLS, each assumption load-bearing (sympy exact): drop positivity -> 4 solutions with e2 ambiguous {0,3,4,5}; sum 3 -> unique but e2 = 3; sum 5 -> not unique; 2 parts -> e2 in {3,4}; 4 parts -> e2 = 6; Mehta-Seshadri-typed RATIONAL weights (scaled by 4) -> e2 = 16/3 resp. 44/9 != 5 -- integrality comes from the SPLITTING-TYPE typing (Birkhoff-Grothendieck: bundles on P^1 split with integer degrees), NOT from MS weights (which are rational). [E] THE v53 SHARPENING: v53 pins (1,1,2) using ALL THREE targets (4,5,2); the sharper lemma needs only e1 = 4 (+ positivity + 3 parts) -- both searches return the same unique multiset. [E] THE SUM RULE: |a|_1 = 4 x (N-1)/2 = 4 iff N = 3 (equidistributed clock spectrum); the v115 mu4-average route |a|_1 = |mu4| tr(A0) = 4 agrees. INDEPENDENCE CHAIN (why not circular in g_car): #marks = 4 from v216 Gauss-Bonnet (P1-side premises only, checks 1/3/5 without g_car); the 3 = rank H^1(P^1 minus 4 marks) = #marks - 1 is pure topology (v137 explicit basis / v228 index gate); |a|_1 = 4 is g_car-free via par-deg-0/(U) (v115) or the mu4-average lemma. [C] HONEST RESIDUAL: P2 is NOT made axiom-free -- the residual is the weight-TYPING postulate (integrality = Birkhoff-Grothendieck splitting exponents; positivity a_i >= 1 = h^0(E) = 0, correlate: the trivial mu4 character absent from H^1, v137 check 1; sum rule = parabolic-degree-0 'given (U)', v115 [I]/[N]); AX.P2.01 stays a DECLARED AXIOM (over-determined, now by one more convergent route). DIRECTION-REVERSAL NOTE: tfpt_constants computes N_fam FROM g_car; here the arrow runs marks -> partition -> g_car -- an over-determination check, not a circle, and it must never be double-counted in witness tallies. No gate closes, no marker moves.

Recorded status: Formal [E] (partition lemma + corollaries + negative controls + v53 sharpening, sympy exact, Wolfram-mirrored) + [C] (weight-typing postulate: splitting-type integrality, h^0 = 0 positivity, (U) sum rule; AX.P2.01 stays Axiom)

Dependencies, status detail and source

Canonical status: Partition corollary [E]/[C]: 4 = 1+1+2 unique in exactly 3 positive parts => g_car = 5, |Z2| = 2, N_fam = 3 as corollaries; all negative controls pass; sharpens v53 (only e1 = 4 needed); residual = the weight-typing postulate -- AX.P2.01 stays a declared axiom; the typing residual is itself sharpened by v499 (P2.TYPING.01, Deligne + BG + stability), v491 stays active

Dependencies: AX.P2.01; ARCH.CORE.01; ANCHOR.GEN.01; MARKS.GB.01; v23; v53; v115; v137; v216; v228

Scripts: v491_p2_partition_corollary.py

Location: introduction;tfpt_1;tfpt_2;origin_theory

Original CSV, line 553

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?