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 All 788 ledger rows, including superseded rows, remain in the download.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 697 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.
The scientific findings include 505 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 3ddcc9643e499ce39900d9c5 · snapshot SHA256 7622b36de7ed79901ae75361b009fa423a6505076f388f4fbaf2d42e1ba7dcf5
Original ledger status
HOR.CLOCK.01
THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the dS2 static patch, so the exact SdS family itself pins the S^2-radius modulus mass m^2 = -2L = -|Z2|L (the Laplace-type form of the Nariai linearization is standard GR - Ginsparg-Perry 1983 / Bousso-Hawking 1997 - typed external; the VALUE is pinned internally). Horizon split linear in the canonical angle, coefficient 1/sqrt(N_fam) [I]. GINSPARG-PERRY TOWER [I]: (l(l+1)-2)L has exactly ONE negative mode -|Z2|L (l=0), zero modes l=1. THE CLOCK [I]: in Hubble units chi_clock(lambda) = lambda^2+lambda-2 = (lambda-1)(lambda+2) = THE ANCHOR QUADRATIC; eigenvalues {1,-2} = the distinct anchor roots; Nariai cubic = (t-1) x chi_clock - the anchor appears as configuration roots (HOR.NARIAI.01), curvature base (HOR.TRISECT.01) and clock spectrum; entropy-deviation rate = 2H = |Z2| x Hubble exactly [I]. HONEST (2/3)-TEST NEGATIVE for the classical clock: eigenvalues are integers (anchor roots), not (2/3)-powers; the 2/3-powers stay in the functional; the one-loop conversion curvature -> rate (quantum (anti-)evaporation) remains external [P] - the flavor-rate bridge is NOT closed; the seam variational principle now has exactly one missing object: the QUANTUM clock
Recorded status: Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)
Dependencies, status detail and source
Canonical status: Identity: clock spectrum = anchor roots; quantum clock = the one [P]
Dependencies: HOR.TRISECT.01; HOR.ORIENT.01; HOR.NARIAI.01; ARCH.CORE.01 (anchor)
Scripts: v104_nariai_clock.py
Location: tfpt_horizon_readouts
Original CSV, line 187Original ledger status
SYNTH.INVENTORY.01
THE RESIDUAL INVENTORY (one constant, one anchor, one clock to find; the COMPLETE machine-pinned gap list): (A) ONE-CONSTANT INVENTORY [I] - 2/3 = |Z2|/N_fam appears exactly in seven independent places across both sectors (flavor: Koide branch point, transfer-gap base (2/3)^6, attractor inside the physical basin; gravity: Nariai entropy bound, SdS branch separation, canonical amplitude+frequency, canonical curvature base (2/3)^N_fam); ANCHOR TRIPTYCH [I]: configuration chi_a = (t-1)^2(t-2), Nariai cubic (t-1)^2(t+2) = traceless anchor, clock quadratic (lam-1)(lam+2); Nariai = (t-1) x clock; a = e2+e3. (B) RELOCATION THEOREM [I]+[P]: the cosmological one-loop clock correction eps = (c/24pi) Lambda/Mbar^2 = 7.6e-122 (c = 8 = the seam central charge, frozen rho_L) is deficient by 121.5 orders against the needed O(1) gap, and the deficit IS the Lambda hierarchy 2 alpha^-1/ln10 = 119.0 (+2.5 prefactors, the v60 split) => the seam clock must live at the SEAM scale, where the only gapped generator is the established boundary transfer operator; the bridge reaches its final form: ONE [P] identification 'transfer operator = seam Nariai clock'. (C) RESIDUAL TABLE (typing contract): exactly FIVE structural objects remain - R1 seam quantum clock [P] (HOR.CLOCK.01), R2 seam net holomorphic + c=8 [P]/[A] (GATE.METRIC.05/06/07), R3 seam determinant => EH form [A] (SEAM.AREACOEFF.03 residual), R4 H2 dictionary [A]/[P] (GATE.RU.01/CONTRACT.U.01), R5 parabolic realisation of Q carrying P1 [P] (GATE.QGEO.01/FLAV.SHEET.03) - plus the two irreducibles (one scale v_geo by dimensional analysis v78; the primitive pi) and the frozen data surfaces (gamma_CP, n_s/A_s, theta13, m_tau, r). COMPLETENESS is itself the claim: a sixth structural gap would FAIL v105. Nothing closed here; everything that remains is named, typed and counted
Recorded status: Identity [I] (inventory + relocation arithmetic) + typing contract (gap completeness)
Dependencies, status detail and source
Canonical status: Residual inventory: 5 named structural objects + 1 scale + pi; completeness machine-pinned
Dependencies: HOR.CLOCK.01; HOR.TRISECT.01; HOR.NARIAI.01; HOR.ORIENT.01; FR.KOIDE.04/05/06; GATE.METRIC.05-07; GATE.RU.01; GATE.QGEO.01; ANCHOR.VGEO.01; REG.FREEZE.01
Scripts: v105_residual_inventory.py
Location: origin_theory;introduction
Original CSV, line 188Original ledger status
ARCH.TRIAD.01
SECOND EXTERNAL-REVIEW VALIDATION (2026-06-11b): the anchor ratio triad, the 121 audit lemma and the normal-form micro-identities, all exact: (1) MICRO-IDENTITIES [I]: Omega_adm = 2 p1 p2 = 48; 10 b1 = 1 + p1 p3 = 41; Delta_Y = e2^2 = p0^2 + 2 rank E8 = 25; h(E8) = e3 p0 e2 = 30; rank E8 = p0 + e2 = 8; |R(E8)| = p1 p2 p3 = 240; dim E8 = 240 + (p4 - p3) = 248. (2) ANCHOR RATIO TRIAD [I] (named lemma): the three elementary symmetric values of the anchor normalised by the family count - e3/p0 = 2/3 (the Koide branch / sheet ratio, cf SYNTH.INVENTORY.01 seven appearances), e1/p0 = 4/3 (the seed gain |mu_4|/N_fam, ARCH.QUAD.01), e2/p0 = 5/3 (the carrier branch: the canonical flow's critical points are EXACTLY (2,5) = (e3,e2), FR.KOIDE.06, inflection 7/2 = (e3+e2)/2) - the recurring fractions 2/3, 4/3, 5/3 are the three normalised anchor coefficients, not scattered numbers. (3) THE 121 AUDIT LEMMA [I, typed AUDIT not load-bearing]: (1+a)^T R (1+a) = 121 = 11^2 = ||Pl(K)||_1^2 = (p3+1)^2 with the established residue operator R (det 8, SNF (1,1,8)) - the quark-ratio 11 (c_u/c_d = 5x11/(9x13)) appears a SECOND independent time as the quadratic anchor norm of R; sensitivity control: the 3 orderings of h = (2,2,3) give {105, 121, 135}, only the canonical anchor ordering yields 121; bonus checksums 1^T R 1 = 22 = 2x11 (entry sum) and a^T R a = 40 = p1 p3 = 10b1 - 1; the oriented Plucker mechanism (FLAV.KQ.01/v42/v49) remains the derivation. (4) FLAVOR SURFACE claim = established FLAV.DIAMOND.01/02 (re-verified, presentational). (5) BOOKKEEPING: mu4 projection = GATE.UWALL.07/08, triptych = HOR.CLOCK.01/SYNTH.INVENTORY.01, interior-free = CAR.QFREE.01 (all closed); anchor-first presentation recorded as editorial item
Recorded status: Identity [I] (exact arithmetic/matrix identities; audit typing for the 121 lemma)
Dependencies, status detail and source
Canonical status: Identity: anchor ratio triad (2/3 4/3 5/3) = e/p0; 121 = anchor norm of R (audit); micro-identities exact
Dependencies: ARCH.QUAD.01; FLAV.KQ.01; FLAV.DIAMOND.01-02; FR.KOIDE.06; SYNTH.INVENTORY.01
Scripts: v119_review_validation_2.py
Location: introduction; tfpt_research_contracts
Original CSV, line 203Original ledger status
HOR.CLOCK.03
THE RESUMMED CLOCK (R1's bend acquires a closed form; the HOR.CLOCK.02 job description transforms): (1) THE SPECTRUM READS (1 - n/N)^{p2} [I]: the frozen transfer eigenvalues {1, (2/3)^6, (1/3)^6} (v54/v69/v95) are EXACTLY lambda_n = (1 - n/N_fam)^{p2} for n = 0, 1, 2, with p2 = 6 = |R+(A3)| the hexagon size. (2) CLOSED-FORM CLOCK [I]: rate(n) = -p2 ln(1 - n/N_fam) reproduces {0, Delta, 6 ln 3} exactly; the HOR.CLOCK.02 bend rate(2)/rate(1) = log_{3/2}3 becomes a one-line consequence. (3) THE LINEARISATION CARRIES THE SHEET [I]: rate(n) = |Z2| n + n^2/3 + 2n^3/27 + ... - the linear (one-loop) term has slope exactly |Z2| = 2 relative to the integer classical Ginsparg-Perry clock {0,-1,-2} (HOR.CLOCK.01): the quantum clock is the SHEET-DOUBLED classical clock plus the geometric tail sum_k (n/N)^k/k. (4) THE WALL AT N_fam [I]: rate -> infinity as n -> N_fam (pole of the resummed logarithm at the family count) => the cusp ladder ends at n = N_fam - 1 = 2: the three-level transfer spectrum is forced by the clock itself. (5) R1 RE-SHARPENED [P] (recorded, not claimed): closed-form semiclassical target - derive rate(n) = -p2 ln(1 - n/N_fam) from the near-Nariai one-loop at kappa = 1/(3pi); the linear response must give slope |Z2| x classical and the resummation must exponentiate the geometric series; all spectra frozen in v54/v69/v95/v104/v107 - nothing fitted
Recorded status: Identity [I] (exact spectral reading + series) + Physical [P] (semiclassical derivation)
Dependencies, status detail and source
Canonical status: Identity: transfer spectrum = (1 - n/N)^6; rate = -6 ln(1 - n/3); linearisation slope |Z2|; pole at N_fam forces three levels; R1 target now closed-form
Dependencies: HOR.CLOCK.02; HOR.CLOCK.01; FR.KOIDE.06 (transfer spectrum); SYNTH.INVENTORY.02 (R1)
Scripts: v124_resummed_clock.py
Location: tfpt_horizon_readouts
Original CSV, line 209Original ledger status
HOR.CLOCK.04
THE CLOCK AND THE WALL SHARE A SPECTRUM (the v124 resummed-clock weights ARE the Mehta-Seshadri parabolic weights; R1's first checkpoint passes classically): (1) THE WEIGHTS ARE THE PARABOLIC WEIGHTS [I]: the arguments n/N_fam = {0, 1/3, 2/3} of the resummed logarithm are EXACTLY spec A0* (the exact U_wall residue, GATE.UWALL.07); the spectral bridge lambda_n = (1 - alpha_n)^{p2} over alpha in spec A0* reproduces the frozen transfer spectrum {1, (2/3)^6, (1/3)^6} - the horizon clock and the flavor wall share their spectrum through the complement map alpha -> 1 - alpha: the transfer eigenvalues are the hexagon-power of the COMPLEMENTARY parabolic weight. (2) CHECKPOINT 1 PASSES CLASSICALLY [I]: the resummed clock's linear coefficient p2/N_fam = 2 = |Z2| equals the established classical entropy-deviation rate 2H = |Z2| x Hubble (HOR.CLOCK.01) - the slope-2 linear response demanded by HOR.CLOCK.03 is already the classical entropy rate; the genuinely QUANTUM content of R1 isolates to the geometric tail sum_{k>=2} alpha^k/k. (3) THE DETERMINANT IS THE ENTROPY CURVATURE [I]: det(1 - A0*) = (1)(2/3)(1/3) = 2/9 = |Z2|/N_fam^2 - exactly the established gravity entropy curvature at the anchor (HOR.ORIENT.01), a fourth independent appearance; tr(1 - A0*) = 2 = |Z2|; det A0* = 0 (the parabolic degree-0 marker). (4) R1 RE-TARGETED [P] (recorded, not claimed): derive 'rate = -p2 ln(1 - alpha)' with alpha the parabolic weight - first order is classical (HOR.CLOCK.01's entropy rate), the tail is the quantum part; ONE SPECTRUM, TWO GATES, ONE OBJECT A0*
Recorded status: Identity [I] (exact spectral bridge + coefficient identities) + Physical [P] (re-target)
Dependencies, status detail and source
Canonical status: Identity: clock weights = parabolic weights (spec A0*); lambda = (1-alpha)^6; linear term = classical entropy rate |Z2|H; det(1-A0*) = entropy curvature 2/9; quantum content = geometric tail
Dependencies: HOR.CLOCK.03; HOR.CLOCK.01; HOR.ORIENT.01; GATE.UWALL.07 (A0*); SYNTH.INVENTORY.02 (R1)
Scripts: v126_clock_wall_bridge.py
Location: tfpt_horizon_readouts
Original CSV, line 211Original ledger status
HOR.CLOCK.05
THE CLOCK IS A LOG-DETERMINANT (the geometric tail of HOR.CLOCK.03/04 is the standard ring/RPA resummation; the 'O(1) resummation' demanded by HOR.CLOCK.02 is now TYPED): (1) LOG-DET IDENTITY [I]: for a rank-1 insertion P (tr P^k = 1), -ln det(1 - alpha P) = -ln(1 - alpha) = sum_k alpha^k/k - so the resummed clock is EXACTLY rate = -p2 Tr ln(1 - alpha P): p2 = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (= positive root of A3), with coupling alpha = the Mehta-Seshadri parabolic weight. (2) RING LADDER [I]: the k = 1 ring is the CLASSICAL term (6 alpha = |Z2| n = the HOR.CLOCK.01/04 entropy rate); the k = 2 ring is the first quantum correction (1/3 at weight 1); the partial sums converge to the exact rates {Delta, 6 ln 3} monotonically from below. (3) COUPLING CROSS-LINK [I, audit]: the established seam coupling kappa = (c/24pi)(Lambda/Mbar^2) at Lambda = Mbar^2 with c = 8 (HOR.CLOCK.02) is 8/(24pi) = 1/(3pi) = alpha_1/pi - the seam coupling is the first parabolic weight over pi. (4) THE WALL = RING DIVERGENCE [I]: radius of convergence |alpha| < 1; at alpha -> 1 (n -> N_fam) the sum diverges - the HOR.CLOCK.03 wall at the family count is the standard RPA instability. (5) R1 FINAL FORM [P] (recorded, not claimed): show that the near-Nariai one-loop effective action of the seam mode, with insertion strength = parabolic weight and multiplicity p2, is the ring sum - 'the seam clock is the RPA determinant of one mode on six sites'; the resummation type is identified, the derivation itself remains open
Recorded status: Identity [I] (log-det + ring ladder + coupling arithmetic) + Physical [P] (derivation)
Dependencies, status detail and source
Canonical status: Identity: clock = -p2 Tr ln(1 - alpha P) (ring/RPA determinant; one tower per hexagon site); k=1 ring = classical entropy rate; wall = RPA instability; kappa = alpha_1/pi
Dependencies: HOR.CLOCK.04; HOR.CLOCK.03; HOR.CLOCK.02; FLAV.H2.02 (hexagon); SYNTH.INVENTORY.02 (R1)
Scripts: v127_ring_resummation.py
Location: tfpt_horizon_readouts
Original CSV, line 212Original ledger status
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 213Original ledger status
HOR.CLOCK.09
THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the HOR.CLOCK.08 'last step' acquires its first exact invariant): (1) SPECTRAL SETUP (re-pinned): the Ginsparg-Perry sphere operator on the unit S^2 is L = -Delta - 2 (the -2 = -|Z2| = the HOR.CLOCK.01 modulus mass); eigenvalues mu_l = l(l+1) - 2 = (l+2)(l-1), degeneracy 2l+1; kernel = the 3 zero modes (l = 1); one negative mode (l = 0). (2) THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a_1 = (1/4pi) Int(R/6 - E) dA = 1/3 + 2 = 1/N_fam + |Z2| = 7/3 - the curvature third and the sheet mass, both compiler atoms. (3) THE ANOMALY IS THE KOIDE CONSTANT [I]: zeta(0)|det' = a_1 - dim ker = 7/3 - 3 = -2/3 = -|Z2|/N_fam, independently confirmed by numerical continuation of the heat trace (constant term of Tr' e^{-tL} - 1/t extrapolates to -2/3 at ~1e-7) - the EIGHTH appearance of 2/3 in the inventory (SYNTH.INVENTORY.01 counted seven) and the first as a SPECTRAL anomaly. (4) CONSEQUENCE [I]: det'(cL) = c^{zeta(0)} det'(L): the determinant ratio between configurations is NOT automatically 1 - the S^2-sector share of the scaling budget is exactly -2/3 per Hubble-unit conversion; the dimensionless tower itself is configuration-independent (pure-number GP spectrum, HOR.CLOCK.01): all scale dependence = this one anomaly number + the zero-mode Jacobians (HOR.CLOCK.08). (5) THE BUDGET STATEMENT [P] (recorded, not claimed): show the FULL zeta(0) budget of the 4d Nariai fluctuation problem (dS2 sector + gauge/ghost sectors + this S^2 sector) vanishes or is absorbed into the established power law; the S^2 share is pinned exactly at -|Z2|/N_fam - nothing claimed about the total
Recorded status: Identity [I] (heat-kernel arithmetic + numerical continuation) + Physical [P] (full budget)
Dependencies, status detail and source
Canonical status: Identity: zeta(0) of the det'-operator = -2/3 = -|Z2|/N_fam (a1 = 1/N_fam + |Z2| = 7/3); det-ratio question = one zeta-budget statement; S^2 share pinned
Dependencies: HOR.CLOCK.08; HOR.CLOCK.01; SYNTH.INVENTORY.01 (2/3 inventory); HOR.NARIAI.01
Scripts: v132_detratio_anomaly.py
Location: tfpt_horizon_readouts
Original CSV, line 217Open 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?