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 All 788 ledger rows, including superseded rows, remain in the download.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
EM.WARD.01
EM Boundary Ward decomposition (Theorem C): F_U(1)=0 read as reduced boundary U(1) Ward identity in three terms - Maxwell alpha^3 + Calderon -2c3^3 alpha^2 (2=|Z2|) + transport -8b1 c3^6 log(1/phi_seam). Coefficient identities EXACT [I]: 8b1=(4/5)M=(4/5)(sumL+N_Phi)=164/5; seam exponent -5/4=-q(D5); transport power c3^6=C6 hexagon. Root reproduces alpha^-1=137.0359992 (v3). Physical Ward ORIGIN (EM1/EM2/EM3: d_tau log Z = each term) is [P] interpretation, NOT machine-proven. SHARPENED 2026-06-22 (v341/ALPHA.QUILLEN.01): the three terms are reassembled as the stationarity of a U(1) determinant line (delta log det Delta_U(1) + counterterm + seam = 0), every coefficient identified as index (8 b1) / heat-kernel (c3^{3,6}) / discriminant (q(D5), q(A3)); the [P] residual is unchanged in scope -- the from-first-principles AQFT proof that this is the EXACT Quillen functional -- only stated more sharply (still [P]/[O], no new gate) UPDATED 2026-08-27 (v974): the cited EM1 inflow step now carries a computed lattice witness -- on the v367 collar model pumped charge == edge spectral flow == Streda count == Chern == 1 per flux quantum (hybrid-Wannier winding residual 0.0; Streda DeltaN = C n_phi as exact integers; the complex-conjugation mutant flips all four readings simultaneously, the wrong-band projector breaks quantization). Single complex copy computed; the 16-copy bookkeeping (c_- = 16 x 1/2 = 8 = g_car + N_fam, kY = 5/3, (1/kY) 41/6 = 41/10 = b1) re-derived as exact Fractions. The physical Ward ORIGIN keeps its [P]/[O] scope -- nothing upgrades here.
Recorded status: Identity [I] + physical origin [P] (sharpened to a Quillen form by v341; to a heat-kernel origin by v342)
Dependencies, status detail and source
Canonical status: Identity [I] + physical origin [P]
Dependencies: EM.FP.01; v3; v341; v342
Scripts: v48_em_ward.py
Location: tfpt_1
Original CSV, line 70Original ledger status
EM.WARD.02
HEAT-KERNEL SHARPENING OF EM.WARD.01 (2026-06-22): derives the ORIGIN and STRUCTURE of the F_U(1) determinant-line terms from textbook Seeley-DeWitt/Gilkey heat-kernel coefficients, advancing the EM-Ward origin from [P] (conjectured) to [E] for the term STRUCTURE; honestly fences the rest. NO new gate (sharpens EM.WARD.01). [E] c3 = 1/(8 pi) is the boundary GAUSS-BONNET heat-kernel coefficient: the seam is the flat pillowcase S^2(2,2,2,2) (chi=2), oint K = 2 pi chi = 4 pi, c3 = 1/(|Z2| oint K) (v216). [E] the alpha^2 term is the GILKEY gauge-curvature coefficient: the U(1) Laplacian a4 contains 30 Omega^2/360 = (1/12) Omega^2 (Gilkey, Invariance Theory Thm 4.8.16), Omega = i alpha F => -(alpha^2/12) F^2, so an alpha^2 term in log det Delta_U(1) is FORCED -- the Calderon -2 c3^3 a^2 is the gauge-curvature (Quillen-curvature) piece, not an ansatz. [E] the c3-ladder {0,3,6} is arithmetic (step 3 = three channels; 6 = |R^+(A3)| C6 hexagon). [E] multiplicities forced: 2 = |Z2| (sheet), 8 b1 = (4/5) M = (rank E8) b1 (b1=41/10, v48/v159). [E] pi-power test: 2 c3^3 = 1/(256 pi^3) carries pi^3 => THREE boundary c3-insertions, not a single bulk a4 (~pi^{-1}). [C] the exact coefficient 2 c3^3 needs the seam F-normalisation. [O] the cubic alpha^3 Maxwell moment (a topological/Chern level, NOT a Seeley-DeWitt integral) + the full identification (this IS the seam U(1) zeta-determinant) = EM.WARD.01's residual, tied to SEAM.EQUIV.01. NOT closed. alpha^-1 stays [E] (v3).
Recorded status: Heat-kernel origin [E]/[C]/[O] (term structure [E]; exact value [C]; cubic moment + identification [O]; no new gate)
Dependencies, status detail and source
Canonical status: [E] the heat-kernel STRUCTURE (c3 = Gauss-Bonnet boundary coefficient; alpha^2 = Gilkey gauge-curvature a4 term; c3-ladder; multiplicities; pi-power); [C] the exact coefficient (seam F-normalisation); [O] the cubic Maxwell moment + the full determinant identification (= EM.WARD.01, tied to SEAM.EQUIV.01). Sharpens EM.WARD.01's origin from [P] toward [E]; no new gate.
Dependencies: EM.WARD.01; v48; v216; v3; v159
Scripts: v342_em_ward_heatkernel.py
Location: tfpt_1_architecture_e8
Original CSV, line 112Original ledger status
ALPHA.QUILLEN.01
THE ALPHA FIXED POINT AS THE STATIONARITY OF A U(1) DETERMINANT LINE (2026-06-22): reformulates the EM closure from 'a very cleverly built fixed point' into 'the stationarity of a named functional', identifying every ingredient as an index / heat-kernel coefficient / discriminant form -- the 'derive the FORM' step (external review). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 written in Quillen form: [a^3 - 2 c3^3 a^2] (determinant-line variation) = [8 b1 c3^6] (anomaly counterterm) * [ln(1/phi_seam)] (seam response), i.e. delta log det Delta_U(1) + counterterm + seam response = 0. [E] M=41 is a U(1) INDEX (EM Ward, v48): (4/5)M = 8 b1 = 164/5 with b1=41/10 the SM one-loop U(1)_Y beta (GUT-norm, v159/v246), so M=10 b1; the counterterm coefficient is 8 b1 c3^6 = (rank E8) b1 c3^6. [E] c3=1/(8 pi) is the GAUSS-BONNET boundary coefficient (8 = rank E8, v216); c3^3 (Quillen-metric) and c3^6 (counterterm) are heat-kernel powers. [E] the exponent -5/4 = -q(D5) is a DISCRIMINANT form (q(D5)+q(A3)=2, v1/v154); phi_base=1/(6 pi)=(4/3)c3 carries q(A3): c3/phi_base=3/4. [E] delta_top=Omega_adm c3^4 (Omega_adm=48). [E] the Quillen split holds at the alpha^-1=137.0359992 root. [E] NO NEW GATE: alpha^-1 stays closed [E] (unique root + ablation, v3); v341 adds NO open item -- it SHARPENS the pre-existing [P] physical Ward origin EM.WARD.01 ('why THIS function') toward [E] by naming every coefficient. [O] the one still-open part IS EM.WARD.01's residual (now sharper): the from-first-principles AQFT proof that F_U(1) is the EXACT Quillen functional of the seam U(1) (the variational principle DERIVED, not assembled). Not a new gate; not closed.
Recorded status: Reformulation [E]/[O] (alpha = stationarity of a named U(1) determinant line; sharpens the existing [P] EM.WARD.01; no new gate)
Dependencies, status detail and source
Canonical status: [E] the coefficient identifications (8 b1 = (4/5)M; c3 Gauss-Bonnet; -5/4=-q(D5); c3/phi_base=q(A3)) + the Quillen-form split at the root + the 'no new gate' clarification (machine-checked); [O] the still-open part = EM.WARD.01's residual (the first-principles AQFT derivation of the functional). Sharpens v3/v48/EM.WARD.01 from fixed point to stationarity; does NOT open a new gate and does NOT prove the variational principle.
Dependencies: EM.WARD.01; v3; v48; v159; v216; v1
Scripts: v341_alpha_quillen.py
Location: tfpt_1_architecture_e8
Original CSV, line 443Original ledger status
ALPHA.QUILLEN.EXACT.01
Names the Quillen determinant-line VARIATION as a tracked [O] target (2026-06-23, review Point 10): delta_tau(log det_zeta Delta_U(1) + 8 b1 c3^6 log phi_seam)=0 on the determinant line over the mu4 seam moduli -- i.e. F_U(1) IS the exact zeta-regularised Quillen functional of the seam U(1), not merely an assembled fixed point. Elevates EM.WARD.01's residual (v341/v342) to its own citable target so the one remaining EM obligation is trackable separately from the seam-net identification, WITHOUT creating a second independent open problem (it is a FACE of SEAM.EQUIV.01). [E] the Quillen split holds at the root a^3-2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at alpha^-1=137.0359992 (F_U(1)=0 IS the stationarity, v341). [E] every coefficient is a named atom: 8 b1=(4/5)*41 a U(1) index, c3=1/(8 pi) the Gauss-Bonnet boundary coeff (c3^3,c3^6 heat-kernel powers), q(D5)+q(A3)=2 discriminant forms (v341/v48/v216). [E] the value alpha^-1=137.0359992168 stays closed (unique root+ablation, v3) -- only 'why this functional' is open. [O] THE TARGET: the from-first-principles AQFT/zeta proof of the variation. [C] FACE OF SEAM.EQUIV.01 (v336): the seam U(1) determinant line lives on the same holomorphic seam net, so once the net is (E8)_1 its U(1) sub-determinant is fixed -- not a second gate. No new number (reuses v341, Wolfram-mirrored). UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the target's c3-ladder rule MERGES with HYP.PHI0.PUNCTURE.01 into one analytic step -- the contact unit c3-per-insertion is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (41 = 10 b1). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (diagonal zero at the KMS scale, closed-form mark determinant, 41 = Y^2-weighted count of the same 48 states); the target's remaining [O] is now EXACTLY its v382 typing -- the SEAM.EQUIV.01 face -- with no separate analytic unknown left. UPDATED 2026-08-27 (v974): both named faces now carry COMPUTED witnesses. The diagonal-zeta face is EXECUTED as the BFK gluing on the seam circle (gluing constant EXACTLY 2^-N, derived symbolically N = 1..4 at general lengths; jump matrix at KMS R_0 = 16 c3 circ(2,-1,0,-1) = (G_m|_marks)^-1; det'R_0 = 2^16 c3^3, glued product (2 pi)^2; the v485 scale channel reproduced exactly via the KMS unit) -- vs the v484 mark matrix there is NO global proportionality (kernels in SWAPPED mu4 channels), but the correspondence is channel-wise exact (same eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling): the diagonal-zeta face is thereby SHARPENED to the channel-swap question. The finite Quillen identity is verified TWO-SIDED on the twist torus (Berry integral == Poincare-Lelong divisor integral == +1, difference an exact form, transition winding == Chern), typed conditional on the quasi-free rigidity premise (measured, not proven -- SEAM.STATE.RPMIXING.01). STAYS [O]: 'why this functional' is not closed -- the remaining content is typed as {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification of the exact-form difference field}; alpha^-1 = 137.0359992168 re-anchored (unique root on the scanned window, split residual 6.4e-58 at 50 digits). EXECUTED NOTE (2026-08-28, completeness wave): the rigidity premise of the finite Quillen identity is now executed at the finite CAR level (v995: 33 mixing directions killed by KMS alone; covariance redundant; 196608 -> 0); type-III/continuum stays [O]. The finite-collar detline curvature converges exponentially to 2pi with rate ~0.6936 ~ ln 2 (v996) -- a numerical Bismut-Freed shadow, not the continuum theorem. STAYS [O]. Python-only / Wolfram mirror deferred. RELATIVE-DETERMINANT NOTE (2026-08-29, review wave 4): the correct object is the RELATIVE determinant Q(A) = log[det' Delta_A / det' Delta_{A0}] + 8 b1 c3^6 log phi(A); the BFK constant 2^{-4} is A/tau/alpha-INDEPENDENT at fixed cut number, so delta log 2^{-4} = 0 -- no physical compensation needed (consistent with COMPENSATION_INTERNAL + the reviewer's correction). Absolute normalization is fixed by the reference A0. Contract stays [O]. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism verified (c_phase constancy 3.7e-16, conjugation covariance exact, C = W_bulk = W_seam = +1 / mirror -1); orientation fixes the conjugate branch (2 -> 1); the residual constant phase is fixed by the A0 reference normalization -- recorded. Continuum Bismut-Freed stays [O]. Contract stays [O].
Recorded status: Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])
Dependencies, status detail and source
Canonical status: [E] the Quillen split at the root + named-atom coefficients + the value alpha^-1=137.0359992 (reused from v3/v48/v341, machine-checked); [O] the from-first-principles exactness proof (the named target); [C] it is a face of SEAM.EQUIV.01, not a second independent gate. A typing/registration of the pre-existing EM.WARD.01 residual, reusing v341's (Wolfram-mirrored) identities; introduces no new number. UPDATE (2026-08-28, external master-object review wave 2, v985): the channel-swap face is resolved at the FINITE level -- the deck swap r -> r+2 maps the jump |spectrum| [0,2,4,2] onto the mark pattern |[4,-2,0,-2]| exactly (odd swap fails), the graded det' difference is c3-free = log(ln2/4), and the channelwise unit ratio is uniform 4/ln2; finite KMS rigidity-premise executed [E] (v995: 33 directions killed; 196608 -> 0); ln-2-rate detline shadow [E-measured] (v996, numerical not theorem); continuum Bismut-Freed, type-III KMS uniqueness and the from-first-principles exactness of F_U(1) stay [O] (BFK 2^{-4} needs no physical compensation: relative det, 2026-08-29). | 2026-08-29: relative det Q(A)=log[det'Delta_A/det'Delta_{A0}]+8 b1 c3^6 log phi(A); BFK 2^{-4} A/tau/alpha-independent at fixed cut number (delta log 2^{-4}=0, no physical compensation). Stays [O]. WAVE-5 (2026-08-29): rigidity premise of SEAM.MMST.TYPEIII.CHARGED.01; no marker move. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes the conjugate branch; the residual constant phase is fixed by the A0 reference normalization -- recorded. Stays [O].
Dependencies: EM.WARD.01; SEAM.EQUIV.01; v341; v342; v3; v48; v216; v336
Scripts: v382_alpha_quillen_exact.py, v985_quillen_channel_swap.py, v995_kms_subnet_rigidity.py, v996_gauge_grammar_kill.py, v1014_bridge_refinements.py
Location: tfpt_1_architecture_e8
Original CSV, line 445Original ledger status
HYP.PHI0.GEOM.01
THE GEOMETRIC SIDE OF THE phi0 PUNCTURE TARGET IS EXACT (2026-07-14, deep-dive round; narrows HYP.PHI0.PUNCTURE.01/v408, does NOT close it): every twisted/orbifold heat trace of the flat tau = i pillowcase is a t-INDEPENDENT RATIONAL, so the pi^-4 in dtop = 48 c3^4 cannot come from flat orbifold geometry at ANY order -- the entire analytic content sits in the coupling normalisation of the contact insertions. [E-num] TWISTED TRACES EXACTLY 1: Tr(gamma e^{t Delta}) = 1 for gamma = sigma (z->-z), rho (z->iz), rho^3 at every tested t in [0.05, 3] (position-space Gaussian image sums / erf closed forms + 2d quadrature, residual < 1e-9; mode-space proof: gamma permutes Fourier modes, only n = 0 is diagonal) -- t-independent, no asymptotic tail. [E] ATIYAH-BOTT MATCH: 1 = 4 x 1/|det(1-dsigma)| with det = 4 = |mu4| (four Z2 marks) and 1 = 2 x 1/|det(1-drho)| with det = 2 = |Z2| (two order-4 points). [E] PILLOWCASE DATA EXACT: orbifold heat trace = (1/2) Tr_T2 + 1/2 -- the Z2 contact term is EXACTLY 1/2 = 4 x (1/8 per mark) for all t; the clock-equivariant pillowcase trace is exactly 1 for all t. [E]/[O] THE REDUCTION: dtop = 48 c3^4 = 3/(256 pi^4) decomposes as 4 = |mu4| contact insertions of per-mark weight c3 (giving c3^4) times the multiplicity Omega_adm = 48; the bare 1/(2 pi)-propagator 4-cycle differs by the exact RATIONAL 3/16; the ONE remaining [O] is the rule 'per-mark insertion weight = c3' (seam zeta/Green normalisation), the same residual class as the EM-Ward c3-ladder (EM.WARD.02). The target narrows from 'derive the term' to 'derive the weight'. Complements the experiments-side Donnelly probe (honest negative). No gate closes, no marker moves.
Recorded status: Reduction [E-num]/[E]/[O] (geometric side exact: t-independent rational twisted traces; value reduces to the one per-mark coupling rule)
Dependencies, status detail and source
Canonical status: Reduction: geometric/equivariant side exact (rationals, all t); dtop's pi^-4 = coupling normalisation; remaining [O] = the per-mark weight rule
Dependencies: HYP.PHI0.PUNCTURE.01; HYP.PHI0.01; ARCH.QUAD.01; EM.WARD.02; v37; v216; v396; v408
Scripts: v483_pillowcase_exact_traces.py
Location: origin_theory
Original CSV, line 544Original ledger status
SEAM.CONTACT.UNIT.01
THE SEAM CONTACT UNIT -- THE MERGED RESIDUAL OF THE TWO ANALYTIC TARGETS (2026-07-14, deep-dive round II): the shared 'c3 per boundary insertion' rule of ALPHA.QUILLEN.EXACT.01 (c3-ladder {0,3,6}, v3/v341/EM.WARD.02) and HYP.PHI0.PUNCTURE.01 (per-mark weight c3, v483) is ONE identity and NOT a new unknown: it is the KMS seam unit 2 pi = 1/(4 c3) with 1/4 = 1/|mu4| (v239) -- one bare boundary propagator ORBIT-AVERAGED over the four marks. [E] UNIT CHAIN: 1/(2 pi) = 4 c3 = |mu4| c3 = |Z2| chi(S^2) c3. [E] MECHANISM DERIVED ON THE SEAM CIRCLE: G(d) = -(1/pi) ln|2 sin(d/2)| (polylog identity, 40 digits) takes INTEGER multiples of c3 ln2 at the mu4 separations (G(pi/2) = -4 c3 ln2, G(pi) = -8 c3 ln2), so G_marks = -4 c3 ln2 x circ(0,1,2,1) with spec {4,-2,0,-2}; the mu4-invariant (orbit-averaged) insertion carries (GV)|_marks = -(c3 ln2) C exactly -- the log-det contact expansion is EXACTLY graded in c3 per insertion, cycle combinatorics Tr(C^k) = 4^k + 2(-2)^k integer. [E] SUITE-WIDE GRAMMAR: F_U(1) ladder {0,3,6} (v3); phi0 ladder {1,4} (v37); Lambda prefactor 3/(4 pi^2) = (8 pi)^2 delta_top = 48 c3^2 (v60) -- the SAME multiplicity Omega_adm = 48 as the puncture at TWO insertions; the g-2 seam loop divides by the same 2 pi = 1/(4 c3). [C]/[O] THE MERGE: the two tracked [O] targets collapse into ONE named analytic step -- the diagonal (self-energy) zeta-renormalisation at the marks + the state-multiplicity matching (48 = Omega_adm = N_fam dim S+, 41 = 10 b1); the finite cycle sector is PROVEN. Anti-numerology: the check integers (circulant, spectrum, traces) are forced by the square mark configuration; no coefficient of either target is claimed. No gate closes, no marker moves. UPDATE 2026-07-14 (v485/SEAM.CONTACT.UNIT.02): the diagonal channel is settled -- G_reg(0) = 0 exactly at the KMS scale, the log is the pure scale channel, the mark determinant resums closed-form, and the 48/41 multiplicities are one state set under two response weights; the merged residual collapses onto the SEAM.EQUIV.01 face. UPDATED 2026-08-27 (v974): the finite cycle sector now has its computed Delta-side partner -- the BFK jump circulant B = circ(2,-1,0,-1) shares the mu4 Fourier eigenbasis with the mark circulant C = circ(0,1,2,1), the |spec| multisets are equal {0,2,2,4}, Tr B^k = 4^k + 2(+2)^k mirrors Tr C^k = 4^k + 2(-2)^k with the sign flip = the kernel swap (B kills the mu4-trivial gauge/zero-mode channel, C the mu4-sign channel), and B + C = 2(I + S). On the doublet channel R_0|_d = (4/ln2) G_marks|_d exactly, with the c3 grading CANCELLING in the ratio -- both matrices carry the same 'c3 per insertion' unit. No global proportionality: the merged residual is sharpened to the channel-swap question, not closed.
Recorded status: Unification/reduction [E]/[C]/[O] (the two analytic targets merge; contact unit = KMS seam unit, derived for the finite cycle sector; diagonal renormalisation + multiplicity matching stay open)
Dependencies, status detail and source
Canonical status: Unification: 'c3 per insertion' = KMS seam unit (bare 1/(2pi) x orbit average 1/|mu4|), cycle sector derived; the two [O] targets are ONE remaining analytic step
Dependencies: ALPHA.QUILLEN.EXACT.01; HYP.PHI0.PUNCTURE.01; HYP.PHI0.GEOM.01; EM.WARD.02; DYN.KMS.01; LAMBDA.BRANCH.01; v3; v37; v58; v60; v239; v341; v408; v483
Scripts: v484_seam_contact_unit.py
Location: tfpt_1;origin_theory
Original CSV, line 545Established within the stated premises
finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation
The active original explicitly treats the three-term decomposition and coefficient identities as exact, retaining the unique alpha root. The same section retains EM.WARD.01/ALPHA.QUILLEN.EXACT.01 as the existing origin obligation for the actual AQFT/zeta determinant functional. Separately the old circle canonically gives Pi and det_F(1-qPi)=1-q. Its actual local EM response, relative Quillen norm and susceptibility exponent5/4 still require identification. This does not retract compiler identities or root uniqueness.
Scope: Source-reviewed status/type correction, not a new general nonderivability theorem or gate. P1/P2 remain accepted starting principles; being axioms is not an objection. The line is derived on the old circle, not an arbitrary vector to select again. v382 replay26October:6/6; literalTrue status checks do not prove open functional origin. Ledger Numerical and full physical status remain unchanged.
Required premises and original source excerpts
- Specified EM function with positive seam response
F(x)=x³−2c³x²+(4/5)c⁶M log(p+q(1−q)^(−5/4)), c=1/(8π), p=1/(6π), q=48c⁴exp(−2x), M>0; original budget M=41. The function and inputs are premises here.
premise:fixed-em-seam-function - Model results remain conditional
Calculations in a fixed E8 net, quotient, family packet, or readout apply only under their stated inputs and do not select those inputs.
premise:fixed-input-models-scoped - P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
premise:declared-p1-p2
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?