Original ledger status
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 2Original ledger status
ANCHOR.GEN.01
anchor-first: a=(1,1,2) elementary symmetric e_k=(4,5,2)=(|mu4|,g_car,|Z2|), c3=1/(2 e1 pi)=1/(8pi); power sums p_n=2+2^n give |R(E8)|=p1p2p3=240, dim E8=248, rank=p4-p3=8, binary ladder 2^n. Inputs reduce {c3,g_car} -> {a,pi}
Recorded status: Identity
Dependencies, status detail and source
Canonical status: Identity
Dependencies: a=(1,1,2) parabolic anchor
Scripts: v23_anchor_generator.py
Location: introduction;tfpt_1
Original CSV, line 24Original ledger status
DIAMOND.PARA.SELFCODE.01
THE PARABOLIC ANCHOR SELF-CODE (2026-07-31; external structural review audited by discovery probe parabolic_selfcode_audit_probe.py 23/23, verdict SELFCODE-VERIFIED, and promoted; one module, 14 checks, ~1 s, exact integer/symbolic sympy, no floats). The v218 sheet-diamond direction operators U = Q diag(1,0,0) (rank-1 winding) and V = Q diag(0,1,1) (rank-2 sheet, Spec V = {0,1,2}) carry a previously unstated exact operator structure. (1) PARABOLIC THEOREM: A = Q<I,U,V> is the FULL line-stabiliser (maximal parabolic) algebra of block type 2|1 -- seven words independent (coordinate det -81), multiplicatively closed (49/49), all seven matrix units contained, dim 7 = 9-2; mutation of Q's third column breaks it. (2) DOUBLE SELF-CODE: Pi2 = V(V-I)/2 idempotent trace-1; H = I + Pi2 has spectrum EXACTLY {1,1,2} = a (ANCHOR.GEN.01/v23); chi_H = x^3 - 4x^2 + 5x - 2 with (e1,e2,e3) = (4,5,2) = (|mu4|, g_car, |Z2|) AND = (dim_R(GL3/P), dim(A/J), dim J) -- the anchor reproduced spectrally (dominant projector of V) and categorically (flag/Levi/radical of A) from ONE structure. (3) UNIQUENESS THEOREM: x^3 - 2m x^2 + (m^2+1) x - m = (x-m)(x^2-mx+1) identically; positive-integer spectra force m^2 - 4 = k^2, (m-k)(m+k) = 4, m = 2 UNIQUELY -- a = (1,1,2) is the only anchor this parabolic family can code. (4) THE 81 AS LATTICE INDEX: the SATURATED integral order (closure stable at word length 4) has elementary divisors (1,1,1,3,3,3,3): [P_Z : Z<U,V>] = 3^4 = 81, cokernel (Z/3)^4 -- equal to the v218 determinant-staircase sum 3+4+8+14+20+32 = N_fam^4 (cross-link typed; the mark-local mechanism, one Z/3 per mu4 mark, stays [O]: if no canonical local decomposition exists the 81 stays a fingerprint). (5) A2 BIT CARRIER: the basic algebra e A e is the A2 path algebra (dim Ext^1 = 1): dim-vector-(1,1) modules fall into EXACTLY two iso classes (split / one nonsplit) -- the alignment bit gains a canonical algebra carrier; uniqueness [E], SELECTION stays with RP/geometry (v528/v534) [C]. (6) TRACE CODE (re-encoding): p_n(a) = 2 + 2^n = 1 + tr(V^n); recurrence, Hankel 2^{n+1}; (1+trV)(1+trV^2)(1+trV^3) = 240 = |R(E8)|; tr(V^4-V^3) = 8 = rank E8 -- AnchorLadder read through V, one object fewer, NO new content. (7) CR TEST DESIGN (CONTRACT.F.01): CR(alpha_{-2},alpha_{-1};alpha_0,alpha_1) = 4/3 exactly on the v533 line; honesty wired (universal arithmetic-progression cross-ratio -- content = preregistered solver-state export); negative control 28/25; y_F forced fit-free. (8) LORENTZ FORM (reformulation): det X = t^2 - x^2 - y^2 under Phi; D(P,Q) = 2<Phi,Phi>_{1,2}; delta = sech^2(atanh r); pencil identities det(B-S) = det B det(I-Z), D(B,S) = det B tr Z, det S = det B det Z -- eigenvalue locking as the named prime-front instrument (no measurement, no RH statement). NAMED LIMITS AS CONTENT: NO P2 REDUCTION -- 'g_car = dim(A/J) derived' is conditional on the OPEN 'No Carrier Reconstruction' audit (rebuild Q/V from mu4, D4, Q_+ = A3 exponent grading, H^1, Q_- = sheet monodromy, WITHOUT g_car, a, rank E8 or carrier-aware budgets; Q's historical provenance runs through such budgets); AX.P2.01 and ANCHOR.GEN.01 markers UNTOUCHED; the 2..9 dimension table is COMPRESSION of one operator system, not nine independent hits (no-free-pattern rule); the bit selection, the mark-local 81 mechanism and the CR-test execution stay open and typed open; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v567): the review's Priority-1 audit is EXECUTED at Stage A -- verdict RECONSTRUCTS-TO-FAMILY: the anchor self-code is carrier-free; Q reconstructs up to one binary sheet-coupling choice; see QGEO.QRECON.01. FURTHER UPDATE (2026-07-31, v568): Priority 3 executed -- the A2 Ext arrow is NONZERO on the whole reconstruction class (the split member collapses to dim 5 and is excluded); Priority 2 sharpened -- the mu4-grading candidate fails, the F3[V]-action on the cokernel exists (see DIAMOND.BIT.SELECT.01). [2026-07-31: the S8 pencil identities are now executed on the REAL Paper-II surface by v569 (machine-tight at 2e-14 on 70 windows, verdict ONE-MODE); see PRIME.PENCIL.ONEMODE.01.] [2026-08-01 X: the per-mark Z/3 mechanism appears geometrically -- v597: the cusp-class group of the mu3-cover is (Z/3)^4 of order 81 with four free local classes; see QGEO.COVER.01.] [2026-08-01 XVI: the self-code algebra has a geometric realization -- v600: (U, V) as Gamma-even degree-2 cusp-Gram operators on the mu3-cover, GL3-conjugate to the compiler pair, with the SAME saturated Z-order structure (index 81 = 3^4, divisors (1,1,1,3,3,3,3)); existence [E], canonicity open; see QGEO.EMBED.01.]
Recorded status: Identity [E] (exact integer/symbolic algebra with mutation controls -- parabolic closure, double self-code, uniqueness enumeration + divisor argument, saturated Smith form, A2 quiver, trace code, cross-ratio identities, Lorentz/pencil identities) + [C] (the TFPT readings of the invariants; the bit-carrier and CR-test interpretations) + [O] (the No-Carrier-Reconstruction audit, the mark-local 81 mechanism, the CR-test execution); NO marker moves
Dependencies, status detail and source
Canonical status: [E] A = full 2|1 parabolic, dim 7, word det -81, closed 49/49, mutation-fragile; a = Spec(I + V(V-I)/2) = (1,1,2) with chi_H = x^3 - flag x^2 + Levi x - radical (4,5,2 double-coded); m = 2 unique (enumeration to 2000 + divisor argument); saturated Smith (1,1,1,3,3,3,3), index 81 = 3^4 = staircase sum; A2 Ext^1 = 1 (two module classes); p_n = 1 + tr V^n (240, rank 8 as traces); CR = 4/3 design with 28/25 control; Lorentz/pencil identities exact; 14/14 checks
Dependencies: DIAMOND.AXIS.01; ANCHOR.GEN.01; AX.P2.01; FLAV.QGEO.01; CONTRACT.F.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v23; v218; v224; v528; v533; v534
Scripts: v566_parabolic_anchor_selfcode.py
Location: tfpt_1;tfpt_2;tfpt_research_contracts
Original CSV, line 605Original ledger status
QGEO.QRECON.01
THE NO-CARRIER-RECONSTRUCTION AUDIT, STAGE A (2026-07-31; Priority 1 of the self-code review; one module, 9 checks, ~1 s, exact enumeration with integer prefilters + sympy verification; discovery probe carrier_free_q_reconstruction_probe.py 10/10, verdict RECONSTRUCTS-TO-FAMILY). THE QUESTION: can Q -- hence V and the v566 parabolic anchor self-code -- be reconstructed WITHOUT carrier/anchor inputs? THE CIRCULARITY LOCATED: v11's uniqueness certificate for Q enumerates over row sums (4,5,6), column sums (9,5,1) and chi_Q = (t-1)(t^2-5t+3) -- the 5 = g_car sits in the budgets and in chi_Q; all of it FORBIDDEN here. ALLOWED (each carrier-free, with corpus source): (S) Sigma = diag(1,-1,-1) [v10 sheet]; (W) Q(I+Sigma) = 2 N_fam W [v10 winding]; (E) Spec(Q_+) = {1,2,3} [FLAV.QGEO.01, A3 exponents]; (M) Q_- != 0, Q_-^2 = N_fam P, P^2 = P [FLAV.QGEO.01]; (Z) nonneg integers, bound 6 (robust at 9); (L) the seam-line demand [geometric, [C]]; (X) the saturation index N_fam^4 = 81 [v566 S4]. RESULTS [E]: (1) exactly 52 admissible matrices under (S)(W)(E)(M)(Z), corpus Q among them, first column forced to N_fam(1,1,1) by (W); (2) the seam-line demand cuts 52 -> 28 (real teeth); (3) THE ANCHOR IS CARRIER-FREE: all 28 parabolic members code the SAME anchor -- H' = I + Pi_dom(V') with char poly x^3 - 4x^2 + 5x - 2, spectrum (1,1,2) = a, ONE code class, no exceptions: the anchor self-code sits UPSTREAM of the carrier budgets, conditional on the declared geometric inputs; (4) THE RESIDUAL BIT: the 81-pin selects EXACTLY TWO members -- the corpus Q (q32 = 2 = |Z2|) and Q_alt (q32 = 0), difference matrix 2 E32 (the sheet-block coupling); every classical carrier-free certificate coincides on the pair (anticommutator spectrum {6,-4,-2} = (|R+(A3)|, -|mu4|, -|Z2|); commutator charpoly t(t^2+12); det = 3; saturation 81), while the ONE separating certificate is the carrier column budget (9,5,1) vs (9,3,1) -- exactly the forbidden input: the residual freedom is ONE binary coupled-vs-uncoupled sheet-block choice; (5) ablations: dropping (W) widens the bound-3 set 28 -> 1376 over 36 first columns (the winding input carries real load); bound robustness 6 -> 9 adds zero new (L)+(X) members; the forbidden inputs were evaluated nowhere. NAMED LIMITS AS LOAD-BEARING CONTENT: STAGE A ONLY -- whether (S)(W)(E)(M)(L) themselves derive from mu4/D4/H^1 parabolic geometry without family/sheet inputs is EXACTLY the open gate GATE.QGEO.01: the audit is RELOCATED there, not closed (N_fam = 3 is used throughout; family data was never forbidden -- the forbidden list is the CARRIER list); the carrier-free selector of the residual bit is OPEN, and its structural resonance with the split/nonsplit alignment-bit dichotomy (v528/v534, v566 S5) is a TYPED OBSERVATION, not a claim; NO P2 reduction -- AX.P2.01 and ANCHOR.GEN.01 markers untouched; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v568, DIAMOND.BIT.SELECT.01): the residual bit is located and given a canonical witness -- the twins generate different integral orders, and the ladder self-consistency (dominant mode = its own eigenvalue ladder (1,2,4)) selects the compiler Q uniquely on all 28 members; the split geometry (q32 = 1) is excluded by the demands already imposed; the physical selection stays open. Markers unchanged. [2026-07-31: Stage B narrowed by v574 -- the involution type is forced by a rank theorem and N_fam = 3 by the double self-consistency (ladder + sat = N^4); (E)(M)(L) stay the remaining gate; see QGEO.WINDING.SELF.01.]
Recorded status: Identity/enumeration [E] (exact admissible-set census 52/28/2 with integer prefilters verified by sympy on survivors; one anchor code class on all 28; separator dissection exact; ablations quantified) + [C] (the seam-line demand as declared geometric input; the bit-resonance observation) + [O] (Stage B = GATE.QGEO.01 relocation; the binary selector); verdict RECONSTRUCTS-TO-FAMILY; no marker moves
Dependencies, status detail and source
Canonical status: [E] 52 admissible under (S)(W)(E)(M)(Z) at B = 6; 28 under the seam-line demand; ONE anchor code x^3-4x^2+5x-2 = spectrum (1,1,2) on all 28 (carrier-free anchor); 81-pin -> exactly 2 (corpus Q vs q32 = 0 twin; all carrier-free certificates equal, separator = the forbidden column budget (9,5,1)); winding ablation 28 -> 1376 at bound 3; bound-stable at 9; 9/9 checks; verdict RECONSTRUCTS-TO-FAMILY
Dependencies: DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; GATE.QGEO.01; FLAV.KQ.01; AX.P2.01; ANCHOR.GEN.01; v10; v11; v218; v566
Scripts: v567_carrier_free_q_reconstruction.py
Location: tfpt_1;tfpt_2
Original CSV, line 606Original ledger status
DIAMOND.BIT.SELECT.01
THE RESIDUAL RECONSTRUCTION BIT: LOCATED, SEPARATED, AND GIVEN A CANONICAL EXACT WITNESS (2026-07-31; Priorities 2+3 of the self-code review fused with the v567 residual bit; one module, 11 checks, ~1 s; discovery probe bit_selector_probe.py 10/10, verdict SELECTOR-FOUND). (1) THE BIT IS INTEGRALLY VISIBLE [E]: the two 81-twins of the v567 audit (q32 = 2 = |Z2| vs q32 = 0) generate DIFFERENT integral orders -- Hermite bases differ at EQUAL index 81 and equal Smith divisors (1,1,1,3,3,3,3): real integral structure where every classical carrier-free invariant coincides. (2) THE SELECTOR [E]: the dominant mode of the sheet direction satisfies V_c (1,2,2c)^T = 2 (1,2,2c)^T identically in the coupling c; the LADDER SELF-CONSISTENCY -- the dominant mode reproduces its own eigenvalue as the geometric ladder (2^0,2^1,2^2) = (1,2,4) -- forces c = 2: on ALL 28 members of the v567 parabolic carrier-free class EXACTLY ONE satisfies it, the compiler Q, with no 81-pin and no column budget. (3) THE WITNESS IS PRIOR STRUCTURE [C] (no-free-pattern): (1,2,4) is the binary AnchorLadder step sequence p_{n+1} - p_n = 2^n (Lean-formalised), 2 = |Z2| the sheet datum, and the v566 trace code p_n(a) = 1 + tr(V^n) = 2 + 2^n rides the same ladder (n = 1..6 re-verified exactly). (4) THE SPLIT GEOMETRY LOCATED AND EXCLUDED [E]: an invariant module complement of the seam line exists IFF q32 = 1 (exact solve: a = 0, b = 1, q32 = 1; the plane span((1,0,0),(0,1,1)) exactly invariant there), and that member's direction algebra COLLAPSES to dimension 5 (Smith (1,1,1,3,3), no full parabolic, no 81): the seam-line + saturation demands admit ONLY nonsplit geometry -- the v566 A2 Ext arrow is NONZERO on the whole reconstruction class; neither twin splits (the complement system is inconsistent for q32 in {0,2}): the bit does NOT toggle split/nonsplit -- it toggles WHICH nonsplit integral order is realised and whether the dominant mode carries the full binary ladder. (5) PRIORITY-2 CANDIDATE TESTS [E], honest both ways: the mu4-grading candidate deg(E_jk) = g_k - g_j mod 4 FAILS (the order is not a graded sublattice: 5 of 7 Hermite vectors homogeneous) -- the review's kill condition does NOT fire and the 81 stays a FINGERPRINT pending a mechanism; left multiplication by V PRESERVES the order lattice and induces a canonical F3-linear action on the cokernel (Z/3)^4 -- the F3[V]-character computation is EXECUTED: the induced action has characteristic polynomial x(x-1)^2(x+1) mod 3 -- eigenvalues {0,1,1,-1}, NOT the regular mu4 pattern x^4 - 1 that 'one Z/3 per mark' would require (not even invertible), U acts as ZERO, and both twins give the identical structure: after two candidates (grading, V-action) the 81 stays a FINGERPRINT; the kill condition (no canonical local decomposition at all) is closer but not proven. NAMED LIMITS AS LOAD-BEARING CONTENT: the PHYSICAL selection is NOT derived -- why the dominant mode should satisfy the ladder self-consistency is the relocated open question, the same structural slot as the RP-selection of the alignment bit (v528/v534); the resonance between the reconstruction bit and the alignment bit is a TYPED OBSERVATION, not an identification; Stage B of v567 (GATE.QGEO.01) untouched; NO P2 reduction; AX.P2.01 and ANCHOR.GEN.01 markers untouched; the word 'derived' appears nowhere for any physics statement. [2026-07-31: the RP form is spectrally blind but integrally ANCHOR-VISIBLE on the twins (v572, Smith slot 18 vs 2 = 9 = N_fam^2); the dynamical RP-slot stays open; see DIAMOND.BIT.RPFORM.01.] [2026-07-31 II: the review's Ext-sensitive marked resolvent chi_Ext(z) = tr(P_seam R N_Ext R) vanishes IDENTICALLY for both twins with the natural markings (P_seam = E33, N_Ext = the radical lattice generators -- which are IDENTICAL between the twins: span{3E31, 3E32}); the review's own kill criteria fire -- the Gibbs pencil (v572) remains the one working marked object; sandbox record, no module.]
Recorded status: Identity [E] (exact integer/symbolic algebra -- Hermite/Smith lattice comparison, the symbolic dominant-mode identity, the uniqueness census on the 28-member class, the split-complement solve, the candidate tests) + [C] (the anchored ladder selector as candidate canonical selection; its physical justification open) + [O] (the selection mechanism; the F3[V]-character question; Stage B); verdict SELECTOR-FOUND; no marker moves
Dependencies, status detail and source
Canonical status: [E] twins integrally distinct (H0 != H2 at equal index 81); v(c) = (1,2,2c) identically; ladder self-consistency <=> c = 2, unique on 28/28; witness = AnchorLadder 2^n / |Z2| / trace code; split member q32 = 1 (complement solve a=0,b=1) collapses to dim 5 -- excluded; mu4-grading candidate fails (5/7 homogeneous); F3[V]-action computed: charpoly x(x-1)^2(x+1) mod 3, eigenvalues {0,1,1,-1} != regular mu4, U-action zero, twins identical; 11/11 checks; verdict SELECTOR-FOUND
Dependencies: QGEO.QRECON.01; DIAMOND.PARA.SELFCODE.01; DIAMOND.AXIS.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v10; v218; v528; v534; v566; v567
Scripts: v568_bit_selector_ladder.py
Location: tfpt_1;tfpt_2
Original CSV, line 607Original ledger status
QGEO.WINDING.SELF.01
Stage B of the No-Carrier-Reconstruction audit, first narrowing (one module, 11 checks, ~6 s; discovery probe stageb_winding_probe.py 12/12, verdict FORCED): the involution TYPE is killed by a rank theorem -- any involution with a two-dimensional positive eigenspace gives V' = Q P_- of rank <= 1 (char poly x^2 (x - t) identically in Q), so the binary trace code Spec V = {0,1,2} (v566) is unreachable: only the corpus type carries the self-code; (E) BOUNDS the winding normalisation (the winding demand forces the first column to (N,N,N), so q11 = N must itself be an A3 exponent -- N in {4,5,6} give EMPTY classes at the declared B = 6); the ladder self-consistency (v568) is ROBUST -- for every N in {1,2,3} it selects EXACTLY ONE parabolic member (28/16/14 -> 1/1/1); and the saturation self-consistency sat = N^4 (v567's (X) read as a self-consistency) holds ONLY at N = 3 (N=1: 32 != 1; N=2: 512 != 16; N=3: 81 = 3^4): the DOUBLE self-consistency pins (N, Q) = (3, compiler Q) uniquely across the whole N-ablated family -- N_fam = 3 relocates from declared input to consistency-forced within the reconstruction; equivalently the V-spectra {0,2,3}/{0,1,3}/{0,1,2}: only N = 3 carries the binary trace code p_n = 2 + 2^n. THE HONEST DECOMPOSITION (spectrum ablation): freeing the exponent spectrum itself, the surviving double-selfconsistent family is EXACTLY spectrum = {1,2,N} with shape Q(N) = [[N,1,0],[N,2,0],[N,2,1]] (the full 35-spectrum scan in the probe finds no other) -- the self-consistency forces the SHEET spectrum {1,2} (binary trace code) and the compiler SHAPE, and the A3 exponent demand (E) contributes exactly ONE datum, N = 3. REDUNDANCY -- (M) AND (L) FALL TOO: relative to the self-code demands (parabolic + ladder + sat = 81) the monodromy budget and the seam-line demand are REDUNDANT at the declared bound (dropping both widens the class to 1274 members and the self-code still picks exactly the compiler Q): the declared geometric input list shrinks to (S)-existence, (W)-form and (E) -- and THE MAXIMAL ABLATION drops (E) too: (W: column 3(1,1,1)) + integrality + the self-code package alone pin the compiler Q uniquely (29 ladder candidates, one hit): what stays declared is the involution EXISTENCE, the winding FORM and N_fam = 3 (independently anchored in the E8 glue, v1: 240 = 16 x 5 x 3); and the winding FORM's content is located exactly: dropping it entirely leaves a FOUR-element column family {(0,1,1),(0,3,3),(3,3,3),(5,1,5)} of which exactly ONE is uniform -- the compiler: the winding demand is precisely the UNIFORMITY of the column (1 of 4), a genuine declared input with sharply located content. NAMED LIMITS: (E) stays DECLARED ((M)/(L) relocate to redundant-given-the-self-code at B = 6) geometric inputs -- deriving them from mu4/D4/H^1 geometry is exactly the remaining GATE.QGEO.01 (narrowed by two items, NOT closed); NO P2 reduction, AX.P2.01/ANCHOR.GEN.01 markers untouched. [2026-08-01: the involution-existence input is DERIVED -- v590: rigidity (Z/2)^3, narrowing to a unique explicit S0 via the v574 type theorem plus two named demands; GATE.QGEO.01 narrows further; see QGEO.INVOL.01.]
Recorded status: Identity [E] + typed gate [C] (rank theorem symbolic; enumerations at declared bound; the remaining gate named)
Dependencies, status detail and source
Canonical status: FORCED: type killed by rank theorem; N <= 3 by (E); double self-consistency (ladder + sat = N^4) pins (N, Q) = (3, compiler Q) uniquely; 11/11 checks; (E)/(M)/(L) ALL redundant, winding form = the uniformity choice (1 of 4) at B = 6 -- the reconstruction needs only involution existence, winding form with N_fam = 3 (E8-glue) and the self-code; gate narrowed by FIVE items; GATE.QGEO.01 narrowed by two items, not closed
Dependencies: QGEO.QRECON.01; DIAMOND.BIT.SELECT.01; DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; v567; v568
Scripts: v574_stageb_winding.py
Location: tfpt_1;tfpt_2
Original CSV, line 610Open 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?