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The original technical record remains available here. For explanations, reviewed conclusions and the history of research questions, start with the knowledge atlas.

Research snapshot 2026-11-02 · 783 active ledger claims · 706 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.

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What does this inventory cover?

Every one of the 783 active ledger IDs is included. All 788 ledger rows, including superseded rows, remain in the download. The reviewed research corpus contains 707 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.

The scientific findings include 515 established scoped results, 63 conditional results and 128 scoped exclusions. These labels describe the recorded finding. They do not upgrade its parent physical goal or overwrite the original ledger.

Sources were matched to their recorded hashes and line ranges at this snapshot. Bounded text excerpts make sources available even when a source is not in the earlier public release. Any omitted administrative lines are explicitly marked. This is source coverage, not a new execution of Python, Lean or Wolfram proofs.

Atlas revision 4d8fcdb3587f8e4cc0898e5c · snapshot SHA256 7c23438352ba021cef5aa0999c31e5c242fbc6ed12b172e4d35fb6a68f65dbb4

3 matching records · page 1 of 1

Original ledger status

TOPO.BRIESKORN.01

TOPO.BRIESKORN.01

BRIESKORN CAPSTONE (2026-06-17): the (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its three exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). (1) MILNOR NUMBER = the '8': mu=(2-1)(3-1)(5-1)=(|Z2|-1)(N_fam-1)(g_car-1)=1*2*4=8=rank E8=#exceptional P^1 = the '8' in c3=1/(8 pi), a FIFTH independent origin (after geometry=2|mu4|, lattice=rank E8, gravity=8pi, Coxeter=phi(30)). (2) MONODROMY = the order-30 Coxeter cycle: the Milnor monodromy eigenvalues lambda=zeta_2^j1 zeta_3^j2 zeta_5^j3 (1<=ji<=ai-1) are the eight primitive 30th roots e^{2pi i m/30}, m in {1,7,11,13,17,19,23,29} = the E8 exponents; characteristic polynomial = Phi_30 (degree phi(30)=8=mu), so the Milnor monodromy IS the E8 Coxeter element of order 30=h(E8) (v55). (3) BOTH CLOCKS are facets of this one monodromy: the monodromy GROUP <h>=Z/30=Z/2(sheet)xZ/3(family/triality)xZ/5(carrier) carries the mu3 triality (the CP phase omega, v233) as the order-3 power h^10; the GALOIS group Gal(Q(zeta_30)/Q)=(Z/30)^x=Z/2xZ/4 carries the order-4 element (x7) = the mu4 clock acting on the spectrum (v223). (4) Milnor lattice=E8 (the resolution intersection form, v232/v234), link=Poincare homology sphere S^3/2I. (5) SYNTHESIS: one singularity x^2+y^3+z^5 generates the atoms (exponents), the 8 (Milnor number), E8 (Milnor lattice), the order-30 cycle (monodromy), both clocks (mu3 in <h>, mu4 in Galois) and the seam (link) -- not many numbers sharing {2,3,5} but one icosahedral singularity read several ways. Unifies the icosahedral round; does NOT close a gate.

Recorded status: Lattice/Topology (exact) [E]/[I]

Dependencies, status detail and source

Canonical status: [E] mu=(2-1)(3-1)(5-1)=8=rank E8 (5th origin of the '8'); Milnor monodromy eigenvalues = E8 exponents/30 = the order-30 Coxeter cycle (charpoly Phi_30); both clocks = mu3 in <h>=Z/30 (CP) + mu4 in Galois (Z/30)^x; one singularity generates the skeleton [I]

Dependencies: MCKAY.E8.01; COX.CLOCK.01; CP.TRIALITY.01; TOPO.E8.01; SEAM.COX.01

Scripts: v236_brieskorn_capstone.py

Location: origin_theory

Original CSV, line 322

Original ledger status

OVERDET.WITNESS.MAP.01

OVERDET.WITNESS.MAP.01

The multiply-vs-compress FRAMEWORK for over-determination (2026-06-25; classification refined by v428/OVERDET.WITNESS.RECLASS.01): a reviewer's methodological correction made machine-explicit -- 'every independent restriction multiplies the implausibility of coincidence' is true ONLY for witnesses from genuinely DISJOINT grammars; witnesses that are projections of the SAME generator count as COMPRESSION, not Bayesian multiplication. [E] SEVEN GRAMMAR READOUTS, each computed from its own syntax and landing on the carrier skeleton: Gauss Z[i] N(3+2i)=13; Eisenstein Z[w] N(3+2w)=7; cyclotomy Q(z5) N(3+2 z5)=55; Galois |Gal Q(z5)|=4; root lattice |det Cartan(E8)|=1; Pascal/exterior C(4,<=2)=11 with 2^4=16=dim S+; Coxeter h(E8)=30=2*3*5 with phi(30)=8=rank E8. [E] SYNTACTIC DISTINCTNESS != INDEPENDENCE: by v236 (TOPO.BRIESKORN.01) these seven are facets of ONE (2,3,5)/E8 object, so they COMPRESS (settled in v428), like the anchor a=(1,1,2) emitting (e1,e2,e3)=(4,5,2)+power sums+the E8 data from one generator. [C] VERDICT: the framework stands but the classification of the seven is refined by v428 -- the genuine multiplicative strength is the multiply-forced inputs (the '8' four independent ways) + foreign witnesses (alpha^-1~137), not the seven readings; coincidence is still an expensive explanation of the discrete core, but this does NOT by itself establish physics (the seam/anchor/transfer bridge problem).

Recorded status: Witness map [E]/[C]: disjoint grammars multiply, same-generator projections compress; the seven arithmetic witnesses are refined by v428 to COMPRESSION (facets of one (2,3,5)/E8 object, v236). The genuine multiplication is the multiply-forced inputs + foreign witnesses (alpha^-1~137); coincidence is expensive for the discrete core; does not by itself establish physics

Dependencies, status detail and source

Canonical status: Numerical

Dependencies: E8.REVERSE.AUDIT.01; ARITH.HULL.01; SEAM.GALOIS.01; CAR.PASCAL.01; TOPO.BRIESKORN.01; ARCH.CORE.01; v415; v417; v418; v419; v422; v45; v53

Scripts: v427_overdet_witness_map.py

Location: tfpt_safeguards

Original CSV, line 494

Original ledger status

OVERDET.WITNESS.RECLASS.01

OVERDET.WITNESS.RECLASS.01

The honest correction of v427 (2026-06-25): applying v427's own multiply-vs-compress test to v427 itself. [E] THE ONE GENERATOR (v236/TOPO.BRIESKORN.01): the (2,3,5) Brieskorn singularity generates E8/Coxeter-30 -- Milnor mu=(2-1)(3-1)(5-1)=8=rank E8, 30=2*3*5=h(E8), phi(30)=8. [E] WITNESS RE-CLASSIFICATION: each of v427's seven witnesses maps to a facet of that SAME object (primes 2,3,5 of 30, the clock 30, or E8), so all seven collapse to ONE generator (distinct objects=1) => COMPRESSION, not seven independent multiplications. [E] THE GENUINE MULTIPLICATION: the '8' in c3=1/(8 pi) forced four independent ways -- rank(E8), the carrier Coxeter h(D5)=2(5-1), the totient phi(30), the Milnor number -- plus the FOREIGN witness alpha^-1~137 (prime, not in the (2,3,5)-skeleton; v305). [C] VERDICT: v427's framework is right, its classification was wrong -- the arithmetic witnesses compress one (2,3,5)/E8 object; the honest over-determination is the multiply-forced inputs + foreign 137. Refines and partly walks back v427; consistent with v236/v305/v313.

Recorded status: Witness re-classification [E]/[C]: v427's seven arithmetic witnesses are facets of ONE (2,3,5)/E8 object (v236) => compression, not seven multiplications. The genuine multiplication is the '8' forced four independent ways (rank E8, h(D5), phi(30), Milnor) + the foreign alpha^-1~137. Honest correction of v427 (consistent with v305/v236/v313)

Dependencies, status detail and source

Canonical status: Identity

Dependencies: OVERDET.WITNESS.MAP.01; TOPO.BRIESKORN.01; ARCH.CORE.01; v305; v313

Scripts: v428_overdet_reclass.py

Location: tfpt_safeguards

Original CSV, line 495

Open questions preserve their achieved subresults

Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.

Future quotient and positive GNS reconstruction

What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?

  • Resolved in scope: Future quotient from complete rRead result
  • Resolved in scope: Conditional GNS reconstruction from supplied KRead result
  • open: Select complete K from the original source
Historical: common source, state and event selection

Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?

Seam connection and family action

Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?

  • Resolved in scope: Separate classes from actual transportRead result
  • open: Derive the common connection from the original source
Physical time and complete transfer

Do the original reflection/projector structures determine the full physical time generator and required field transfer?

  • Resolved in scope: Reuse the sign-projector counterexampleRead result
  • Resolved in scope: Reuse conditional full-transfer reconstructionRead result
  • open: Identify the physical complete TFPT transfer
  • Resolved in scope: Reuse complete collar reconstructionRead result
  • Resolved in scope: Classify homogeneous GKLS embedding of the shared register familyRead result
  • Resolved in scope: Decide every homogeneous GKSL logarithm of the fixed M4 channelRead result
Flavor ratio and absolute amplitude scale

Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?

  • Resolved in scope: Reuse the derived flavor ratioRead result
  • open: Determine the absolute holonomy amplitude
Alpha closure for fixed inputs

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

  • Resolved in scope: Separate root calculation from source selectionRead result
  • open: Derive alpha inputs and Thomson transfer
  • Resolved in scope: Establish the unique global positive rootRead result
Geometric flow and gravity normalization

Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?

  • Resolved in scope: Record scope of fixed original functionalRead result
  • open: Derive geometric modular response and area coefficient
Clocks and complete neutral source response

Which complete quadratic response can the actual clock images reconstruct?

  • Resolved in scope: Reconstruct all neutral quadratic matrix directionsRead result
  • open: Derive physically admissible probe access
Clock action on charge, time and quarter transition

How does the actual Gaussian J act on the complete marked source?

  • Resolved in scope: Construct original J lift with complete time/charge actionRead result
  • open: Derive physical meaning of the frame orbit
Which responses distinguish charged time action?

Which data separate sources with identical complete neutral vacuum response?

  • Resolved in scope: Determine twist blindness completelyRead result
  • Resolved in scope: Reconstruct twist from charged responsesRead result
  • open: Derive actual charged source probes
Which seam action distinguishes native opposite charges?

Can existing native charge fields produce the quarter-twist time response of the seam?

  • Resolved in scope: Check native fields and response discriminatorRead result
  • open: Derive actual marked seam/state action
Constructive seam search: operators, state and source compatibility

What does the complete phase search decide, and which additional state information prevents a false source solution?

  • Resolved in scope: Finite search closed, actual winding and parity equivalenceRead result
  • Resolved in scope: Positive finite-word state extensionRead result
  • Resolved in scope: E8 current group conditionally determines the P signRead result
  • Resolved in scope: The same shift functional hides distinct ground statesRead result
  • Resolved in scope: No phase hit realizes the unchanged sourceRead result
Which partner actually belongs to the original seam?

Which charge, state type and time action belong to the root partner and original sheet pairing?

  • Resolved in scope: Concrete pair operator; source neutrality is not hypercharge neutralityRead result
  • Resolved in scope: Fixed quarter time splits the color/weak multipletRead result
  • Resolved in scope: Explicit conjugation for the existing sheet pairingRead result
  • Resolved in scope: Actual partner map between quarter domainsRead result
  • Resolved in scope: Bilinear sheet pairing is not Hermitian kernel selectionRead result
  • Resolved in scope: Actual quarter conjugation transports the supplied markingRead result
  • Resolved in scope: No time-stabilizing orthogonal repair of the fixed markingRead result
  • Resolved in scope: Spinor16 is a state sector, not a 16-real one-particle fieldRead result
Automated construction of operator maps and sources

Which tools generate operator maps, learn counterexamples, and can search for the full positive source?

  • Resolved in scope: Calibrate new search without supplying the target mapRead result
  • open: Synthesize a joint field, marking and transfer dictionary
  • open: Search for the positive common source kernel itself
  • Resolved in scope: Automatically construct, certify and distinguish finite kernelsRead result
  • Resolved in scope: Repair search conditions against source types and collar controlsRead result
  • Resolved in scope: Reconstruct multi-field sewing of the canonically identified boundary sourceRead result
  • Resolved in scope: Retain absolute reference amplitude in searchRead result
  • Resolved in scope: Integrate supplied free source including boundary response and scalarRead result
  • Resolved in scope: Convert the full finite CAR kernel into a link functionalRead result
  • Resolved in scope: Close original recursive word reconstruction with memoryRead resultRead result
  • Resolved in scope: Retain whole original caller through scale and readoutRead resultRead result
  • Resolved in scope: Execute actual shared Higgs source with full matter words and local RPRead resultRead result
  • Resolved in scope: Reduce whole constant original Higgs spectral fiberRead result
  • open: Resolve original geometric Higgs residue sign and field map
  • Resolved in scope: Evaluate local original Higgs heat identification and whole finite consumerRead resultRead result
  • Resolved in scope: Execute whole variable bound Higgs reference and original scale mapRead resultRead result
  • Resolved in scope: Execute whole inner Higgs scale/source and normal kernel transportRead resultRead result
  • Resolved in scope: Execute given whole superconnection and normal spectral readerRead resultRead result
  • Resolved in scope: Determine own-admissibility and whole total-chiral spectral readersRead resultRead result
  • Resolved in scope: Derive whole scale-energy map,normal profile and relative flowRead resultRead result
  • Resolved in scope: Execute original Green energy producer and mixed scale readoutRead resultRead result
  • Resolved in scope: Match current action argument and common Higgs/gravity weightsRead resultRead result
  • Resolved in scope: Execute whole original curvature consumers and Higgs radial sourceRead resultRead resultRead result
  • Resolved in scope: Execute original whole four-ghost source and geometric type testRead resultRead result
  • Resolved in scope: Execute original moving normal kernel derivative and whole source responseRead result
  • Resolved in scope: Decide fixed original O1 source and normal operator placementRead result
  • Resolved in scope: Compare whole Higgs mixture and covariance reader on invariant four-field witnessRead result
  • Resolved in scope: Test exact bounded cutoff on whole ordinary Higgs volumeRead result
  • Resolved in scope: Test whole original circle joint mode and IR Higgs normalizationRead result
  • Resolved in scope: Test original O1 mode covariance against whole Higgs-law classRead result
  • open: Reconstruct original localization from the whole process
  • Resolved in scope: Test bare native-code word compression against actual localityRead result
  • Resolved in scope: Decide original geometric local-time class and execute actual interval readerRead resultRead result
  • Resolved in scope: Execute actual regional two-face partner and supported charged wordRead resultRead result
  • Resolved in scope: Execute original color marginal, modular field law and complete class readerRead resultRead resultRead result
  • Resolved in scope: Reconstruct common Higgs law from whole original quarter source towerRead resultRead resultRead result
  • Resolved in scope: Execute original record action on Doily and ordered whole source responseRead resultRead resultRead resultRead result
  • Resolved in scope: Locally implement original record process and test unchanged exterior sourceRead resultRead resultRead result
  • Resolved in scope: Execute original elliptic insertion,whole source and causal responseRead resultRead resultRead result
  • Resolved in scope: Evaluate actual joint Higgs and color group sourceRead resultRead result
  • Resolved in scope: Execute whole original graph color reader with typed original center selectorRead resultRead result
  • Resolved in scope: Execute original color fixed source and first inherited grading testRead resultRead result
  • Resolved in scope: Execute actual original color-spinor CAR four-word and complete spin-sector sewingRead resultRead result
  • Resolved in scope: Decide actual color admissibility of density operations and coordinate regionsRead resultRead result
  • Resolved in scope: Execute actual whole seam-operation class and two-face responseRead resultRead result
  • Resolved in scope: Execute entire original C6 word expansion with source amplitudeRead resultRead result
  • Resolved in scope: Execute original collective Higgs force source and entire mean dualRead resultRead resultRead result
  • Resolved in scope: Execute original all-mode force with actual time and whole sourceRead resultRead result
  • Resolved in scope: Execute original local space/time force source and causal liftRead resultRead result
Origin reverse selection, field dictionary and original P1 kernel

What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?

Observable reality: minimal conditions and counterworlds

Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?

Formal carrier core: unbounded Pascal uniqueness and finite glue

Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?

  • Resolved in scope: Classify the unbounded Pascal proofRead result
  • Resolved in scope: Classify the formal finite glue scopeRead result
Active mathematical program: marked seam monodromies and lattice lifts

Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.

  • Resolved in scope: Define marked seam category and factor formulaRead result
  • Resolved in scope: Completely classify quarter-clock four-puncture liftsRead result
  • Resolved in scope: Determine central class and all subgroup restrictionsRead result
  • Resolved in scope: Determine full G0 cocycle and classRead result
  • Resolved in scope: Determine native4/5/6local cohomologyRead result
  • Resolved in scope: Classify unrestricted G31 reflection monodromiesRead resultRead result
  • Resolved in scope: Determine lift class beyond G0Read result
  • open: Classify additional reflection/clock equivariance and mapping-class quotients
  • Resolved in scope: Equivariant lifting and divisibility by eightRead result
  • Resolved in scope: All62clock obstructions and central transport variantsRead result
  • Resolved in scope: Actual group comparison and central pushout exclusionRead result
  • Resolved in scope: Complete invariants and explicit collisionsRead result
  • Resolved in scope: Compare E6 and E7 slices with the actual quarter clockRead resultRead resultRead resultRead result
  • Resolved in scope: Classify original character-valued G31monodromy liftsRead resultRead result
  • Resolved in scope: Determine E7-pair action on all original lattice fieldsRead result
  • Resolved in scope: Completely connect E6/E7 cuts to the original compilerRead result
  • Resolved in scope: Compare common covers and actual clock carriersRead result
  • Resolved in scope: Prove shared representation consequence for48,4/3 and5/4Read result
  • Resolved in scope: Completely decide joint compiler-field-cover constructionRead resultRead resultRead resultRead result
  • Resolved in scope: Reconstruct canonical local compiler field source from C4Read resultRead result
  • Resolved in scope: Eliminate redundant sector and multiplicity assumptionsRead result
  • Resolved in scope: Classify native equivariant markingsRead result
  • Resolved in scope: Classify pure quarter clock mapping class quotientRead result
  • Resolved in scope: Determine complete cut algebra and lossless tetrahedron transformRead resultRead resultRead resultRead result
  • Resolved in scope: Completely compare scalar glue and actual native compiler classRead resultRead resultRead resultRead result
Common clock sectors, quartic geometry and operational reconstruction

Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?

Automatic response search with original-source decision

Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?