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 All 788 ledger rows, including superseded rows, remain in the download.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 785 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.
The scientific findings include 587 established scoped results, 63 conditional results and 134 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 85a73be77d6a100b54e15e8b · snapshot SHA256 a38278550b16a82e80bddb59fff74ce50f5d97a91b1b21933ae7d7c15dc10134
Established within the stated premises
finding:craig-fixed-product-free-operator-equality-fails
At the same free p=(pi/2,0,0,0),a1 the ordinary product gives K=i gamma1 pi/2, actual Craig D=1+i gamma1 and Cayley-required D(1-D/2)^-1=2i gamma1. The fixed Cayley identity fails. Nor can a two-sided unitary chiral map identify the distinct singular values pi/2 and sqrt2. A_-^dagger A_-=I2/2 yields Berezin Jacobian magnitude2 per two-dimensional Weyl fiber with unchanged anti-leg. This example and an independently formed product action do not compute the whole original TFPT measure identity.
Scope: Exact counterexample to the specified unblocked ordinary product identification at the stated momentum. No exclusion of derived nonunitary blocking, other regulators, continuum equivalence or TFPT; no already produced TFPT lattice kernel assumed.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Compatible GW operator and Berezin domain
Mathematical scope: finite gamma5 Hermitian GW operator with coefficient1 and actual compatible ordered fermion spaces. Inverse formulas apply only on a common invertible domain; fulfillment by the original TFPT source is not assumed.
premise:craig-finite-gw-compatible-source-domain
Established within the stated premises
finding:craig-color-selector-requires-whole-exterior-kernel
On the existing original Splus16 CAR representation the Z3 center selector has rank21856 in the65536D exterior space,degree-one rank4 and degree-two rank42. No one-particle projection can generate it by exterior lifting: degree one forces p0,whose whole rank is16 and degree-two rank6. All84 original v252 matrix directions commute with color center. On any genuinely compatible conditional quadratic CAR transfer the whole center kernel is exactly Kc(barv,u)=1/3 sum exp(barv z^k R_b u). Thermal terms have boundary conditions psi(beta)=-z^-k psi(0) and explicit Green inverses. Selector coefficients are boundary operations,not thereby derived local bulk vertices.
Scope: Actual center rule on the named existing CAR realization and explicit conditional transfer application;no primitive carrier/Padm/field identity established. Remaining selectors,dynamic bosons,reference and R068 whole diagonally neutral Slater source retain their types. No extra96 CAR duplication,new source or physical promotion.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:craig-flat-color-sector-average-breaks-gw-and-chirality
Actual Craig Eq16 on the periodic flat one-site4torus with temporal SU3 center z0^k=diag(omega^k,omega^k,omega^k,1,1) embedded in SU5 gives triality-one D0=0,D1=3I/2+i sqrt3 gamma4/2,D2=3I/2-i sqrt3 gamma4/2. All plaquettes areI,HW²=I and all three GW/projector identities hold. Mean D=I has GW residual gamma5;mean hatPminus=I/2 has projector defect-I/4. Projection must transport whole sources with their own operators,field spaces and measures. Operator averaging is not valid source averaging.
Scope: Exact counterexample only to naive operator/projector averaging on the specified actual flat Craig background. Does not exclude whole-source sums or derived blocking or prove original TFPT/GW equality.29 checks of the addendum pass,no Lean validation or ledger promotion.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Compatible GW operator and Berezin domain
Mathematical scope: finite gamma5 Hermitian GW operator with coefficient1 and actual compatible ordered fermion spaces. Inverse formulas apply only on a common invertible domain; fulfillment by the original TFPT source is not assumed.
premise:craig-finite-gw-compatible-source-domain
Established within the stated premises
finding:cyclic-genesis-press-identification-and-source-gap
Carroll/Diachenko/Dulani2605.30405v1 of28May2026 matches BILD4October2026 and September/October coverage, although the specific press article is not uniquely identified. The source imposes commensurate energy gaps and a low thermodynamic entropy state, while its spacetime map remains conjectural. Their selection and a spatial Genesis point are not derived. Unitary whole-state return differs from collapsing distinct orthogonal states to a single whole state; the latter does not preserve inner products.
Scope: Original paper SectionsII,III,V,VI and traced press attribution; no observational confirmation or independent full validation of observer estimates.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:original-genesis-family-transfer-not-carroll-cycle
Original v395 _family_M has spectrum1,2/3,1/3 and determinant2/9. Whole positive powers are not I and no invertible similarity makes it unitary. Under the additional Euclidean identification M=exp(-tau H_M), gaps log(3/2)/tau and log3/tau are incommensurate: a rational ratio m/n would force3^(n-m)=2^n. Thus this whole H_M has no nontrivial exact real-time period. This does not identify H_phys or exclude general TFPT/cosmology. The physical connection must evaluate the original energy support and same-source geometry response from S/Z.
Scope: Only actual internal v395 family operator,5 exact matrix checks and analytic prime-factor proof. Existing Perron fixed point, P1 carrier/3/5 views and other clock results retained; no new model choice or physical completion.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - 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
Established within the stated premises
finding:constant-inventory-has-three-independent-dimensionless-readouts
For c,hbar,G,kB,e,me,epsilon0,rho_energy the dimension matrix has rank5 and nullity3, with alpha, Gme²/(hbar c) and rho_energy hbar³/(me⁴c⁵) as a basis. Existing TFPT vacuum u=(8pi)² alphaG_e² I_vac. The Einstein de Sitter rewrite S/kB=24pi²/u=32pi⁴exp(2/alpha) is conditional and not independent evidence. The supplied alpha contract gives u=7.1253295267e-121. SI definitions do not derive a common physical action.
Scope: Exact dimensional statement only for the named inventory; existing alpha/vacuum formula is input, SI numbers use CODATA2022, Planck2018 is only a dated illustration without a current fit or covariance test. No new prediction or source derivation.
Required premises and original source excerpts
- 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 - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:relative-single-heat-product-cannot-match-small-vacuum-and-finite-einstein-at-unit-profile
In the explicitly chosen ordinary4D Spin Dirac product with arbitrary constant selfadjoint M,Mref and the same covaried metric,trace,rankN, the relative heat response factors: T=Tr exp(-M²/chi²)-Tr exp(-Mref²/chi²)<=N; V=m0chi⁴T/(4pi²), Mbar²=m0chi²T/(24pi²). Positive Einstein response requires T>0 and V/Mbar⁴>=144pi²/(m0N). At N96,m0=1 this gives14.8044 instead of7.12533e-121. T=0 also removes Einstein. All constant masses are resummed. A numerical rank2 relative Poisson witness has DeltaA2=0,DeltaA1=0.5262558>0 and prevents generalization to all relative profiles; its freely chosen spectra are not a TFPT candidate.
Scope: Analytic statement under ordinary4D product geometry, constant internal masses, squared-argument F(u)=m0 exp(-u), and direct classical bulk matching. Exact in all masses, only the first local curvature coefficient. No claim about full dynamic boson integration, quantum corrections, other original reference maps or the general TFPT source. R044/R045 is retained; new is the joint vacuum test with full constant mass dependence. No ledger promotion.
Required premises and original source excerpts
- Conditional equal-rank heat product with constant masses
Additionally chosen ordinary4D Spin Dirac product,constant selfadjoint internal M and Mref,same covaried metric and trace,rankN; exactly F(u)=m0 exp(-u),u=D²/chi²; volume and Einstein bulk coefficients solely from this relative classical source without other contributions. No claim that P1/P2 or original S_adm selects these premises.
premise:equal-rank-co-metric-constant-mass-single-heat-direct-classical-source - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
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: derived terms, unique root and physical EM identification
Where do the factors and closed alpha equation come from, which provenance steps are proved, and which precise physical EM identification remains open?
- Resolved in scope: Separate root calculation from source selectionRead result
- open: Derive the actual EM functional variation and Thomson identification
- 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 joint origin hypotheses and source responses
Which simple joint rules connect the existing P1 source chain,double cover,information and compiler,and which whole candidate classes can be decided automatically using actual source consequences?
- Resolved in scope: Decide even-matter word class and check actual AI operator expressionsRead resultRead result
Existing TFPT derivations and correction of repeated gap diagnoses
Which common source/reconstruction chain already exists in the old original papers, and which purported global gaps arose from reducing P1 or choosing an optional CAR route?
Complete physical Hamiltonian source with Gauss sector and thermal word limit
Which whole source is constructed on the original local Hamiltonian route, how do physical constraints and thermal words follow, and how is its actual IR response distinguished from the original covariant geometric source branch?
Original TFPT source versus DET16 mirror vertex
Does the same original TFPT source produce the concrete DET16 generator and whole responses,or is a computable parent supplied as extra input?
Whole original source and canonical vacuum attachment
Which vacuum joins are already in the whole original source,and how do H ground source and R104 field/Gauss source join completely without second state choice or parent change?
Craig chiral measure and the original whole TFPT source
Which concrete operator and Berezin measure map preserves the original TFPT source when connecting Craig overlap measure?
- open: Compare original4D fermion Hessian and measure line with Craig
Cyclic quantum universe and original Genesis connection
Does original TFPT dynamics yield the exact cyclic quantum return in the September/October press lead and a geometric Genesis transition?
- open: Test periodicity and Genesis response on the same whole source
Physical constants as joint constraints on the TFPT source
Which independent constants constrain the original common source, and can one relative heat product supply gravity and vacuum energy together?
- open: Evaluate original volume, curvature and gauge responses together