Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Quantum and boundary structure
The published foundation in this area
32 authored claim references lead into the original ledger and paper sections. This source record remains available even where no separate reviewed research packet is attached.
Finite E8, Pauli/Clifford, code, state, covariance, and instrument constructions supply internal quantum models and scoped guarantees. A code or successful channel is not yet a selected, repeatable physical source with the same parent dynamics.
Starting structure in the Atlas orientation
Concrete finite code and operator structures exist, with local results within explicitly specified source and instrument menus.
Which connection is sought
Open items include common physical preparation, source, interaction, repetition, record preservation, and connection to the TFPT parent.
How it connects
Codes and clocks specify internal information and symmetry structures; gravity additionally requires local geometry and dynamics.
Standard residual representation consequence and explicit counterexamples, not a new ontology. Distinguishability, repeatability, context reproduction and serial availability are separate assumptions. Separate L1/L2 from L3.
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Result
The separate benchmark assumptions give at least two continuation-distinguishable classes and preserve the selected report label under uninterrupted repetition. This largely restates the substantive repeatability premise rather than explaining physical origin. A test can preserve its report while incrementing a separately readable modulo3 counter; result repetition therefore forces no complete idempotence, preservation of all correlations, metric time or eternal material memory. Possible reports alone select no numerical weights.
Required assumptions
Explicit repeatable-distinction benchmark
Recognizable reports, reproducibility of a declared context and available serial continuations are separate commitments. The sharp benchmark additionally has an immediately result-repeatable test and two preparations with different certain reports. These conditions are stronger than mere observability; probability, free erasure, re-preparation, replica control or physical time are not assumed to follow.
Three countermodels, not an exhaustive classification of operational worlds. I/D assume probabilities/convexity; their numbers are predictions, not new measurements or physical dimensions. All-context equality follows analytically from linearity, not the finite word check.
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Result
Three explicit single-system theories satisfy the same sharp repeatability benchmark and are operationally inequivalent: R has two classes without mixing, I a classical simplex, D a square with nonunique decompositions. XZX preserves the first X report with probability1 in I and1/2 in D; D identifies both diagonal mixtures under all generated protocols while I distinguishes them by parity. All30 X/Z words through length4 were checked exactly. D has a classical hidden two-bit implementation of its generators; not all classical models are excluded.
Required assumptions
Explicit repeatable-distinction benchmark
Recognizable reports, reproducibility of a declared context and available serial continuations are separate commitments. The sharp benchmark additionally has an immediately result-repeatable test and two preparations with different certain reports. These conditions are stronger than mere observability; probability, free erasure, re-preparation, replica control or physical time are not assumed to follow.
Three explicit operational countermodels
R has deterministic preparation/read traces and continued partial-identity branches only, no primitive mixing or internal re-preparation. I is the classical two-bit simplex with probabilities and nondisturbing joint access. D is the square with explicit positive X/Z branches, square symmetries, preparations, mixtures and finite serial/adaptive closure. These selected rules define counterworlds rather than necessary physics.
Refinement of already reviewed diagnosis and explicit counterworld comparison of new classes; no refutation of all TFPT and no closure of a physical goal.
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Result
The checked origin attempts leave operation alphabet, state/correlation family and intervention rule unspecified. This motivates a methodology change but does not prove global underdetermination of all complete P1/P2 models: scalar/matrix comparisons change A, while A, state and time belong to the full source tuple. The four independent classes force neither a five-direction carrier,3+2,E8,quartic nor TFPT clocks. Compare TFPT only after their characterization.
Required assumptions
TFPT for later comparison only
The explicit research reset studies independent starting classes. E8, five,3+2, SM algebra, Yukawa data, Hilbert space, complex amplitudes and TFPT clocks are not inputs. Preserve existing TFPT results. After at most three failed origin attempts on unchanged premises change at least one fundamental premise or direction; coding bugs do not count. State assumptions, necessary consequences and newly explained properties.
Separate classes with separate premises, no shared physical derivation. Exact poset/endofunction censuses through size4 and elementary structural claims checked. Cycles do not select a canonical phase origin.
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Result
Event posets provide ideal states and possible histories but do not generally select growth weights. Supplied finite updates give cycles/transients and closed record cells relative to errors/observation; sink SCCs count maximal separated record cells, not necessarily exhaustive invariant record functions. Transformation monoids allow stable sectors, periodic steps and visible classical noncommutativity together; action and effects remain inputs. Counterworlds show these properties do not follow from composition or information alone.
Required assumptions
Finite event order as starting data
A finite strict partial order is supplied as event/precedence structure without metric, space, rates or probability. Order is an input in this class.
Supplied finite update, observation and errors
Finite X, deterministic step f and observation o, optionally error support T, are inputs. A record-cell system is a family of disjoint nonempty forward-closed observationally distinguishable sets, not automatically an exhaustive invariant partition.
Supplied finite operational action and effects
A transformation monoid acts on finite X; effects define operational distinguishability. Composition, action, effects and any selected time generator are separate starting data.
Complete bounded classification of three binary interfaces; no particle/generation/dimension interpretation. One-shot consistency does not force a fixed order.
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Result
Of 4096 no-self-influence candidates,744 are uniquely consistent under all64 local one-shot contexts.488 are acyclic; each of the remaining256 has an explicit reversible local two-copy control with zero or two fixed points (128 each). All744 process/order entries and256 witnesses were independently reproduced. The488 positive cases analytically work for all replica counts and arbitrary joint deterministic controls.
Required assumptions
Finite deterministic processes with full joint replica control
Supply finite nonempty local input/output sets and total w:product O->product I. Every finite number of coordinatewise independent replicas allows every joint deterministic map I_k^M->O_k^M at corresponding interfaces, including constants/erasure. Require at least one global solution for every such experiment; do not assume a global order.
General elementary finite deterministic theorem, mathematically reviewed twice. Arbitrary encoders, decoders and erasure are used; no general reversible two-copy theorem. Interfaces are not derived events. No novelty priority claim.
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Result
For arbitrary finite alphabets/interfaces, existence under every finite joint local replica control, uniqueness under every such control, acyclic static influence and compatibility with at least one fixed total order are equivalent. A directed cycle of length m allows at most m copies with separately sensitized edges and odd XOR feedback without a solution. Acyclicity gives unique triangular recursion. No unique total order or physical time is selected.
Required assumptions
Finite deterministic processes with full joint replica control
Supply finite nonempty local input/output sets and total w:product O->product I. Every finite number of coordinatewise independent replicas allows every joint deterministic map I_k^M->O_k^M at corresponding interfaces, including constants/erasure. Require at least one global solution for every such experiment; do not assume a global order.
Exact algebraic equivalence of original unmarked pairs and covariance of full passive form transport. No claimed physical P1 symmetry, spatial mirror interpretation of detG, or independently produced source normalization. Original fixed source form and reader still distinguish marked realizations.
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Result
Actual v568 pairs (U0,V0) and (U2,V2) have simultaneous GL3(Z) intertwiner G=[[1,0,0],[0,1,0],[0,2,-1]], G²=I,detG=-1, commuting with Sigma and fixing the specified winding data while sending leading vector (1,2,0) to (1,2,4). All simultaneous intertwiners are tG. The fixed theta(A)=Sigma A^T Sigma is not preserved and its reflected word gives4/8; transporting the entire form gives4/4. Explicit linear intertwiners connect the original three-rate clock to both Qplus/3, so rates alone do not select a twin.
Required assumptions
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.
Exact finite original case. No nonexistence of B_N, selected continuum state or E8 refutation. Previous energy test uses twist1 without zero modes and is unchanged. Numerical norm diagnostics normal and -OO byte-identical; independent proof review and rerun accepted.
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Result
On unchanged v988 Nx16 Ny6 M1, explicit integral boundary zero vectors, modular ranks over F65537 and exact sign pairing prove ranks190/192/192/192. Periodic counts are95 negative,95 positive,2 zero; other twists96/96/0. Original covariance C=Pminus+Pi0/2 differs from pure occ_frame projector P=Pminus+Q with rankQ1 in the nullspace: norm(C-P)HS²=1/2 and norm(C-C²)HS²=1/8. Both original functions are valid and deliberately distinct. A state-preserving microscopic dictionary cannot silently exchange these periodic states.
Required assumptions
Actual periodic v988 state and occupied frame
Keep unchanged qwz_cylinder, occ_frame and fermi_cov at Nx16 Ny6 M1 and original twists0,1,2,3. Compare their actual finite CAR covariances. Physical selection of either state or equality with the E8 vacuum is not assumed.
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.
Only this proxy-fitted constant in this actual finite original case is excluded. The formula is exact; numerical values are checked to1e-9 tolerance. Larger constants, separate historical value2.86 and general continuum estimates are not excluded.
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Result
On unchanged v988 data Nx16,Ny6,M1 the twist1 Slater state against h0 has exact variance formula Tr(P h0(1-P)h0P)=||(1-P)h0P||HS^2. Numerically it gives7.0875042817 and first excitation norm2.6622367065. The original first central sum proxy is identically0; its fit C=1.2040009128 gives C^2=1.4496181980 and already fails to bound the actual norm here.
Required assumptions
Literal charged scaling contract and original Slater case
Audit actual H_N, Psi_lambda,N and bosonic refinement definitions in the original charged scaling contract and unchanged v988 qwz_cylinder/occ_frame functions at Nx16,Ny6,M1, h0 at twist0 and Slater state at twist1. This audits that source path and finite energy case, without assuming microscopic bosonization or a uniform continuum bound.
Source audit of this particular original path. No nonexistence claim for B_N and no rejection of the established P1/P2 compiler or mathematical E8 field extension.
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Result
The original charged scaling contract starts with H_N as the actual QWZ/CAR GNS space and declares Psi_lambda,N by a normal boson exponential. Its concrete refinements I_charge tensor Gamma_s(j) act instead on a separately chosen bosonic lattice Fock space. No microscopic B_N between these systems with B_2N J_N,2N=V_N,2N B_N and state, energy, parity, sector and localization compatibility is constructed there. The exact charge-lattice isometry F(2q)=lambda does not replace this field morphism.
Required assumptions
Literal charged scaling contract and original Slater case
Audit actual H_N, Psi_lambda,N and bosonic refinement definitions in the original charged scaling contract and unchanged v988 qwz_cylinder/occ_frame functions at Nx16,Ny6,M1, h0 at twist0 and Slater state at twist1. This audits that source path and finite energy case, without assuming microscopic bosonization or a uniform continuum bound.
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.
Stipulated E8_1 lattice vacuum representation. Bosonic currents are not identified with elementary4D fermions or native CCR mediators. Internal quarter grading is not physical quarter time. Contact terms, Z[0], absolute phase and original P1 Phi-dependence do not follow from these normalized coefficients.
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Result
The executable E8 dictionary contains240 root vertices and8 Cartan currents with cocycle, adjoint signs and quarter grades60/64/60/64. The vertex formula and Cartan Ward recursion determine all separated current coefficients of the normalized source series. Mixed spinor currents have5/8+3/8=1; the checked connected four-point response is nonzero. Standard lattice theory implemented and independently checked here, not a new physical interaction.
Required assumptions
Reverse selection in the discrete closure framework
The origin paper discrete E8 closure framework with rank, family, spinor and simple-current conditions is given. Its numerical fixed-point identities are not identified with a physical operator realization.
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
Quarter phase is retained
Comparisons retain the original charged quarter phase; switching to another phase branch is not an admissible solution to the selection problem.
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.
Source audit of the specified reverse chain. No retraction of numerical self-consistency and no independent derivation of the framework.
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Result
Origin954–981 and v6/v15/v350–v352 recover g_car=5 and eight within the chosen closure framework; v154 supplies the conditional local extension. The checked v350–v352 functions do not construct Phi-dependent D_rel/D_ref or physical insertion operators. This scopes those calculations, rather than asserting general impossibility.
Required assumptions
Reverse selection in the discrete closure framework
The origin paper discrete E8 closure framework with rank, family, spinor and simple-current conditions is given. Its numerical fixed-point identities are not identified with a physical operator realization.
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.