157 sections found. Current publication documents are listed before historical material.
tfpt research contracts · Research contracts
tocsectionResearch consolidation: source fields and dynamics (2026-09-09) Status and provenance. The research archive after Round 27 is now integrated, including the Round 28–50 development chain and the subsequent named branches. These are written, model-specific arguments accompanied by executable controls, not newly formalized or independently reviewed theorems. All physical T1–T8 gates and TFPT.TOE.COMPLETE.01 re
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 2 to 15
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
tfpt research contracts · Research contracts
Fix the original complex, number-conserving QWZ strip at width eight, mass one and holonomy sector [formula in source] . Its one-particle space has dimension [formula in source] over [formula in source] ; it is not the compiler's sixteen real Majoranas. Write [formula in source] for its negative-energy projector of rank [formula in source] and [formula in source] for the actually filled sea. Set [formula in source] H
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 16 to 96
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
For the same strip and filled projector, the alternating four-word [formula in source] cancels the outer history ramps. Normal ordering is the actual finite-sea trace subtraction. Positive heat regularization, Jensen and Cauchy–Schwarz give uniform [formula in source] bounds for [formula in source] on the full four-endpoint torus, including collisions. They promote the separated-point limit to an [formula in source]
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 97 to 114
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
A different, explicitly declared compact- [formula in source] rotor/CAR test parent keeps [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] and all integer electric fluxes. It is not selected by the TFPT compiler. The all-electric source majorant has contraction [formula in source] The subsequent all-observable argument counts all three vertices of each two-st
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 115 to 158
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The charge-sign quotient [formula in source] loses commutator information. The minimal additive refinement is the eight-bit symplectic space [formula in source] , with four-dimensional kernel [formula in source] . There are 64 quadratic-form-preserving sections, four compatible with the family marking; the deck exchanges complementary sections. The full target on [formula in source] has charge shifts, cocycle and [fo
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 159 to 192
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The integer charged CAR field is substantial progress beyond neutral determinants, but is not yet the half-charged [formula in source] spin field. A sharp half-twist has a divergent polarization Hilbert–Schmidt sum [formula in source] . Its unrenormalized unitary limit is therefore not justified. The next construction must provide a renormalized, smeared inter-sector field, both adjoints, source energy bounds and cha
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_research_20260909.tex · lines 193 to 215
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 1 to 1
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The previously local research contracts through Round 27 are now shipped with their proof sources, source-pinned checkers, negative controls and saved validation records under experiments/theory-contracts/. They extend the positive matter/constraint constructions to an interacting scalar/charge model, local charge transport, exact scalar elimination and controlled signed history sums. Additional off-shell fields, sel
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 2 to 17
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
tfpt research contracts · Research contracts
The geometry branch realizes the proposed elliptic boundary data but exposes its unselected markings and symmetry enlargement; it supplies neither physical dimension selection nor a selected chiral measure. The local positive and constraint-domain branches distinguish the separated completion from the first-vertex-preserving completion, including their different off-shell terms and form domains. The charge branch ret
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 18 to 35
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
Fix [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , a time step [formula in source] , [formula in source] and [formula in source] . Every site's charge remains in [formula in source] . The original signed hopping and potential are [formula in source] The [formula in source] directed elementary shifts include their original phases. Thus [formula in source]
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 36 to 65
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
Let [formula in source] be the sum of moduli before cancellation, resolved into elementary hopping words, initial charge profiles and scalar integrals. Then Every elementary hop changes the complete profile, hence [formula in source] . Scalar spectral Jensen gives [formula in source] . Pinching [formula in source] into its charge blocks [formula in source] contracts the Schatten [formula in source] norm, so [formula
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 66 to 113
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The exact Gram inverse satisfies [formula in source] , so [formula in source] , [formula in source] . On the neutral sector define [formula in source] Let [formula in source] bound all charge coordinates at sampled slice boundaries and [formula in source] bound total elementary hopping order. If [formula in source] , [formula in source] For the first estimate, insert the boundary projection [formula in source] in the
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 114 to 154
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The planner uses integers and fractions, with upward roots, [formula in source] , [formula in source] and [formula in source] for [formula in source] . At [formula in source] , full memory and a [formula in source] omission target, the published Round 26 [formula in source] improve to [formula in source] . Applying the same first-passing-integer search to the old inequalities gives [formula in source] : the gain is n
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 155 to 187
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
tfpt research contracts · Research contracts
For overlapping original hops [formula in source] and [formula in source] , the word [formula in source] closes with phase [formula in source] because [formula in source] . Its actual hopping matrix-element product is [formula in source] for [formula in source] . Diagonal configuration rephasing telescopes around this loop and cannot remove it. This excludes that particular stoquastic rephasing, not all bases, regrou
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round27_full_reference.tex · lines 188 to 198
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 1 to 1
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The following results concern the explicitly stated regulators and algebras. They do not identify a single complete physical [formula in source] D parent. All T1–T8 and TFPT.TOE.COMPLETE.01 remain . The finite regressions are checks of the proofs below, not substitutes for their quantifiers.
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 2 to 8
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
tfpt research contracts · Research contracts
SEAM.MMST.TELB.NORM.01. For the frozen [formula in source] , [formula in source] collar, the original remainder obeys [formula in source] The interval inputs are v1022 (TV and potential), v1025 (C1/C2a), and v1026_ telb_ round4_ closure.py (CF, DG, signed CROSS, validated Fourier core and all-volume aliases). This is not a proof of the historical sharper [formula in source] or Bound-B target [formula in source] . In
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 9 to 22
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
tfpt research contracts · Research contracts
Put [formula in source] , [formula in source] , [formula in source] , [formula in source] and let bars denote normalized means over [formula in source] . Define [formula in source] Partial fractions give [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] , with [formula in source] . The identities used are the standard cotangent and polygamma identities https
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 23 to 113
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
The csc-squared finite product identity and trigamma recurrence for the original remainder give, for [formula in source] , [formula in source] where [formula in source] and [formula in source] . Since [formula in source] for [formula in source] , [formula in source] . The [formula in source] -point Peano kernel and [formula in source] imply [formula in source] On each diagonal cell the imaginary mean vanishes, [formu
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 114 to 142
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.
tfpt research contracts · Research contracts
Let [formula in source] be the unitary fractional shift with entries [formula in source] , let [formula in source] restrict to [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] . Crucially [formula in source] . For the finite unitary overlap [formula in source] and [formula in source] , the source identity is [formula in source] Hence [formula in source] . P
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
tex-artefacts/toe_round4_proofs.tex · lines 143 to 174
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
No explicit verification citation is attached to this section in the registry.