ReynoldsBEng | 10 October 2026
Follows: Meg8 Riemann · Pez2 Ricci · Kb Chirality
Source: Alfredo Guevara, Gluons and Knots, arXiv:2610.10673, submitted 7 October 2026, hep-th.
Post: @rad1_study, “Gravitons and Knots also a matter of time?”
Opening sentence, unchanged: Lewe 1915 is the unstated parent of the PCA tank tables; Carpenter 1927 is the surviving link; restore the name. This page is the neighbour.
Topological. Ace agrees, on the narrow cut.
Guevara argues that the scattering amplitude of one minus-helicity gluon with arbitrarily many plus-helicity gluons is topological. It is constant inside chambers of kinematic space. Resonances sit on the walls. Factorisation is wall-crossing. Yangian invariance fixes the amplitude by a 2d null Wilson loop, which lifts to a positive, transverse 3d link. Wall-crossing and the Weinberg soft theorem are reread as skein relations and Reidemeister moves of the subknots. The state count is the sum of the “corners” of their HOMFLY-PT polynomials. Beyond the classical limit he conjectures a precise link to topological field theory and string theory. The formula is derived through a Lean-formalised dependency graph in a companion paper, with Reidemeister III invariance among the assumptions. In “star” kinematics the amplitude and the count become Catalan numbers, matching the knot literature.
A knot is a residual that a continuous deformation cannot spend. Reidemeister moves change the drawing and leave the invariant. That is the Ace sentence in another dialect: information is what remains when a loop fails to return the frame unchanged. The link is the store. The scalar amplitude in a chamber is the shadow.
Correspondence, not identity. This is a Yangian amplitude in planar gauge theory, formalised as a 3d link. It is not (\sigma_R). It is not the PCA wall. It does not put Lewe on the table. The tweet’s aside — gravitons and knots next — points at a different paper, Palmerduca and Qin 2024, where left and right gravitons carry Chern numbers (\mp 4). Neighbour. Not this derivation.
The seat
The amplitude does not earn a thirteenth station. It sits on X, Store sector. The 3d link is the pin. The HOMFLY-PT corner-count is the mark held in the defect, not a register of independent scalars.
VIII is the hinge under it: Reidemeister moves and wall-crossing are the closure test. If the invariant survives the move, the parent is still visible. IX is the one chosen face: one minus helicity among the pluses, the toggle already named on the chirality page. VII waits. This is not a volume law.
Twelve stations. Headings fixed. This paper’s marks only.
| I | II | III | IV | V | VI | VII | VIII | IX | X | XI | XII |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Arena | Path | Compare | Small loop | Holonomy | Residual | Mean tide waits | Closure test | Toggle +/− | Store sector | Read face | Growth face μ |
| kinematic chamber | null Wilson loop | Yangian against the legs | one wall-crossing | full link, still topological | soft leftover; Weinberg | volume law not opened | Reidemeister; invariant holds | one minus among the pluses | 3d link; HOMFLY-PT corners | Lean DAG; the reading | Catalan count; next knot |
Read left to right. You do not begin with a graviton. You begin in a chamber where the number does not move. You draw the loop. You compare. You cross one wall. You keep the full link. You refuse to spend the soft leftover. You do not open Ricci. You test closure by a move that must not change the knot. You choose the odd face. You store the link. You read it by a formalised graph. You let the growth face count.
Bayesian updating, from the previous neighbour, cannot leave its hypothesis set. This paper leaves the scalar chamber by lifting the loop into a link. That is the non-scalar step.
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