#OpusSolve |

Hodge conjecture |

Let |

Story |

Errata |

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Presented here are wrong/incorrect approaches to tackling the problem. These are offered as case studies of what to avoid.
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+Hodge conjecture

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+brane

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+coverage

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+loop

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+twistorspace

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Showing posts with label **geometry/topology**. Show all posts

Showing posts with label **geometry/topology**. Show all posts

#OpusSolve |

Hodge conjecture |

Let |

Story |

Errata |

Let *X* be a non-singular complex projective manifold. Then every Hodge class on *X* is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of *X*.

A **brane** (short for **membrane**) is some mathematical generalization of a category to one (1) or more higher dimensions.

My portfolio is a twenty-six dimensional (26-dim) toy [๐งฉpuzzleware] with**braneworld** structure according to pitch class:

**0-brane** = particle

**1-brane** = string

**2-brane** = manifold/sheet/tape

**3-brane** = cell

.

.

.

**25-brane**

(see also Egglepple, mesh, patch, walk)

My portfolio is a twenty-six dimensional (26-dim) toy [๐งฉpuzzleware] with

.

.

.

(see also Egglepple, mesh, patch, walk)

A **coverage** is the twistorspace posture (ie. formation) for surjectively graphing a [supersymmetric] zone on(to) some pitch.

As cryptographic shape schemes [puzzles๐งฉ],**coverages** are fundamentally mutable and dynamic; spanning the entire range of branes(SMALL + BIG). A **coverage** can be (strategically) both *preventive* and *responsive*. (see also #coverage, egg, epp, patchwork, cassette, Honne Bay)

As cryptographic shape schemes [puzzles๐งฉ],

Mathematically, a **loop** is a closed๐ string with no knots or tanglements whose path starts and terminates at the same point. Ludologically, a **loop** is a simple infinite walk; such that it encloses leaves (reading frames) on a loopstring. In both cases, a **loop** is continuous with either no nuts, or has homologically conjoined endpoints.

/// For sake of**loop** is just a completed walk that has become unavailable for recycling.

/// For sake of

`stew choreography`

, a
Ludologically, **twistorspace** or **"slot"** is a complex configuration space (eg. geotop) of solutions to the **twistor** identity ||f(u,u)=0||. Because a fibor is encoded to close๐ its loopstring the __exact__ same way every time (ascertained from the uniqueness property), there must exist an acoustic bound in place enforcing these conformations (bubble or vacuum); without such a (force) field, the fibor (as measured in ¢ents) would not bifurcate (into MONEY or bubblegum) as a function of symmetry-breaking.

/// +We assume that each**twistor field** is unique to some

+Everything in**twistorspace** is dyadic (u,u).
**Twistorspace**' complexity is *curvilinear* (**T**)*.More accurately, *sesquilinear*. (see also handicap, jukespace, coverage)

/// +We assume that each

`fibor`

. Essentially, this is a `mapped`

spinor. The 'spin' (an object's spinning `metric signature`

) here is identifiable with the quantum fields of arbitrary spin.+Everything in

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