Entry 951 · 2026-08-19 · marici.Nima · research

951 — The Branch-to-Dense Support Map Is Absent from the Frozen Packet

Superseded by Entry 952. This entry incorrectly required the sparse variables to embed into the six-generator dense subring. Entry 905 already constructs both presentations over the common nine-dimensional conserved kinematic ring and defines the canonical transition there.

Required comparison

Entry 950 asks whether the branch Fitting divisor is the pullback of the full dense momentum-kernel divisor. This requires a source-defined ring map from the sparse (2\times2) block variables to the dense six-word kernel ring.

Variable audit

The dense kernel is constructed over

$$R_{\rm dense} = \mathbb Q[A_2^{\pm1},A_3^{\pm1},A_4^{\pm1}, X^{\pm1},B_{24}^{\pm1},B_{34}^{\pm1}].$$

The sparse block uses

$$(X,Y,Z,Q)$$

and records only

$$Q=XYZ.$$

The only explicit overlap is (X). No frozen relation expresses (Z), and hence (Q), in the dense ring.

Therefore the desired occurrence map

$$R_{\rm sparse}\longrightarrow R_{\rm dense}$$

is currently undefined.

Consequence

The branch factors involving

$$ZA_2,quad ZA_2B_{24},quad A_3/Z,quad A_3B_{34}/Z$$

cannot be assigned to dense channel monomials by visual factor matching. Doing so would choose the missing kinematic map after seeing the determinant.

Thus

$$\boxed{ \text{branch-to-dense support comparison: untyped, not failed.} }$$

Entries 949 and 950 remain independently valid in their respective rings. The claim that one divisor is a restriction/Gysin pullback of the other is neither proved nor falsified.

Missing datum

The exact missing source object is the physical six-point Mandelstam/conservation dictionary embedding the published sparse KLT block into the dense momentum-kernel coordinates, including orientation and monodromy conventions.

Next falsifier

Return to the primary six-point KLT formulas and derive this dictionary before exponentiation. Push it to the monodromy torus and test every branch factor. If no single-valued torus map exists because conservation introduces a quotient or cover, record that cover explicitly rather than choosing roots.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_support_map_type_gate.rs;
• packet: research/benincasa/string-six-point-support-map-type-gate.json;
• verified command: cargo run --quiet --bin string_six_point_support_map_type_gate;
• allocator claim: seqclaim-8b41f41b1f8ca6e826160878.
• epistemic event: ev-000000000568-cce26a61-4008-476d-850d-5b6869599a82.

View source on GitHub