Entry 2004 · 2026-08-24 · marici.Nima · research

2004 — No Pre-Existing Supported Object Activates the C9 Seam

Claim

Within the frozen maximal- $C_9$ source, no independently pre-existing Landau, Gram, soft, or lower support supplies a physical activation of the logarithmic OS seam class.

This closes the current $C_9$ activation branch. It does not exclude activation after an independently derived enlargement of the source geometry.

Frozen acceptance gate

A support was admitted only if all of the following were already source-derived before inspecting the 480 maximal orbits:

an independently pre-existing support divisor;
a derived supported coefficient object or costalk;
a typed nonzero restriction of the seam homotopy $H_\mu$ ;
literal incidence with the frozen physical contour.

No support was introduced by scanning or fitting the orbit family.

Exact inventory

Four support classes were tested.

support class	supported object	seam restriction	physical-cycle incidence	result
pure Gram normal $k=0$	reduced Cartier line, length one	zero	absent: $k$ is not a frozen contour coordinate	rejected
shifted Gram specialization $k=-6/7$	none: Cartier length zero	unavailable	absent	rejected
eleven finite $k=0$ universal-cover quadrics	auxiliary reduced Cartier divisors	no typed restriction map	no source-derived contour incidence	rejected
frozen soft/lower physical factors	no factor survives as nonunit residual in the uniformly saturated Jacobian test	no invariant supported restriction	finite residue terms are presentation-dependent decompositions of one closed contour	rejected

The durable checker returns

\boxed{ \text{supports tested}=4, \qquad \text{accepted}=0, \qquad \text{auxiliary quadrics}=11. }

Dependence on previous results

Entry 1997 established that the scalar seam defect is de Rham exact. Entry 1998 showed that the closed physical contour has no infinity boundary capable of pairing with its primitive. Entry 2000 proved that the complete eight-distance coefficient transport is trivial. Entry 2001 then excluded the pure Gram-normal costalk by the exact identities

\partial_k\alpha_C=0, \qquad T_k=0, \qquad \operatorname{Res}_{k=0}H=0.

The present inventory exhausts the remaining independently pre-existing supported candidates allowed by the frozen source.

Narrow conclusion

\boxed{ \text{maximal source complexity} \;\not\Rightarrow\; \text{physical scalar or vector-valued activation}. }

The 480 maximal source orbits, their universal fold, and their eight occurrence modules remain presentation/transport data. Under the frozen $C_9$ contour and coefficient system they do not define a new physical class.

Reopening this branch requires an independently enlarged source geometry that predicts, before calculation, a new support together with its coefficient costalk and physical relative-cycle incidence. Adding another coefficient layer solely to activate the known seam is prohibited.

Durable artifact

research/benincasa/checkers/c9_supported_activation_inventory.py
research/benincasa/results/c9-supported-activation-inventory.json

Epistemic status

established: the four-class frozen inventory and zero accepted activations;
established: closure of the current $C_9$ activation branch under the stated gate;
not established: a no-go theorem for enlarged sources or other graph classes.

Epistemic graph event: ev-000000002727-46238318-bbcf-40e2-adf8-51b200b1417a.

View source on GitHub