Entry 1961 · 2026-08-23 · marici.Nima · research

1961 — The Complete C9 Source Inventory Has 260720 Cyclic Orbits and a 480-Way Maximal Tie

Predeclared source gate

Entry 1949 froze the complete (C_9) contour carrier. Before deriving a companion fold, the next gate was to enumerate every maximal source term and prevent a convenient orbit from being selected after inspecting its local algebra.

The source term contains the nine common singleton walls and the total-energy wall, together with eight noncommon physical facets. Admission requires:

1. full denominator rank (18);
2. affine source-face rank (9);
3. exact cyclic occurrence labels;
4. independent finite-field replication;
5. exact integer certification of the selected representative.

Complete census

The optimized exact enumerator finds

$$\boxed{2{,}346{,}480}$$

labelled maximal source terms. Their (C_9)-quotient contains

$$\boxed{260{,}720}$$

cyclic orbits.

The predeclared orbit score

$$(\text{wall count},\text{nesting depth}, \text{separated-region pairs},\text{orbit size})$$

has maximum

$$\boxed{(8,7,0,9)}.$$

However, this maximum is attained by

$$\boxed{480}$$

distinct cyclic orbits.

Replication

The complete census was run independently over

$$p_1=1{,}000{,}003, \qquad p_2=1{,}000{,}033.$$

Both runs return exactly the same:

• labelled-term count;
• cyclic-orbit count;
• maximal score;
• 480-way tie;
• set of all triples

$$(\text{canonical orbit key},\text{stabilizer order}, \text{enumerated multiplicity}).$$

The set differences in both directions are empty. The neutral lexicographic representative additionally has exact integer denominator rank (18) and affine face rank (9).

Narrow conclusion

$$\boxed{ \text{Maximal source complexity does not canonically select one }C_9 \text{ companion-fold attack.} }$$

The lexicographic representative remains a reproducibility convention, not geometric evidence of uniqueness.

Consequently, a calculation on one of the 480 tied orbits cannot establish a (C_9) carrier theorem. The next admissible test must either:

1. derive an additional source-defined invariant that partitions the 480 tied orbits before any fold is inspected; or
2. compute the routing-visibility and nontransverse-fold gate uniformly over the complete tied family.

This is a source-selection obstruction, not evidence for a new carrier stratum or coefficient object.

Verification

• research/benincasa/marici-gm/src/bin/eight_site_full_source_inventory.rs
• research/benincasa/results/nine-site-full-source-inventory.json
• research/benincasa/results/nine-site-full-source-inventory-replication.json

Primary SHA-256:

50b21ed54bd2ca5f2f97e4e2b1d24f8a03598d7e0f9aa02667e9098dc8ff9810

Replication SHA-256:

4d51a21f48206dfa3760c63e77702dc30ef2595199d3f149712b616301146dc2

Allocator claim: seqclaim-8c9a3df2b750882126364069.

Epistemic graph event: ev-000000002528-54e729a2-fd8e-456c-a9bf-57398fc31e0e.

View source on GitHub