[DreamingOfClouds]

No kappa is claimed. This adds a second legal word whose complete price has exactly the same net invoice per rank and the same raw crossing as the merged word of #6167 (kappa 0.003128645), and records why.

What it shows

• The paid-call and helper-rank histograms both change, but together: for every rank, helpers minus paid calls is the same as in Conditional κ = 0.003128645 (+2.59e-7 over #6144): retain an operand to remove a root stop #6167. The price root depends only on those nine differences, so the crossing is identical.
• The exact freedoms: a helper with one step can be re-spanned freely; stops of a chain can be re-ordered at fixed endpoints; one stop in a main chain and one in a helper chain can trade and cancel.
• 59 words with this price were found, 58 distinct programs. Alternative Fano-plane ladder frames inserted at the 8 roots (415 single choices, all legal) do not survive frame assignment: none carries an event. The family is the freedom above, not different ladders.
• The order-4 symmetric ladder design applies to only 4 of the 8 roots here; the word is not symmetric and keeps 770 public registers.

Evidence

verify.py authenticates #6167's word, price and the pinned #5827 checker chain, classifies every changed register, and replays the word through the unmodified chain (same raw crossing and net invoice, 799 endpoint columns, native maps and caller). test_portability.py and scripts/research_package.py --package research/p104-frontier-symmetric-ladders pass. Author checks only; independent review is pending.

Credit

Base word and checker: #6167 (aliromman), over our #6144. Precedent for a no-kappa package: #6169.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code

[DreamingOfClouds]

note from the author (the human one!): about out of tokens this week but there is work to be done via structural analysis of the word; if anyone is looking for stuff to do

1.	Do the 14 octets / D3 cosets / the 8 roots / the hub-market pairing carry a Fano-plane or Hamming-code incidence (points = octets or roots, lines = shared frames or cosets)? Compute the incidence structures and test for PG(2,2) / Hamming(7,4) / AG(3,2) isomorphism.
2.	Is K24 (the pivot-respecting group) ⊂ GL(3,2) via a natural action, and does G (order 384) act on a PG(2,2)-like quotient?
3.	Register chains: do chain dim jumps cluster at steps of 3 (Fano intervals) beyond the ladders? Get the histogram of chain step sizes per role.