Dimensional Chess: C1 through C8 / Note

Dimensional Chess C8: Movement-Frequency Relations

Current15 Sept 2026 · saved

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01 / THE QUESTION

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C8 tests the proposal that chess pieces exhibit reusable relational movement rhythms.

02 / WHAT THE RECORD SAYS

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C8 tests the proposal that chess pieces exhibit reusable relational movement rhythms. A move is mapped to a class describing piece type, displacement, capture status, square-color phase, distance changes to both kings, geometric relations to both kings, edge-to-center motion, and home-relative rank phase. The learner records which defender classes terminate bounded mating claims in eight deterministic phase-shuffled five-ply searches. A later exact search orders defender moves by the frozen empirical score.

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03 / LIMITS & OPEN POINTS

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The observed frequency is therefore role-specific, not a universal color-normalized law.

04 / THE NEXT QUESTION

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The next frontier is a learned relation that carries a sound interval or a proof obligation.

05 / CHECKS IN THE RECORD

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The C8 result agrees with the separately implemented and independently verified C7 certificate that neither side can force mate within nine plies. A structural audit samples 960 deterministically reachable states and checks seven ordering schemes over 168,882 legal-move instances. Every ordered list is exactly a permutation of the corresponding legal list. Of the state/scheme cases, 6,720 actually change order, establishing that the test is not a lexical no-op. Audit status: PASS.

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Previous connections

Dimensional Chess C7: Horizon-Safe State Projectionseries order (mechanical)

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Access: Public
Dates declared in the record: Date: 15 September 2026
Project basis: Explicit project source citation
Origin: d0re research collection (snapshot 1 October 2026)
Original path: /Dimensional_Chess_Movement_Frequency_C8.md
Authorship basis: Collection attribution; original record retains its own credits
Title basis: From the source
Date: 15 Sept 2026 · saved
Status basis: r-709ba3d90a0c is the last record of the chess line in the register and states where it stands: "C8 still does not compress the game state or narrow the unbounded root interval".
Size: 6,611 bytes
Word count: 986 words
SHA-256 of indexed source: 709ba3d90a0c3bb881ccf93be06a2c1d8ea5f7aa364d9de90e3c57a40c0f3e3a

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Dimensional Chess C8: Movement-Frequency Relations
Version 8
2026-09-15
d0re research record r-709ba3d90a0c
https://www.d0re.com/library/records/r-709ba3d90a0c.html
Authorship basis: Collection attribution; original record retains its own credits
Date basis: saved
Source SHA-256: 709ba3d90a0c3bb881ccf93be06a2c1d8ea5f7aa364d9de90e3c57a40c0f3e3a