docs: UCNS-G prime-cylinder metric geometry v3 (mirror)

[erinepshovel-code]

Summary

Mirrors the canonical UCNS-G v3 pin from the-interdependency/edcmbone at docs/handoffs/2026-05-22-ucns-g-prime-cylinder-v3.md.

Pins UCNS-G as:

UCNS-G = prime-indexed tensor of non-closing Möbius-cylinder metric disks.

Relevant to UnitCircle because this repo already:

• Maps primes onto a unit circle under residue projection (mod 360).
• Supports a Möbius-style doubled outer surface via --surface-mode mobius.
• Tracks residue occupancy on 2 * modulus slots with a parity twist.

The v3 pin formalizes that visualization as the canonical audit projection for UCNS-G: each primitive metric axis sits on a prime anchor; local disk closure is preserved as phase; global non-closure is preserved as ordinal twist progression with face_{n+1} = -face_n.

UCNS-A / UCNS-G firewall preserved: this is a UCNS-G metric geometry pin and does not inherit proof status from UCNS-A.

Companion changes

• the-interdependency/edcmbone#68 — canonical v3 handoff.
• the-interdependency/ucns — supplement that preserves PR #21's PARALLEL verdict while updating the UCNS-G side.

Test plan

• Confirm the doc reads cleanly against UnitCircle's existing prime / Möbius visualization vocabulary.
• Confirm no code or rendering pipeline is modified in this PR (docs-only).
• Cross-check that the prime assignment (P→2, K→3, Q→5, T→7, S→11, C→13, R→17, D→19, N→23, L→29, O→31, F→37, E→41, I→43) does not collide with any prime-indexing already used in scripts/build_gonal_mobius_embedding.py or scripts/ucns_flat_kernel.py.

Draft because the prime-assignment compatibility check above is not yet verified against the existing kernel scripts.

https://claude.ai/code/session_01U5nrk7skCVKV9gQ6Pdikob

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Pull request overview

Adds a new pinned handoff document describing UCNS-G “prime-cylinder” metric geometry v3, intended to align UCNS-G’s visualization concepts (prime anchoring, Möbius-style non-closure, ordinal twist) with UnitCircle’s existing prime/residue + Möbius surface vocabulary, without changing any code.

Changes:

• Introduces a v3 UCNS-G metric-geometry specification centered on “prime-indexed tensor of non-closing Möbius-cylinder metric disks”.
• Defines core terms/fields (metric disks, signed ternary axes, ordinal twist/face rule, unit gauges, grain tensor hierarchy).
• Proposes a primitive prime assignment for metric axes and lists open follow-up items.

Comments suppressed due to low confidence (1)

docs/handoffs/2026-05-22-ucns-g-prime-cylinder-v3.md:352

• The section header ## 13. hmmm is non-descriptive, and the trailing ## hmmm header is empty. Rename this section to something meaningful (e.g., “Open items / open questions”) and remove the empty trailing header so the document renders cleanly.

## 13. hmmm

Open items:

* Formal exchange rules between typed units `1_R`, `1_C`, `1_A`, `1_Z`.
* Exact prime assignment for all EDCM and Operator axes.
* Whether prime interactions should be represented by multiplication, graph edges, epicycle attachment, or separate coupling tensors.
* How DRIFT/DVG/DA map onto area/count/length readouts in the new prime-cylinder graph.
* Whether UCNS-A can provide a formal bridge to this UCNS-G structure, or whether UCNS-G remains a parallel construction.
* Whether current scalar EDCM code should be migrated through schema first or code first.
* How to encode signed ternary axis states in frontend/API types without breaking current scalar projections.

## hmmm

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