YangDim prescribed-dual bridge realization

Use this skill for the prescribed-dual bridge-realization theorem, its proof archive, and refinement work around bridge frontiers. Pair stable reference packets with the live sources of truth; do not rely on chat memory.

Required first packet

Read references/prescribed-dual-bridge.md, then read prescribed_dual_bridge_realization.tex and ledgers/proof_route_topological_dictionary.md for current status before continuing the route.

Common child packets

• Closed frontier feeding the bridge problem: references/prescribed-bridge-closed-frontier.md.
• Antipodal suspension normal forms and bridge recursion criteria: references/antipodal-bridge-classification.md.
• Split-lift route overview: references/split-lift-route.md.
• Exact split-lift formulation and repair variables: references/split-lift-exact-formulation.md.
• Endpoint separation and local missing-path diagnostics: references/split-lift-endpoint-separation.md.
• Wall/provenance descent, singleton-collar handoffs, dual-clean projection, and anchored swallowing: references/split-lift-wall-provenance.md.
• Row-torsor and row-nerve routes: references/row-torsor-route.md and references/split-lift-row-nerve-diagnostics.md.
• Finite signature diagnostics: start with references/m6d2-finite-signatures.md.

Guardrails

• Prescribed-dual bridge realization is closed at theorem level. Use thm:prescribed_dual_bridge_realization in main.tex for the paper theorem, prescribed_dual_bridge_realization.tex for the clean companion proof note, and drafts/signature_exchange_exactness.tex for the detailed exactness proof archive.
• Do not reopen local row-top, parity, finite-signature, partial-cube, or square-boundary routes unless an actual gap is found in the accepted-exit contract, the focused draft's final no-counterexample corollary, or the promoted main theorem.
• Finite (5,2), (6,2), and higher sampled diagnostics are regression/calibration context after closure, not active proof routes.
• Legitimate future bridge work is refinement: explicit enumeration of admissible signatures, algorithms for listing frontiers, or derived/cubical/teaching interpretations of the already-realized frontier torsor.
• Keep historical campaign material out of active ledgers. Put route archaeology under archive/; put clean proof statements in main.tex, prescribed_dual_bridge_realization.tex, or the focused exactness proof archive.