SU32 comparison actions, static content and boundary operations
Reported transported-preparation symmetry and finite operation span; static-payload identification excluded
This page summarizes the linked research at its stated verification level. It is not a new proof certificate or experimental confirmation.
Reported result
Symmetry is not same-preparation reconciliation
At the fixed reading, exactly one of 24 coordinate permutations maps the complete first five-cell incidence presentation to the second. It transports all 104 oriented interfaces in that reading. Uniqueness is within that searched class, not among all possible comparisons. Its reference action exchanges P+ and P- while retaining complete input records and fixing the E references.
The candidate law is S(channel_A(r)) = channel_B(S_*r), not channel_B(r) at the original registry and binding. Geometric endpoints and the E reading can agree while the full record reader distinguishes the witnesses. At the common terminal N, two of four outgoing incidences are exchanged. Each outgoing edge must be transported with the preparation; fixing the terminal cell does not license leaving that edge unchanged. This is incidence symmetry, not executed payload transport: nativeSu32ComparisonCompiled: false.
The static-content identification is inconsistent
The rejected conjunction gives each of 80 named fibres one static finite JSON value, identifies its paired P/E presentations, uses the reference reader to retrieve that value, and identifies the full comparison packet with the literal fibre content. In 48 of 136 producer constraints, the unchanged constructor puts that same input value at a strict subtree of the output. A finite tree cannot equal a tree strictly containing itself: node rank strictly increases.
The identification fails, not every content-bearing fibration. A positive control performs 544 producer comparisons over unchanged static values while keeping generated packets separate. Static content and retained operation witnesses can coexist; their literal identification causes the contradiction. The source's Agda theorem concerns strict natural-number rank, while extraction of the JSON containment and native fibre associations is an executable audit, not an Agda formalization of the whole JavaScript model.
A composite operation is not a static payload
The successor constructs 448 motifs of a three-vertex source-generated tree with two internal shared-face matches and five external ports. Restricting a compatible decoration to its local operation rows and gluing them back recovers the decoration. The other span map denotes a composite boundary operation, retaining generators and sewn interfaces; it does not overwrite an external fibre's static value.
Two-edge contraction orders agree in this formal source-generated envelope. The source separately retains all eight local cyclic orientations as declared planar choices. The variance is explicit: adding retained edges refines a presentation; contraction runs in the opposite direction. Boundary cyclic order and gaps are preserved. The source reports 14,336 contraction squares and the same number of gluing round trips and rejected internal mismatches; these are distinct checks, not independent empirical evidence.
Controls and exclusions
The symmetry audit rejects unchanged-preparation substitution and unchanged-edge continuation. The static-content audit preserves the positive packet-separation control. The span audit rejects internal-point mismatches and detects changes of boundary order under a single local reversal. The finite span is not a full homotopy-coherent nerve or a proof of cyclic 2-Segal structure. Five boundary ports do not imply a five-step physical period.
First unresolved obligation
The comparison still needs its actual source-admitted operands, complete reader/preparation policy and continuation binding. Separately, the operation envelope needs a map into the native boundary-corolla operation fibre respecting generators, contraction and cyclic structure. Its gap data needs a source-supported content interpretation. No new reader, role transport, physical cyclic embedding or global assembly is installed by naming these missing maps.
Verification and sources
The comparison and span sources report exact executable checks; the static-content source additionally reports a safe Cubical rank theorem. These checks were not rerun for publication. Full commands, coverage, controls and local receipt provenance are in the source packets, not advertised as ignored receipt downloads. Comparison action and preparation policy · Static-payload exclusion · Operation-valued composition span.
Checker: research/strominger/checkers/check_su32_comparison_license.mjs; research/strominger/checkers/check_finite_payload_occurs_agda.py; research/strominger/checkers/check_su32_static_payload_identification.mjs; research/strominger/checkers/check_su32_boundary_composition_span.mjs
Publication provenance: Versioned source/checker and historical receipt identifiers. Metadata validation is not scientific replay.