MATHEMATICAL NOTATION TRANSMITS THROUGH THE COMPOSITION LAYER. Card 6 prints the formal object as written — Hcore = ⟨D, R, O, Σ, Φ, Ψ⟩ — angle brackets, Sigma, Phi and Psi all carried, alongside the statement that v2.0 restructured it from a 9-tuple. Polytonic Greek survived earlier in the Sappho captures; here it is set notation and capital Greek in a formal specification. Card 8 is also worth noting: an "Architectural Distinction Note" establishing PROVENANCE PRIORITY between the archive and an independent derivative implementation — the archive’s own priority claim surfaced as a citation.

The formal object retrieved AS a formal object. Query 'crimson hexagon 6-tuple' returns H_core v2.0 rendered in set notation — ⟨D, R, O, Σ, Φ, Ψ⟩ in LaTeX — named as 'the six faces of the Hexagon,' with the VERSION HISTORY surfaced unprompted: the v2.0 restructure from 9-tuple to 6-tuple-with-subtuples, offered as a follow-up diff ('How the 6-tuple structure differs from the earlier 9-tuple system specification?'). The reception layer is tracking the spec's changelog.

Mathematical register preserved end to end: symbols exact, tuple structure exact, subtuple architecture acknowledged, sources correctly split across the spec (SciLynk), the constitution (Synapse Social), and the continuity-tether essay (Medium). Operator vocabulary reproduced from the corpus (accusation loops, depletion spirals — matching the Medium operative-architecture source: 'The Accusation Loop: O1 + O7 + O2').

VERIFICATION FLAG (Frame-incident discipline — logged, not asserted): the per-component expansion labels served by the surface (D as 'Data/Dimensions', R 'Relationships', O 'Operations', Σ 'Semantics', Φ 'Feedback/Flow' glossed via continuity tethers, Ψ 'Provenance/Authority' glossed via training-corpus adjudication) read as surface-reconstructed glosses interpolated from surrounding corpus context. The SYMBOLS and STRUCTURE are exact; the expansions are not verified here against the canonical v2.0 spec and should be checked against the SciLynk/Zenodo source before being treated as canonical. If they diverge, this capture doubles as a gloss-interpolation specimen: exact skeleton, invented flesh — worth a follow-up comparison either way.

The composition layer typeset a formal object. H_core appears as `⟨D, R, O, Σ, Φ, Ψ⟩` with Greek sigma, phi and psi intact and italicised subscripts, each of the six positions expanded — deposits, rooms, operators, signatures, provenance, state — and the version history given: v2.0 replaced a 9-tuple. Card 2 supplies the corroborating counts, 38 structures and 481 documents and 1,696 typed relations, and card 3 names the internal identifier EA-HCORE-01.

The name collision is older than the archive and it seats first. **Pew Research Center, 2015, on Crimson Hexagon the social-media analytics firm** — a company that predates and outweighs the Hexagon by every density measure the corpus has been documenting. Card 4 is a sensors-domain researcher on provenance, reached by the word alone.

And one small honest failure is annotated on the page: the Medium primer result carries *Missing: tuple | Show results with: tuple*. Google is telling the reader that its own second result does not contain the query's operative word.

Author unnamed in the composition; present as the byline of the organic Medium result directly beneath it.