Proper Cross-Domain Retrieval Sweep — far-domain instances → exact-prime rank (2026-05-22)

Question (the rigorous version the self-paraphrase sweep couldn't answer): when a prime is instantiated as a concrete far-domain scenario, does semantic search retrieve the prime — and do structural primes transfer (retrieve) better than framed primes, as the structural/framed theory predicts?

Design (bias-controlled). Reused the 15 blind neutral structural paraphrases (7 framed, 8 structural). An independent agent — blind to each prime's identity and to the framed/structural label — instantiated each paraphrase as a concrete ~110-word scenario in an applied/everyday domain (banquet kitchen, shipping port, power grid, winemaking, hospital credentialing, brewing, orchestra, bicycle factory, allotment garden, carpet weaving, classification society, wetland food chain, ED triage, tidal estuary), forbidden from naming the abstraction or using its jargon. Each raw scenario was embedded (bge-small) and queried against the structural_signature corpus; we recorded the target prime's rank. Compared to the self-paraphrase rank ("meta") to isolate the cross-domain gap.

Result — framed retrieve better; replicates the self-paraphrase sweep

	raw far-domain ranks	median	mean	in top-10
Framed (7)	1, 1, 2, 3, 9, 10, 55	3	12	6/7
Structural (8)	1, 1, 2, 8, 13, 55, 91, 280	10	56	4/8

Clean cross-domain hits: due_process #1 (from hospital credentialing), epistemic_justice #1 (ED triage), hierarchy #1 (wetland food chain), modularity #1 (bicycle factory), network #2 (courier routes), sovereignty #2 (harbor berth). Misses: recursion 280 (croquembouche), symmetry 91 (carpet weaving), equilibrium 55 (estuary), moral_relativism 55 (winemaking).

Why — distinctiveness, not portability (and it's the governing variable)

Both sweeps now point to the same cause: exact-prime retrievability is governed by the prime's neighborhood density (distinctiveness), not by whether it's framed or structural.

• Structural primes are generic patterns sitting in dense near-synonym clusters. When the far-domain instance is embedded, it lands in the correct neighborhood but the exact slug is crowded out by siblings: recursion → cardinality/aggregation/dimension; symmetry → pattern_in_design/periodization/composition; equilibrium → attractor_selection/homeostasis/propagation. So the structure does transfer (the instance retrieves the right region of abstraction space) — but exact identification fails because the region is full of near-equivalents.
• Framed primes are distinctive, sparsely-neighbored patterns, so an instance lands precisely on them (the hospital scenario's notice→hearing→impartial-panel→reasons is unmistakably due_process). The exception proves the rule: authority retrieved at 10 because its near-synonym sovereignty outranked it — a framed pair that is itself a dense neighborhood.

So the naive reading "framed primes don't transfer across domains" is wrong; and "structural primes transfer better" is half-right — they transfer to the right neighborhood but are the hardest to pin to an exact slug because they're generic. The variable that actually predicts exact retrieval is sparsity of the prime's semantic neighborhood.

This also reframes the original forward-case failure (due_process @ 45 in immunology)

Here, a clean far-domain instance of due process (hospital credentialing, where due-process IS the theme) retrieves due_process at rank 1. The immunology forward case retrieved it at 45 not because due_process is "far in embedding space" but because that scenario was oblique and multi-structure — due process was one latent pattern among irreversibility, uncertainty, and asymmetric harm, none of which is the surface theme. So cross-domain retrievability degrades with instance obliqueness/messiness, not just domain distance. Real problems are oblique; clean textbook instances are not.

Implications for the MCP semantic-search question (to discuss next)

1. Semantic search clearly beats lexical and bridges many clean cross-domain instances to the exact prime — adopt it; query with the meta-model, embed structural_signature.
2. Return a neighborhood/family, not just top-1 — because structural primes are crowded, the useful unit of retrieval is a cluster the reasoner then disambiguates. (For framed primes top-1 is often right.)
3. Consider deduplicating or explicitly linking structural near-synonyms (recursion/iteration/self-similarity; symmetry/invariance/conservation; equilibrium/steady-state/homeostasis) so the cluster is legible rather than competing.
4. Oblique, realistic, multi-structure queries (the cases that matter) still under-retrieve latent primes; this is where a fine-tuned/instructed retriever or multi-vector decomposition of the query would help — i.e., retrieve against each structural facet of the meta-model, not one blended vector.

Caveats

N=15 (7+8), one modest embedding model (bge-small, 384-d), exact-slug metric (penalizes crowded structural primes by design). Instances were generated from neutral paraphrases that retained more distinctive fingerprints for framed primes than structural ones, which contributes to (and is itself part of) the distinctiveness effect. Some structural instances leaned on a sibling surface (croquembouche reads as "stacking/counting" more than self-reference), lowering their rank. Treat the framed>structural ordering as evidence about neighborhood density / distinctiveness, not about transferability of the underlying pattern, which appears to hold for both (instances reliably retrieve the correct neighborhood).

Artifacts: /tmp/scen.json (the 15 blind instances), /tmp/xdomain.py; embeddings in _models/.