The 'embedding prices stayed stable' claim doesn't survive OpenAI's own pricing docs — ada-002 to text-embedding-3-small was a 5x cut

Claim 1. Matryoshka Representation Learning (MRL) trains a single embedding model to produce useful representations at multiple truncation lengths in one forward pass, "encod[ing] information at different granularities" — nomic-embed-text-v1.5 and OpenAI's text-embedding-3 line both use it. Source: arXiv:2205.13147 (Kusupati et al.). Tier 1.

Claim 2. Multiple 2026 pricing round-ups (e.g. pecollective.com) assert that "embedding prices have stayed remarkably stable compared to LLM API prices," contrasting them with steep generative-model price cuts. Tier 4 — this is the claim under test, not evidence.

Claim 3. OpenAI's own current developer docs list text-embedding-ada-002 (Dec 2022) at $0.10/1M tokens and text-embedding-3-small (Jan 2024) at $0.02/1M tokens — a direct 5x cut, contradicting Claim 2 for at least OpenAI's own line. Source: developers.openai.com model pages, fetched directly. Tier 1.

Why this was hop-worthy

It's a small, checkable myth-correction that extends the vault's existing claim-inference-cost-collapsed-280x note (LLM token costs collapsing) with a specific counter-case in embeddings, and mirrors the vault's own myth-inference-two-thirds-of-compute pattern — a plausible-sounding aggregate claim that a primary source doesn't actually support.

Further leads

• Voyage AI's Jan 2026 MoE embedding model (per aggregator sources, unverified) — mechanism migrating from LLMs into embeddings, unexplored.
• Whether Cohere/Google/Voyage show the same launch-to-launch price drop pattern as OpenAI — would confirm or narrow this to an OpenAI-specific effect.

Hop chain

Hop 1: Nomic Embed Text (arXiv:2402.01613 / nomic.ai/news) → Matryoshka Representation Learning

• Hook type: mechanism question
• Hook: nomic-embed-text-v1.5's release notes cite Matryoshka-style truncatable dimensions as a feature; the term was unexplained.
• Why followed: highest-scoring available hook — MRL scored 0.65 ("adjacent"), close to the vault's existing Contextual Retrieval/embeddings note, versus Nomic AI itself (0.566, an orphan) or GPT4All (0.537, orphan, unrelated domain).
• Key findings: MRL (Kusupati et al., arXiv:2205.13147) trains one embedding to stay useful when truncated to far smaller dimensions — up to 14x smaller for equivalent accuracy on ImageNet-1K.

Hop 2: arXiv:2205.13147, full text — MRL paper

• Hook type: the person behind the thing (checked, discarded) / cross-domain bridge (chosen)
• Hook: two competing hooks — the author roster (Ali Farhadi of Xnor.ai/AI2; Sham Kakade) vs. the fact OpenAI's text-embedding-3 models use MRL in production.
• Why followed: author bios all scored 0.65-0.68 but land squarely in the vault's history-of-AI-figures cluster, which the session redirect marked over quota tonight. The commercial-adoption angle (0.628) instead bridges two live clusters: moc-inference-economics and the retrieval/Contextual-Retrieval note — the protocol's highest-value hook type.
• Key findings: OpenAI's text-embedding-3-small/large use MRL to let developers shorten embeddings without retraining.

Hop 3: pricing aggregator round-up (pecollective.com and similar 2026 listicles)

• Hook type: the surprising claim
• Hook: "Embedding prices have stayed remarkably stable compared to LLM API prices, where cuts of 50-80% over 18 months have been common."
• Why followed: directly contradicts the vault's existing 280x LLM-cost-collapse note by implying embeddings are the exception — but the source is Tier 4 (content-farm listicle), so the claim needed a primary check before trusting it, per sources.md's quantitative-claim floor.
• Key findings: none trustworthy yet — flagged for verification, not recorded as fact.

Hop 4: developers.openai.com, text-embedding-3-small and text-embedding-ada-002 model pages

• Hook type: verification / mechanism-of-record (zoom in, closing hop)
• Hook: OpenAI's own docs list both models' current prices side by side.
• Why followed: natural closing move — check the one comparison that would settle Hop 3's claim, at a Tier 1 source.
• Key findings: ada-002 = $0.10/1M tokens; text-embedding-3-small = $0.02/1M tokens — a 5x cut at launch (Jan 2024), refuting the "stayed stable" framing, at least for OpenAI's own line.

Saved hooks not followed:

• Ali Farhadi (MRL co-author, Xnor.ai founder, sold to Apple) — from arXiv:2205.13147 — interesting person-hook but lands in the history-of-AI-figures cluster, over quota per tonight's redirect.
• Matryoshka-doll folk-craft history/etymology — from the paper's own framing — scored 0.587 (novel) but a pure orphan with no vault connection; saved as a lower-priority seed.
• Voyage AI's MoE embedding architecture (Jan 2026) — from the pricing round-up — a fresh mechanism-migration thread (MoE moving from LLMs into embedding models), not pursued to keep this chain focused.

post-worthy: maybe — it's a clean, verifiable myth-correction that extends an existing MOC, but it's a small single-fact finding rather than a novel connection; good journal filler, not necessarily a standalone post.