Research: ground Semantic Projection Networks in prior art

docs/research/U7-semantic-projection-networks-literature.md

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+# U7 — Semantic Projection Networks: preliminary literature grounding
+
+Status: **research note, non-normative**
+
+Date: 2026-08-22
+
+## Why this note exists
+
+OSIL is exploring a possible generalization of interoperability from pairwise conversion to **networks of heterogeneous semantic projections**. Before promoting that idea into the specification, this note maps the closest established research traditions and narrows the novelty claim.
+
+The working phrase is **Semantic Projection Networks (SPNs)**:
+
+```text
+representation A ──contracted projection──> representation B
+       │                                      │
+       └────────── alternative paths ─────────┘
+
+nodes  = heterogeneous representational regimes
+edges  = transformations with explicit preservation/loss claims
+paths  = composed transformations
+cycles = opportunities to test semantic stability/drift
+```
+
+This is deliberately a research hypothesis, not yet an OSIL language construct.
+
+## Search-status disclosure
+
+A requested Consensus literature search could not be completed on 2026-08-22 because the connected Consensus account had exhausted its monthly search quota. The literature below was therefore collected from primary/publisher sources and bibliographic records through an independent academic-web search. **Do not describe this note as a Consensus systematic review.** Re-run the queries through Consensus after quota renewal and update this note if that search materially changes the map.
+
+## Closest prior art
+
+### 1. Bidirectional transformations and lenses
+
+The lenses literature already gives a rigorous vocabulary for lawful transformations between related representations.
+
+- Bohannon, Foster, Pierce, Pilkiewicz, and Schmitt, **“Boomerang: Resourceful Lenses for String Data,”** POPL 2008. A lens is treated as a bidirectional program, with laws governing forward and backward behavior. DOI: `10.1145/1328438.1328487`.
+- Hofmann, Pierce, and Wagner, **“Symmetric Lenses,”** POPL 2011. Removes the privileged “source/view” asymmetry and studies composition of symmetric bidirectional transformations. DOI: `10.1145/1926385.1926428`.
+
+**Implication for OSIL:** pairwise `encode/decode` is not a sufficient novelty claim. Lawful bidirectional and symmetric transformations are established territory.
+
+### 2. Multiary lenses and networks of models — the nearest conceptual neighbor
+
+The most important prior-art cluster for SPNs is not ordinary lenses but work that explicitly moves beyond two models.
+
+- Diskin, König, and Lawford, **“Multiple Model Synchronization with Multiary Delta Lenses,”** FASE 2018. It formalizes synchronization of more than two inter-related models and emphasizes composition. DOI: `10.1007/978-3-319-89363-1_2`.
+- Diskin, König, and Lawford, **“Multiple Model Synchronization with Multiary Delta Lenses with Amendment and K-Putput,”** Formal Aspects of Computing 31(5), 2019, 611–640. Extends the framework with reflective updates and composition laws. DOI: `10.1007/s00165-019-00493-0`.
+- Stevens, **“Maintaining consistency in networks of models: bidirectional transformations in the large,”** Software and Systems Modeling 19, 2020, 39–65. Models collections of representations as networks and studies consistency restoration, decomposition, and non-interference. DOI: `10.1007/s10270-019-00736-x`.
+
+This literature already contains the graph-level intuition:
+
+```text
+model sets  -> nodes
+consistency relations / bx -> edges or hyperedges
+```
+
+**Implication for OSIL:** “representations form a network and transformations compose” is prior art. SPN should not be presented as discovering network-shaped interoperability.
+
+### 3. Multi-level and heterogeneous intermediate representations
+
+Lattner et al., **“MLIR: Scaling Compiler Infrastructure for Domain Specific Computation,”** CGO 2021, pp. 2–14, develops infrastructure for transformations across multiple abstraction levels, application domains, hardware targets, and execution environments. DOI: `10.1109/CGO51591.2021.9370308`.
+
+**Implication for OSIL:** heterogeneous multi-IR computation and cross-level lowering are also established. OSIL needs a sharper claim than “many IRs connected together.”
+
+### 4. Semantics-preserving compilation
+
+Leroy, **“A Formally Verified Compiler Back-end,”** Journal of Automated Reasoning 43, 2009, develops machine-checked semantic-preservation proofs for compiler transformations.
+
+**Implication for OSIL:** semantic preservation across transformations has a deep formal-verification literature. OSIL's distinctive question is not whether preservation matters, but how **declared, partial, heterogeneous preservation obligations compose across arbitrary interoperability paths**.
+
+### 5. Equality saturation and equivalence classes of realizations
+
+Willsey et al., **“egg: Fast and Extensible Equality Saturation,”** POPL 2021, develops e-graphs as efficient representations of congruence relations over many equivalent expressions and uses equality saturation to search among rewrites.
+
+**Implication for OSIL:** representing many equivalent realizations and searching them is established compiler technology. OSIL can use this machinery, but should not make equivalence-class search itself the novelty claim.
+
+## Adjacent mathematical inspiration, not current prior-art basis
+
+### Recurrent / associative computation
+
+Ramsauer et al., **“Hopfield Networks is All You Need,”** ICLR 2021, characterize modern Hopfield networks through update dynamics, fixed points, metastable states, and associative retrieval (arXiv:2008.02217).
+
+This is useful for thinking about repeated projection, convergence, and attractor-like behavior. It does **not** currently establish a direct theoretical relationship to semantic interoperability.
+
+### Cross-cortical communication subspaces
+
+Semedo et al., **“Cortical Areas Interact through a Communication Subspace,”** Neuron 102(1), 2019, proposes that interactions between cortical populations occur through low-dimensional communication subspaces. DOI: `10.1016/j.neuron.2019.01.026`.
+
+This motivates a useful design intuition: heterogeneous local representational regimes may coordinate through restricted projections without collapsing into one universal representation. For OSIL this remains **analogy/inspiration**, not evidence that software interoperability should literally be modeled neurobiologically.
+
+## Revised novelty boundary
+
+The literature search changes the strongest defensible public claim.
+
+### Claims OSIL should *not* make
+
+Do not claim that OSIL newly introduces:
+
+- bidirectional or symmetric transformations;
+- multi-model or network-shaped synchronization;
+- composition of transformations;
+- heterogeneous/multi-level IR infrastructure;
+- semantics-preserving compilation;
+- equivalence-class search.
+
+All have substantial prior art.
+
+### Candidate OSIL contribution
+
+The research opportunity is instead the conjunction of the following properties:
+
+1. **Heterogeneous computational ecosystems remain semantically sovereign.** OSIL references native/versioned meanings rather than replacing them with one global operational semantics.
+2. **Every projection carries an explicit preservation contract** describing what is preserved, weakened, or permitted to be lost.
+3. **Contracts compose at path level**, making a multi-hop interoperability claim inspectable rather than treating each converter independently.
+4. **Alternative paths are comparable** with respect to declared semantic preservation, allowing path dependence/path independence to become an empirical or formal property.
+5. **Cycles expose semantic drift** by returning to a comparable regime under an explicit equivalence relation rather than byte equality.
+6. **Path selection becomes constrained optimization:** search for a realization/path subject to semantic guarantees, cost, target requirements, and possibly security invariants.
+7. **OSIL itself participates as an ordinary node**, allowing self-application of the same projection and preservation machinery.
+
+A sharper working thesis is therefore:
+
+> **OSIL investigates evidence-carrying semantic transport across heterogeneous computational representation networks, where preservation obligations compose over paths and can constrain path/realization search.**
+
+That wording is intentionally narrower than “interoperability as a network.”
+
+## Formal research object
+
+Let each ecosystem-local representational regime be a node `R_i`.
+
+A projection is not merely a function `R_i -> R_j`, but a transformation bundled with an explicit contract and resulting evidence:
+
+```text
+P_ij : (R_i, C_ij) -> (R_j, E_ij)
+```
+
+where:
+
+- `C_ij` is the declared preservation obligation;
+- `E_ij` records observed/proved preservation and allowed loss.
+
+For a path
+
+```text
+R_A --P_AB--> R_B --P_BC--> R_C
+```
+
+we want a composition operator
+
+```text
+C_AC = C_AB ⊗ C_BC
+```
+
+and evidence composition
+
+```text
+E_AC = E_AB ⊙ E_BC
+```
+
+whose laws remain an open research question.
+
+Alternative paths create a directly testable condition:
+
+```text
+       path α
+A ----------------> D
+ \                  ↑
+  \-> B -> C -> E -/
+       path β
+```
+
+Ask whether
+
+```text
+P_α(x) ≈_K P_β(x)
+```
+
+for declared semantic property set/equivalence regime `K`.
+
+Cycles create a second condition:
+
+```text
+A -> B -> C -> A'
+```
+
+Ask what is preserved in `A'` relative to `A`, and whether repeated cycling converges, oscillates, or accumulates loss.
+
+## Research questions after prior-art correction
+
+**RQ1 — Contract composition.** What algebra correctly composes preservation, weakening, and loss claims over a heterogeneous projection path?
+
+**RQ2 — Path equivalence.** Under what conditions do distinct projection paths between the same ecosystems preserve equivalent declared semantics?
+
+**RQ3 — Drift.** How should semantic loss be measured and attributed across cyclic or recurrent paths?
+
+**RQ4 — Convergence.** Are there useful classes of projection networks for which repeated transformations reach fixed points or stable equivalence classes?
+
+**RQ5 — Search.** Can a projection path be selected by optimizing cost/performance subject to preservation constraints, rather than optimizing execution alone?
+
+**RQ6 — Relationship to bx/multiary lenses.** Can OSIL preservation contracts be embedded into, derived from, or contrasted formally with multiary delta-lens consistency relations and laws?
+
+RQ6 is particularly important: the right outcome may be that part of the proposed SPN formalism should reuse existing lens machinery rather than invent a parallel algebra.
+
+## Immediate falsifiable experiments for OSIL
+
+1. Register OSIL itself as an ecosystem and establish an OSIL -> OSIL preservation baseline.
+2. Construct at least two distinct paths between the same endpoints, e.g. `OSIL -> A -> C` and `OSIL -> B -> C`.
+3. Compute preservation reports for both and compare the path-level contracts.
+4. Add a cycle and measure whether declared semantic properties are monotonically lost, recovered, or stable.
+5. Introduce a path cost function and test whether the cheapest path differs from the highest-preservation path.
+6. Re-express one experiment using a known lens/multiary-lens formalism to identify exactly what OSIL adds.
+
+## Public posture
+
+Until the formal comparison with multiary lenses and networks-of-models work is complete, public material should use language such as:
+
+> We are exploring evidence-carrying semantic projection networks as an OSIL research direction. Networked and multiary transformations have substantial prior art in bidirectional transformation and model-synchronization research; our current question is whether OSIL's explicit, composable preservation/loss contracts over heterogeneous computational ecosystems enable a distinct and useful layer of path-level reasoning and optimization.
+
+This is stronger scientifically than presenting the graph topology itself as novel.
+
+## Core references
+
+1. A. Bohannon, J. N. Foster, B. C. Pierce, A. Pilkiewicz, A. Schmitt. *Boomerang: Resourceful Lenses for String Data.* POPL 2008. DOI: `10.1145/1328438.1328487`.
+2. M. Hofmann, B. C. Pierce, D. Wagner. *Symmetric Lenses.* POPL 2011. DOI: `10.1145/1926385.1926428`.
+3. Z. Diskin, H. König, M. Lawford. *Multiple Model Synchronization with Multiary Delta Lenses.* FASE 2018. DOI: `10.1007/978-3-319-89363-1_2`.
+4. Z. Diskin, H. König, M. Lawford. *Multiple Model Synchronization with Multiary Delta Lenses with Amendment and K-Putput.* Formal Aspects of Computing 31(5), 2019. DOI: `10.1007/s00165-019-00493-0`.
+5. P. Stevens. *Maintaining consistency in networks of models: bidirectional transformations in the large.* Software and Systems Modeling 19, 2020. DOI: `10.1007/s10270-019-00736-x`.
+6. C. Lattner et al. *MLIR: Scaling Compiler Infrastructure for Domain Specific Computation.* CGO 2021. DOI: `10.1109/CGO51591.2021.9370308`.
+7. X. Leroy. *A Formally Verified Compiler Back-end.* Journal of Automated Reasoning 43, 2009. arXiv:0902.2137.
+8. M. Willsey et al. *egg: Fast and Extensible Equality Saturation.* POPL 2021. arXiv:2004.03082.
+9. J. D. Semedo et al. *Cortical Areas Interact through a Communication Subspace.* Neuron 102(1), 2019. DOI: `10.1016/j.neuron.2019.01.026`.
+10. H. Ramsauer et al. *Hopfield Networks is All You Need.* ICLR 2021. arXiv:2008.02217.
+
+## Next literature pass
+
+When Consensus search becomes available again, query at minimum:
+
+```text
+"multiary delta lenses" composition model synchronization
+"networks of models" bidirectional transformations consistency
+"semantic preservation" heterogeneous intermediate representations compiler
+"path independence" bidirectional transformation lens
+"contract composition" semantic interoperability software
+"information loss" model transformation composition
+```
+
+The purpose of that pass is not to accumulate citations but to try to **falsify the narrowed novelty boundary above**.