docs: plan — universal structure + field<->symbol coherence gate
Planning-only design doc for the comprehension->structure->solve->verify spine: converge reading onto the binding-graph interlingua; field comprehends, structure bridges, symbol verifies; their AGREEMENT is the wrong=0 gate and the genuine second derivation that unblocks t2_precision. Field-as-reasoner must EARN each domain against independent gold (Phase 1.5 wedge: field-decides-entailment vs ROBDD oracle); never asserted unfalsifiably. INV-25 is Phase 0.
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<!-- CANONICAL | docs/analysis/universal-structure-and-field-symbol-coherence-gate-2026-06-04.md | 2026-06-04 | strategy/architecture-plan | the universal comprehension->structure->solve->verify spine, the binding-graph interlingua, and the field<->symbol coherence gate | verified: planning-only, no ADR number assigned; Phase 0 (INV-25) shipped -->
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# Universal structure + the field↔symbol coherence gate
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A plan for the most robust, clean, logical, and masterful path to **breaking
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reading and inputs of any modality into a logical structure** — so the engine can
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comprehend, articulate, and solve a problem in any field for which it has adequate
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packs. GSM8K (math logic) is the first proving ground; the same spine must lift
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GSM8K *and* be confirmed by independent problem-solving in other fields.
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This document is planning-only. It assigns no ADR number, changes no serving path,
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and introduces no capability claim. It records the architecture so later, gated
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PRs can build it without re-deriving the rationale.
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## 0. End goal
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```text
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input (any modality)
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-> comprehended into ONE logical structure
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-> reasoned over to produce a solution AND an articulated "understanding"
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(what the problem is, the approach)
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-> verified against INDEPENDENT gold
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-> refuses when grounding is incomplete
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```
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Success = held-out GSM8K rises **drastically** with `wrong == 0`, **and** the
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identical machinery clears an independent gold in ≥2 other fields.
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## 1. The honest grounding (what exists today)
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**The bottleneck is comprehension→structure, not arithmetic.** The GSM8K composer
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is epistemically *unsafe* on real data (`resolve_pooled` = 2 right / 87 wrong on
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holdout); bespoke per-shape readers do not compose. Capability is *real* only where
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the conclusion is **checkable against independent gold** — deductive propositional
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entailment (ROBDD) vs. an independent truth-table oracle: dev 200/200, holdout
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500/500, `wrong = 0`.
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**There are several disjoint problem-structure representations:**
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- `generate/math_problem_graph.py::MathProblemGraph` — the GSM8K candidate-graph solver IR.
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- `generate/derivation/model.py::GroundedDerivation` — the (unsafe-as-serving) derivation reader IR.
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- `generate/binding_graph/SemanticSymbolicBindingGraph` (ADR-0132/0133/0134/0135) —
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a **field-agnostic, unit-aware, provenance-carrying, acyclic, refusal-first**
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semantic-symbolic DAG. It already unifies two domains: math (`bind_math_problem_graph`)
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and proofs (`generate/proof_chain/builder.py`, ADR-0204 — "the binding graph's first consumer").
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- `generate/proof_chain` + `generate/logic_canonical.py` (ROBDD) — the deductive decision IR.
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- `generate/graph_planner.py::PropositionGraph -> ArticulationTarget` — the *articulation* IR (for saying the answer), separate from reasoning.
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**The reasoning readers have zero field/algebra dependency.** `generate/derivation`,
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`generate/proof_chain`, `math_solver`, `math_candidate_graph` import no
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`versor_apply` / `cga_inner` / `holonomy` / `field.propagate`. The CL(4,1) field
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engine participates in the **cognition turn loop** (capture field state, ratify
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intent, recall, identity) — **not** in problem reasoning. Any claim of
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"field-as-reasoner" is therefore currently *unverified*.
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**The dormant lever.** The reliability gate (ADR-0175) already exposes
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`checker="t2_precision"` ("widening past gold"), but it is inert: no genuinely
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structurally-distinct second derivation exists, and nothing consumes it.
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## 2. The synthesis — field comprehends, structure bridges, symbol verifies
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The correct architecture is not "field OR symbol." It is a precise division of
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labor with a **checkable handshake**:
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- **Field/manifold engine = comprehension & constraint-resolution master (right-mode).**
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A problem's entities/relations embed as geometric objects in CGA; solving =
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propagating constraints via `versor_apply` until the configuration is *coherent*
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(`versor_condition < 1e-6`). The converged field **is** the holistic understanding —
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apprehended as a whole, context-first, in CORE's *native* operations.
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- **Binding-graph DAG = interlingua / corpus callosum.** The typed, unit-checked,
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provenance-carrying form the field configuration is read **into and out of**: the
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inspectable, checkable commitment where holistic apprehension hands off to analysis
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and analysis hands corrections back. Not master, not mere servant.
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- **Symbolic servants (parser, ROBDD, solver, oracle) = analyze & dispose.** They
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verify the structure against independent gold, refute incoherence, articulate.
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They never originate truth.
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### 2.1 Why this is correct, not a compromise
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**The field-derivation and the symbolic-derivation are two structurally-distinct
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canonical decodings of the same problem. Their *agreement* is the `wrong = 0` gate.**
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1. **It operationalizes the deepest axiom — "Truth is coherent."** Two independent
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canonical decodings (geometric field + algebraic ROBDD) agreeing is coherence
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across vantage points. Agreement → admit; disagreement → **refuse**. This is
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exactly McGilchrist's "right apprehends, left analyzes, right re-integrates."
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2. **It is the genuine second derivation that is currently missing.** The Tier-2
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spine and `t2_precision` lever are inert because solver-vs-verifier shares
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structure (decoration) and the two GSM8K readers never co-fire. **Field ⟂ symbol
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is that second derivation.** Activating the field as a reasoner is *what unblocks
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the dormant capability lever* — mechanism, not metaphor.
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3. **It makes the field earn its role checkably (conforms to `wrong = 0` / no
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decoration).** The field is load-bearing *only where its answer agrees with an
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independent symbolic/gold derivation*. It can never serve an unagreed answer —
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disagreement refuses. This is INV-25 (Phase 0) generalized.
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### 2.2 Conformance to the governing axes
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| Axis | Conformance |
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|---|---|
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| Philosophical ("decoding, not generating") | Field & symbol are two canonical decodings of a reality that already is; agreement = it tracks the canonical form. |
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| Axiomatic | Reasoning *is* `versor_apply` + `cga_inner` + `versor_condition` (the actual primitives); exact recall stays exact. |
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| Ethical / `wrong = 0` | The field never serves an unagreed answer; refusal is the correction surface. |
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| Mechanical sympathy | Field does vectorized geometric propagation (native strength, Rust-parity-ready); symbol does discrete checks. |
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| Logical per "intelligence" | Holistic grasp + analytic check + refuse-on-incoherence is what integrated understanding *is*, with the non-negotiable twist that both modes must cohere or it declines. |
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## 3. The earning path (the field must *prove* it reasons)
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Today the readers have zero field dependency, so field-as-reasoner is a research arc
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that earns its role on the **safest checkable micro-domain first**. A negative
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result is an acceptable, honest outcome: where the field cannot earn agreement, it
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**stays a servant** and the symbolic path carries that domain, refusing where it
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cannot verify. **No unfalsifiable "the field knows" claim ever enters the codebase.**
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**The wedge (Phase 1.5):** *Can the field decide propositional entailment
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geometrically and agree with the ROBDD oracle on held-out, `wrong = 0`?* Logic is
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the ideal first test — the ROBDD + independent oracle already give a rock-solid gold
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(500/500). Embed atoms/clauses as geometric objects; decide entailment by
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incidence/coherence; require `field_verdict == ROBDD_verdict == oracle` on a
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held-out set. Agree → the field has earned a reasoning role and we have our first
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genuine second derivation. Cannot → we learned it cheaply and honestly.
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## 4. Phased plan
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- **Phase 0 — independent-gold discipline. ✅ SHIPPED.** INV-25
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(`tests/test_architectural_invariants.py`): no capability claim without an
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independent gold sharing no code with the SUT; deductive lane SHA-pinned
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(`deductive_logic_v1`). The foundation every later phase rides on.
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- **Phase 1 — canonize the universal structure.** Promote
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`SemanticSymbolicBindingGraph` to *the* documented problem-structure interlingua;
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resolve its closed-vocab placeholder (`semantic_role="unknown"`) only when a
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load-bearing consumer defines it. Add a **hemisphere-role invariant**: servant
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modules (parsers, metrics, vault) may not bypass the structure's consistency
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checks. (The taxonomy is a proposal to validate before the enforcing INV lands.)
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- **Phase 1.5 — the keystone wedge.** Field-decides-entailment vs. ROBDD oracle on
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the deductive lane. Prove (or honestly refute) field-as-reasoner on the safest
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gold. Gate to everything geometric.
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- **Phase 2 — comprehension compiler → binding graph** (finite-entity grounding
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first), with **field ⟂ symbol agreement** as the admission gate from the moment
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Phase 1.5 succeeds.
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- **Phase 3 — activate `t2_precision`.** The field⟂symbol agreement *is* the t2
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signal; wire the propose-loop consuming `checker="t2_precision"`. No invented
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second derivation needed — it is real now.
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- **Phase 4 — GSM8K on the universal structure** (the drastic-lift phase), gated by
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field⟂symbol agreement + independent gold + held-out/sealed validation (never
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train_sample — the overfit firewall). Safe by construction.
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- **Phase 5 — cross-domain confirmation.** Systems/software arena (execution = a
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third independent decoding; ADR-0199's first non-math arena), then a second
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non-executable field with a proof-checker gold. The generalization proof.
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- **Phase 6 — multimodal grounding.** Connect the sensorium modality compilers
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(`sensorium/compiler` `CompilerLike`/`CompilationUnitLike`) → binding graph. A
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modality becomes "just another reader" grounding into the universal structure;
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stays afferent/gated per ADR-0198.
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### Cross-cutting (every phase) — checkable budgets, adjoints, phenomenology
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- **Distortion budgets as first-class CI gates**, but *only checkable ones*:
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grounding completeness %, unit-proof coverage, acyclicity, and **structural
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perturbation stability** (paraphrase/reorder the input → the binding graph and
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answer are invariant, or it refuses). Regressions gate the build as hard as
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accuracy. This is the antidote to metric-capture (the train_sample trap).
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- **Adjoint-per-operator.** Every new transform ships with its verifier/correction
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pass + a test that it reduces a *structural* error, not just a string.
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- **Phenomenology harness.** Sample full structured articulations (the
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"understanding": problem restatement + approach) for periodic trusted review;
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qualitative depth as an explicit but *subordinate* signal (never a new truth
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criterion — that would re-open left-mode capture under a different name).
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## 5. Risks & honest tensions
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- **HIGH — Phase 4 `wrong = 0`.** GSM8K serving breached it before. Mitigation:
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agreement gate + independent gold + held-out/sealed + pre-push verification
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(auto-merge pipeline).
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- **MEDIUM — field-reasoning may not pan out** in a given domain. Expected and
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acceptable: it stays a servant there; the symbolic path carries it, refusing where
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unverifiable.
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- **MEDIUM — McGilchrist over-reach.** "Field as master of reasoning" is realized
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only through the *checkable* agreement gate; never asserted as unfalsifiable fact.
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- **MEDIUM — IR convergence cost.** Converge the disjoint reasoning IRs incrementally
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(adapters first, direct targeting later), never a big-bang rewrite.
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## 6. What this supersedes
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The earlier 554/555/556 sequence is reframed: 554 (Tier-2 verifier) was inert →
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Phase 3 done *right* (field⟂symbol is the genuine second derivation); 555
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(target-slot composition) was unsafe via the composer → Phase 4 (comprehension on
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the universal structure, gated); 556 (systems/software arena) → Phase 5.
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