Spike #24 — Cross-domain primitive vocabulary + ephemerides residual analysis

Status: SCOPE locked 2026-05-15; Phase 1 inventory begins. Branch: research/spike-24-primitive-vocabulary-2026-05-15 Predecessor: PR #416 (pin-and-slot algebra + algebraic-uniqueness synthesis), merged as fba3065 to main.

Genesis question

PR #416 closed with the §11.6.17 algebraic-uniqueness finding: the bronze's structure is forced by the algebra; anyone with the same period observations + same engineering substrate + minimum-cost optimization lands on the same gear-grouping. The user then extended this to a universal:

"if keplers equation is just gears and slots and pins, it does apply to anything else that moves the same way. I don't think that we can argue against that anymore."

The burden of proof flipped (per [[user_stance_kepler_shape_universal]]): any Kepler-shape system instantiates pin-slot-gear primitives in some substrate; the counter-claim requires producing a Kepler-shape system that is NOT primitive-composable. Spike #24 tests this across the spectral collection's plug-ins.

Methodology — disciplines locked

Five disciplines locked through the planning conductor calls of 2026-05-15:

1. Abstraction-layer-first. srmech is the score (abstraction); the spectral plug-ins (antikythera-spectral, ephemerides-spectral, chess-spectral, doom-spectral, othello-spectral, logo) are the instruments (instantiation). Phase 1 identifies primitives at the srmech abstraction layer first, ignoring all plug-in-specific cosmos / chess / doom content. What survives is abstraction-layer-real. "Ignore the plug-in as one step of our research" per user instruction.

2. Mechanical-first abstraction-layer identification. What is in the srmech python package source = abstraction layer. What is in plug-in packages = instantiation. Phase 2's "extends" cells flag promotion candidates for a future PR pass.

3. Pi-as-projection. Integer-cyclic upstream, continuous (pi-bearing) downstream. Per [[user_stance_pi_as_projection]]. Name primitives in integer-cyclic terms where possible; pi-bearing forms are documentation aids for cross-referencing continuous-frame literature, not load-bearing primitive descriptions.

4. Real-coupling subtraction before primitive claims. Earned-frontier discipline. For Phase 3, extract known couplings from JPL data + existing ephemerides-spectral structures (Sol Resonance Graph, breathing-Laplacian, spin-orbit-resonance, tidal, secular, J2/J4 gravitational harmonics) and subtract their contributions from the residual against DE441 before naming any "missing primitive." A residual that resolves to a real coupling is NOT a primitive — it's an under-modelled physics term. "Learn how to learn what we don't know" applies only at the residual that survives the subtraction.

5. Two-table CPU mapping with bronze-standalone column. Per user 2026-05-15: "cpu mapping is great, but it's only one perspective. an additional table that is bronze-operator mapping will reveal things we don't know." Table 2A = bronze→CPU correspondence (where it's clean). Table 2B = bronze-standalone (where bronze content has no clean CPU analog, OR has a lossy/leaky CPU analog — document both lossy and leaks, not just absence). The bronze isn't a degenerate CPU; it's its own algebra, and the CPU mapping might lose content.

Phases

Phase 1 — Abstraction-layer-only inventory

Walk the srmech python package source. Identify each module, function, dataclass, and data structure. For each: name the primitive transformation it represents, in substrate-agnostic terms (integer-cyclic algebra when possible).

Output: spike_24_primitive_vocabulary_findings_2026-05-15.md Phase 1 section. Format: bullet-list per primitive with (name, what-it-does, where-it-lives, integer-algebraic form, CPU-analog if obvious).

Expected character: srmech currently is the provenance scaffolding (AMSC attestation, NDJSON streaming, profile loading) more than the algebraic scaffolding. The algebraic primitives (cyclic-group ops, period-relation factorization, pin-slot atan2, etc.) currently live mostly in plug-ins. This is itself a Phase 1 finding worth recording — the abstraction layer may need promotion-from-plug-in to be complete.

Phase 2 — Per-plug-in instantiation matrix

For each spectral plug-in (antikythera-spectral, ephemerides-spectral, chess-spectral, doom-spectral, othello-spectral, logo), audit which Phase 1 primitives it uses, which it extends with plug-in-specific content, and which it doesn't touch. Output: a markdown matrix in the findings doc + an NDJSON tabular form.

For each "extends" cell: the plug-in-specific extension is a candidate for promotion to the abstraction layer (if substrate-agnostic) OR a genuine plug-in-bound primitive that should stay (if domain-specific). Phase 2 doesn't decide promotions; it surfaces candidates.

Plus the two CPU tables: - Table 2A — bronze→CPU correspondence: primitive name, bronze instantiation, CPU operator analog, mapping fidelity (exact / lossy / leaky). - Table 2B — bronze-standalone: bronze primitives where the CPU analog is lossy (CPU has an operator but it elides bronze algebra), leaks (CPU operator captures less than bronze content carries), or absent (no clean CPU analog at all).

Phase 3 — Ephemerides residual analysis (full body sweep)

Real-coupling subtraction first, then partition the surviving residual into integer-algebraic / continuous-projection / unexplained.

• 3a. Abstraction-only forward-sweep. Predict per-body motion using ONLY abstraction-layer primitives (cyclic-group period ratios, integer mesh), no ephemerides-spectral plug-in cosmos functions. Compare to DE441 truth over the design epoch. Residual = what the abstraction layer alone cannot say.
• 3b. Subtract abstraction-layer-predictable content. What srmech alone can predict gets subtracted. What remains is plug-in territory.
• 3c. Enable the ephemerides-spectral plug-in and subtract real couplings. Extract from JPL data + existing package structures:
• Mean-motion resonances (Sol Resonance Graph; gateway_graph_laplacian.py)
• Secular resonances (Laskar planetary tables; apsidal/nodal alignments)
• Tidal couplings (tidal_migration_data.py; per-body Q values)
• Gravitational harmonics J₂, J₄ (geodetic + magnetic catalog data)
• Breathing-Laplacian state-dependent terms (Phase 9 dynamic coupling)
• Spin-orbit resonance locks (spin_orbit_resonance_data.py)

For each (body, coupling-source) pair, compute the coupling's predicted contribution analytically (fast, structural), then validate numerically (slower, catches what analytical misses). If analytical and numerical diverge for a particular body, the divergence itself is a finding worth recording.

Subtract the real-coupling contributions from the post-3b residual.

• 3d. Partition the surviving residual.
• Integer-algebraic structure at period-ratio-derived frequencies, amplitudes that factor through ℤ/n cleanly → candidate missing primitive. Goes to primitive inventory pipeline (Phase 1 / 2 promotion candidates).
• Continuous-frame structure without integer-algebraic content (irrational frequencies, transcendental basis, broadband) → projection artifact. Documented but not claimed as primitive.
• Unexplained content (neither integer-algebraic nor pure projection) → the earned frontier. "Learn how to learn what we don't know" applies here, not earlier.

Output per tier: NDJSON record per (body, residual-component, classification).

Phase 4 — Ephemerides handoff packet

Single notes file spike_24_ephemerides_handoff_2026-05-15.md for the next-door session that handles ephemerides-spectral code work. Contains: - Per-body real-coupling subtractions made (so they can verify the package models these correctly; discrepancies are bugs they fix, not primitives we name). - Surviving residuals with classification (missing-primitive candidate / projection artifact / unexplained). - Specific code changes the next-door session would need to instantiate any primitives we name (NOT executed here — we only describe).

Phase 5 — Notebook landing

Update docs/srmech/srmech_research_notebook.md with a primitive-vocabulary cross-domain section. Concrete shape: a new subsection in srmech's §3.5 cross-manifold pattern, or a new §3.6 specifically for the primitive inventory. Per [[user_stance_kepler_shape_universal]], the inventory should explicitly note that Kepler-shape behavior across any plug-in domain identifies the same pin-slot-gear primitive composition.

Bounds and disciplines

• Single PR for the analysis. ephemerides-spectral code work goes to a separate session via the Phase 4 handoff packet.
• No ephemerides-spectral version bump in this PR. Any code changes the analysis recommends are deferred.
• No naming yet — Phase 1 produces an inventory list; naming convention decisions come later.
• No closure claim — we're not proving the primitive vocabulary complete in this spike. The user explicitly: "our inquiries don't necessarily terminate with a long series of 7 null results." Open question remains open.
• NDJSON output for all tabular content (per [[feedback_ndjson_over_bloated_json]]).
• No squash merge when ready (per [[feedback_no_squash_merges]]).

Cross-references

• PR #416 (merged fba3065) — pin-and-slot algebra + §11.6.17 algebraic-uniqueness synthesis
• [[user_stance_kepler_shape_universal]] — the universal claim that drives Spike #24
• [[user_stance_pi_as_projection]] — integer-cyclic upstream methodology
• [[user_stance_fiber_as_spatially_absent_encoding]] — algebra-upstream-projection-downstream pattern
• [[user_stance_string_theory_instrument_first]] — burden-of-proof discipline; counter-claims must produce instruments, not extra dimensions
• [[feedback_orchestration_metaphor]] — score/instrument metaphor for srmech/plug-ins
• [[user_explanation_discipline]] — preserve user vocabulary in derived artifacts