# Programme Algebra Parallel Lane **Date:** 26 October 2026 **Status:** parallel compilation lane; complete structural projection, partial epistemic, route, empirical-return and scientific admission **Authority:** the existing corpus remains canonical; this lane may not replace or promote it without an explicit later decision ## Purpose This lane expresses the science programme through the same compositional grammar used by Sourcery's `common-algebra-2` work. It is deliberately parallel to the existing corpus. Its first job is to reveal whether an algebraic representation can preserve more structure, provenance and refusal information than the current filesystem-and-link projection before it is considered as a replacement. The compilation route is: \[ \text{canonical corpus sources} \longrightarrow \text{typed programme algebra} \longrightarrow \text{receipts, navigation and generated readings}. \] The generated algebra is not another editable source of truth. Corpus Markdown remains canonical for prose, argument and explanation. Authored algebra declarations remain canonical for object identities, profiles and admitted transformations. Generated JSON and reports are disposable projections of those two source classes. The first held-out retrieval tranche establishes a narrower result. Algebraic retrieval finds machine ledgers that Markdown-only search cannot see, but it is not uniformly better for prose. Naive score fusion and keyword-only routing both failed frozen gates. A later explicit `machine`/`prose` source-kind facet found all six fresh targets within the top ten while retaining the earlier failures. This supports a complementary typed retrieval surface, not corpus replacement. ## Six depths of conversion 1. **Structural projection.** Every retained corpus Markdown document, JSON ledger and image becomes a hash-bound object. Every Markdown heading and bounded semantic unit receives its own address. Containment and explicit links become observed relations. This layer is complete by construction. 2. **Epistemic projection.** Declared status, date, evidence, parent, continuation, source, generator and verifier fields become typed coordinates or relations. Missing declarations remain visible as missing; the compiler does not invent them. 3. **Scientific admission.** A movement is a scientific transformation only when its endpoint signatures, changed coordinates, dimensions, assumptions, losses, evidence and authority pass the common-algebra gates. The four D02 families are the initial admitted seed. Ordinary Markdown links never become scientific transformations merely because they connect scientific prose. 4. **Research-state transformations.** An explicit `Parent` declaration may become a proposal-only epistemic transformation when both documents exist, the target has a declared status, evidence is attached and every changed kernel coordinate is named. Failed candidates remain refusal records. 5. **Composed routes.** Maximal parent chains are composed into bounded ALE receipts: assumptions, losses and evidence travel with the route. One failed edge, a cycle or a depth overflow rejects the whole route without erasing it. 6. **Empirical return.** Experiment-shaped records are normalized to preparation, intervention, detector, nuisance model, record and decision rule. A complete six-field packet means the proposed protocol closes syntactically; it does not mean the experiment ran or its hypothesis was confirmed. ## Shared kernel and profiles Every object carries the twelve-coordinate epistemic kernel \[ (K,D,R,C,F,S,G,E,U,P,A,T), \] meaning kind, domain, role, context, form, status, governing scheme, equivalence, admissibility, support, authority and time. Domain profiles extend that kernel without changing its meanings. The initial profiles are declared in [`programme_algebra_profiles_v1.json`](programme_algebra_profiles_v1.json). Machine-record schema views and their deliberately provisional matching rules are declared separately in [`programme_algebra_adapters_v1.json`](programme_algebra_adapters_v1.json). This is a family of typed categories, not one forced vector algebra. Scientific, mathematical, physical, experimental, epistemic and governance objects may compose internally under profile rules. A cross-profile passage is partial and must retain its assumptions, losses, evidence, falsifier and authority ceiling. ## Articles These are the reader-facing entrances to the lane. The first three are compiled from the current corpus and may be regenerated; the conversion register is the authored audit of what the compiler does and does not claim. - **[Programme Algebra Journeys](generated/PROGRAMME_ALGEBRA_JOURNEYS.md)** — follow admitted and refused research lineages, their assumptions, losses and evidence, and the empirical-return surfaces they reach. - **[Programme Algebra Coverage](generated/PROGRAMME_ALGEBRA_COVERAGE.md)** — inspect conversion depth, machine-record adapters, exclusions and the honest remainder. - **[Programme Algebra Retrieval Benchmark](generated/PROGRAMME_ALGEBRA_RETRIEVAL_BENCHMARK.md)** — compare canonical prose search with algebraic retrieval, including the failed controls and the typed-facet candidate. - **[Whole-Corpus Conversion Register](CONVERSION_REGISTER.md)** — inspect the authored L0–L6 completion audit and the boundary between structural coverage and scientific admission. ## Generated outputs Run: ~~~powershell node tooling/programme-algebra/compile_programme_algebra.mjs --write node tooling/programme-algebra/run_retrieval_benchmark.mjs --out corpus/programmes/programme-algebra/generated/PROGRAMME_ALGEBRA_RETRIEVAL_BENCHMARK.json --report corpus/programmes/programme-algebra/generated/PROGRAMME_ALGEBRA_RETRIEVAL_BENCHMARK.md node verification/admissibility/verify_programme_algebra_parallel_lane.mjs node verification/admissibility/verify_programme_algebra_retrieval_benchmark.mjs ~~~ The compiler writes: - `generated/programme_algebra_v1.json` — the inspectable manifest, source identities, counts, coverage and archive hashes; - `generated/programme_algebra_records_v1.json.gz` — the deterministic complete machine-readable projection and admission receipts, compressed to avoid repeating the twelve-coordinate kernel tens of thousands of times. This disposable archive is intentionally ignored by Git and is regenerated locally or in CI; its exact hashes and sizes remain in the tracked manifest; - `generated/PROGRAMME_ALGEBRA_COVERAGE.md` — the human-readable coverage and boundary report; - `generated/PROGRAMME_ALGEBRA_JOURNEYS.md` — the human reading projection for composed ALE routes, empirical-return surfaces and the honest remainder; - `generated/PROGRAMME_ALGEBRA_RETRIEVAL_BENCHMARK.md` — the preregistered canonical-versus-algebra retrieval comparison, including failed fusion and validation gates. Its current verdict is open, so it does not authorize replacement. Running without `--write` performs the same compilation and prints the summary without changing files. ## Replacement gate This lane may replace any part of the existing corpus only after it demonstrates: 1. lossless source identity and stable object identity; 2. no silent status, authority or evidence promotion; 3. explicit failure on stale or mismatched endpoint signatures; 4. strictly better retrieval or reasoning on held-out tasks; 5. readable generated journeys for humans; 6. reproducible compilation without a live Claimipedia or Sourcery service; and 7. an explicit migration and rollback decision. Until those gates close, the lane is an instrument for examining the corpus, not its successor.