Orthemology

Status: research-stage draft (R6); not peer reviewed; fresh-session repository review completed; not external human peer review; not empirically validated. Coined terminology is benchmark-gated, not adopted. See STATUS.md.

Orthemology is a proposed theory of how concrete cases get correctly classified, handled, and audited by rule-governed processes — human, institutional, or automated. It gives first-class, auditable structure to a familiar but usually implicit architecture:

Term (candidate)	Ordinary-language meaning	Pillar example
orthemma	the concrete situated case, with an identity key and version	this particular pillar, as it now stands
ortheme	a repeatable, consequence-bearing state-type the case may instantiate	orthogonal to a declared reference plane within tolerance ε
metaortheme	a repeatable higher-order governing standard or configuration	the standard fixing which reference frame, tolerance, instruments, calibration, evidence, and validation count
metaorthemma	the concrete, case-bound configuration token of that standard	this standard bound to this plane, tolerance, instrument, and calibration, for this pillar, now
orthing	the whole rule-governed handling process	identifying the pillar, applying the bound standard, gathering evidence, placing, validating, routing, closing
orthing episode	one dated, concrete run of that process (may contain several metaorthemmata)	the record of today's check on this pillar

The final assertion ("this pillar is orthogonal") is a placement claim judged for correctness; the ortheme is the state-type itself.

What to read

• Current main manuscript: manuscript/orthemma-ortheme-systems-revised-draft.md — the one current draft (Orthemma–Ortheme Systems: An Analysis-Relative Architecture for Auditable Classification and Handling); earlier renderings are superseded.
• Current formal core: theory/orthemic-core-formalization.md, with the derived multi-actor extension in theory/orthemic-multi-actor-conflict-note.md.
• Normative registries: docs/verdict-registry.yaml (verdict semantic IDs + display aliases) and docs/notation-registry.yaml (symbol table) — both machine-enforced.
• Worked case: examples/compaction-stale-steer.md (the stale-directive pattern) plus nine machine-readable episode examples under examples/ validated against schemas/.
• Companion (metaphysical/theological — complete drafts, separate and firewalled): companion/.
• Terminology program (Pilot-0 v2 READY_FOR_HUMAN_MATCHING_REVIEW; Pilot 1 / confirmatory templates DRAFT; NOT RUN, no term adopted): terminology/.
• Decision records: docs/decisions/ — 0001–0036: 0001–0003 (owner reconciliation R1), 0004–0008 (autonomous closure R2), 0009–0010 (type/token, soundness bearers, orthability senses — R3), 0011–0015 (claim-relative reasoning paths, reference-model semantic contract, source-status normalization, generated project state, latent-state boundary — R4), 0016–0017 (review-state contract, private-evidence boundary — R5), 0018–0019 (experiment-packet readiness/registration, current sourcing state — R6), 0020–0022 (experiment inferential readiness/versioning, daee noetic application, experiment methods gate — R7), 0023–0025 (mathematical typesetting pipeline, dynamic orthing / representation learning, meta-noetic memetics and sound corrective dynamics — R7B), 0026–0028 (candidate and multi-target state — R7C), 0029–0033 (live candidate, representation, ecology, and governed correction — R7D), and 0034–0036 (independent repair and Somnic contracts — R7E). Git integration and public custody records do not establish theory adoption, terminology adoption, empirical validation, or natural campaign closure.
• Generated project state: docs/current-state.yaml — the canonical machine-readable revision, counts, statuses, and burdens; VERSION/README/STATUS/OPEN-DECISIONS are checked against it in CI.
• Sourcing: references/orthemology.bib + docs/sourcing/ — per-claim verification statuses.
• Closure accounting: docs/project-closure/ — formal audit, counterexample ledger, reviews, burden ledger.
• AR8R V11 reconciliation: docs/project-closure/ar8r-v11/ — sanitized evidence dispositions, bounded theorem and synthetic-pilot packets, provenance reconciliation, and active/deferred research-program memory; no private transcript or natural-closure claim.
• Reconciliation history: archive/reconciliation/ — exact patches, ledgers, and validation reports (immutable; retain pre-R2 notation by design).
• Draft PDFs: artifacts/ — DRAFT-stamped, commit-pinned renderings with source-hash sidecars.

Two ideas that carry the theory

Result correctness is not pathway adequacy. An episode's result can be right while the process that produced it was defective (the stopped-clock validator; the wrongly-calibrated check that happens to agree), and a genuinely reliable, correctly-run process can still miss a rare case. The verdict layer keeps these axes independent: V1 judges the placed result; a result-free pathway core (evidential support, configured-procedure truth-conduciveness, evidence currentness, rule/policy/token/execution adequacy, decision-time justification, route safety, closure truthfulness, robustness) judges the process. All four result × pathway combinations are representable, with deterministic fixtures proving it.

Ground truth is analysis-relative. Which state-types a case truly instantiates is defined relative to a declared, versioned analysis A (boundary, task, repertoires, loss, tolerance, representation and merger families): O*(m; A). The familiar task-relative notation (O*_T(m)) survives only as explicitly scoped shorthand once a single analysis is fixed — it is an abbreviation, not a second ontology. The case itself and its worldly facts are not created by the analysis; only the state-type description is indexed.

Honesty notes

• No empirical experiment has validated the framework. The designed public studies stand at their canonical packet-index states — FCSP-2 and ER-2 READY_TO_RUN; FCSP-1 and ER-1 historical DETERMINISTICALLY_VALIDATED (superseded); terminology Pilot-0 v2 READY_FOR_HUMAN_MATCHING_REVIEW; Pilot 1 and confirmatory templates DRAFT — none of those packets has been run, none externally registered, and no term adopted. A distinct recovered AR8R record documents an eight-seed internal synthetic T299/T300 pilot with a negative, methodologically bounded result; it is not a public experiment packet or external empirical validation. The deterministic fixtures and validators are internally conformance-checked over the declared schemas, examples, fixtures, and adversarial operators — never a mathematical consistency proof. The private source records are not published; the public custody summary supports only its explicit negative disposition.
• The coined vocabulary (orthemma/ortheme/metaortheme/metaorthemma/orthing) is candidate terminology, gated on a designed-but-unrun comparative benchmark; every document can be read with ordinary-language substitutes.
• The companion theological/metaphysical papers are complete drafts, deliberately separated from the main manuscript: philosophical conclusions are conditional on labeled premises, creed-internal material is explicitly Atharī-school-labeled, and no engineering evidence supports any metaphysical claim (absolute firewall).
• Related-work claims are cited with per-claim verification statuses — current state starts at docs/sourcing/CURRENT-SOURCING-LEDGER.md (Decision 0019; R2 ledgers are banners-marked historical baselines); statuses are honest about what was and was not re-fetched.
• Historical candidate overlay and current integration evidence (R7E Sol review, Decisions 0034–0036). The authoritative docs/current-candidate-state.yaml and timestamped CANDIDATE-TOPOLOGY-INPUT.yaml preserve the exact pre-integration branch/base/head_at_observation/draft/CI/provenance facts observed at 2026-07-21T18:10:22Z; they are historical candidate-era evidence, not timeless live-head claims. The reviewed lineage subsequently reached protected main through ordinary PR #13 → #12 → #11 → #10 → #9 → #8 merges at 8db1630ab715b0931907c627be97b32399d6f4fc, with exact-SHA CI and fresh-main proof recorded in R7E-SOL-MERGED-MAIN-VERIFICATION.md. Git integration does not establish empirical validation, external peer review, terminology adoption, publication, or approval of interrupted research.

Citing

No stable release, DOI, or citation metadata exists (license and identity decisions are owner-only — see OPEN-DECISIONS.md). Cite by commit per docs/CITING.md.

AR8R V11 reconciliation expansion

The current public reconciliation packet is indexed at docs/project-closure/ar8r-v11/. Task 7 adds exact-but-deferred Candidate E/G custody, current A–N / M–T–N and transcendental bridge owners, typed proper-function/ontology/TAC matrices, a noncircular formalization queue, and an unresolved Connes-rigidity specification-warrant case. These additions do not adopt the deferred candidates or PMR proposals, repair T354, establish a Lean/kernel proof, select a champion, reach a meniscus, or claim natural closure.