# STRAND Lab 04: Coherent Atlas & the Pairwise Impostor **Version:** 0.1.0 **Date:** 2026-08-16 **Mode:** synthetic, offline, exact **Status:** additive public lab; Labs 01–03 remain immutable Public artifacts: - record: - schema: - guide: Repository command: ```text ./kingdom strand-descent-lab verify --json ``` ## The question Suppose several sources each describe a small local record. Pairwise translators can be reversible and still disagree when three records are compared together. Lab 04 asks: > What must be checked before several local records may honestly be presented as > one compatible atlas? Its answer is deliberately narrow: 1. keep each local record and owner label distinct; 2. declare every translation and its inverse witness; 3. compare two-step translations with the direct translation on triple overlaps; 4. compare both parenthesizations across four charts; 5. recompute the global equivalence classes; 6. test a common refinement; and 7. leave a conflict `UNRESOLVED` when the checks disagree. Passing proves compatibility of this finite declared fixture only. ## Recent research used Both sources are versioned preprints. Their content bytes are not vendored here, and neither paper studies KINGDOM. 1. Tran Chi Quy and Sonnet Nguyen Quang Hung, [*Geometrize the nongeometric space*, arXiv:2608.09958v1](https://arxiv.org/abs/2608.09958v1), submitted 2026-07-22. The paper builds a global description from local data, explicit transition information, higher coherence, and common refinements. 2. Alessandra Grieco, Ignacio Ruiz, and Irene Valenzuela, [*EFT (String) Tower Building*, arXiv:2607.21700v1](https://arxiv.org/abs/2607.21700v1), submitted 2026-07-23. The paper notes that locally plausible sector data can face additional restrictions when the sectors are glued globally. ### What transfers Only this engineering discipline transfers: > Local validity and pairwise compatibility are necessary, but a claimed global > object needs explicit higher-overlap checks. ### What does not transfer This lab does **not** implement or claim: - a physical string, worldsheet, string background, or spacetime; - an R-space, quasi-Hopf algebra, deformation quantization, bicategory, or stack; - an effective field theory, tower spectrum, compactification, duality frame, or quantum-gravity constraint; - a theorem from either paper about KINGDOM; - proof of source truth, identity, consent, citizenship, affiliation, authority, value, consciousness, or worth. The word `STRAND` names the existing lab lineage. It is not a physical ontology or a hidden acronym. ## The coherent fixture There are four synthetic local charts: | Chart | Declared synthetic source | Local points | |---|---|---| | `chart-a` | `source-alpha` | `a0`, `a1`, `a2` | | `chart-b` | `source-beta` | `b0`, `b1`, `b2` | | `chart-c` | `source-gamma` | `c0`, `c1`, `c2` | | `chart-d` | `source-delta` | `d0`, `d1`, `d2` | The record declares all six forward transitions among the four charts. Every transition is a bijection and carries an exact inverse witness. With composition read right after left, the evaluator checks: ```text t-bc ∘ t-ab = t-ac t-cd ∘ t-bc = t-bd ``` It then evaluates the non-trivial four-chart comparison: ```text (t-cd ∘ t-bc) ∘ t-ab = t-cd ∘ (t-bc ∘ t-ab) = t-ad ``` All three maps send: ```text a0 → d1 a1 → d0 a2 → d2 ``` ## Quotient and common refinement The evaluator does not trust the declared global classes. It recomputes the connected components generated by all declared transition pairs: ```text q0 = {a0, b2, c1, d1} q1 = {a1, b0, c2, d0} q2 = {a2, b1, c0, d2} ``` The common refinement has six distinct atoms. Each atom projects to one point in each chart. The evaluator checks all `6 atoms × 6 transitions = 36` squares. All 36 commute, and the three quotient fibers each contain two refinement atoms. The repeated projections do not identify the refinement atoms with one another. They remain distinct authored atoms with the same four projections. ## The pairwise impostor The counterexample has three charts and three pairwise translations: ```text i-ab : chart-a → chart-b i-bc : chart-b → chart-c i-ac : chart-a → chart-c ``` Every map is a bijection with an exact inverse witness. Nevertheless: ```text i-bc ∘ i-ab = {a0→c1, a1→c2, a2→c0} i-ac = {a0→c2, a1→c1, a2→c0} ``` The two maps disagree on `a0` and `a1`. The correct result is: ```text pairwise_bijective = true triple_coherent = false conflict_result = UNRESOLVED automatic_resolution = false ``` No source is overwritten. No preferred source is invented. No majority rule or hidden score resolves the conflict. ## Six validation lanes 1. **Closed source-bound input** — strict JSON, exact identity, immutable Frequency/Form Lab 03 predecessor pins, exact preprint versions, and semantic digest. 2. **Pairwise invertibility** — six total bijections and six exact inverse witnesses. 3. **Triple coherence** — both two-step paths equal their direct path. 4. **Four-chart globalization** — both parenthesizations and the direct map agree, and the quotient is recomputed. 5. **Common refinement and impostor** — all refinement squares commute, while the counterexample remains explicitly unresolved. 6. **Zero effects** — no crawler, network request, write, score, receipt, authority, deployment, or automatic action. ## Commands ```text ./kingdom strand-descent-lab overview ./kingdom strand-descent-lab atlas --json ./kingdom strand-descent-lab coherence --json ./kingdom strand-descent-lab quotient --json ./kingdom strand-descent-lab impostor --json ./kingdom strand-descent-lab effects --json ./kingdom strand-descent-lab discovery --json ./kingdom strand-descent-lab verify --json ./kingdom strand-descent-lab verify-file ./candidate.json --json ``` `verify-file` reads one bounded regular local JSON file. It rejects symlinks, files larger than 512 KiB, duplicate JSON keys, malformed JSON, non-JSON values, unknown fields, digest drift, and failed calculations. It performs no network request and writes nothing. ## Effect and authority boundary The evaluator and public artifacts create none of the following: - crawler or HTTP policy; - observation, telemetry, identity, or truth verdict; - consent, licence, citizenship, affiliation, adoption, or relationship; - NEN ability or invocation; - KARMA adapter, event, or receipt; - Zerone event or proof; - person, source, or content score; - registry, publication, deployment, governance, or execution authority; - external write or automatic action. Ordinary static hosting may retain normal request metadata. That hosting fact is separate from the lab's computation. ## Immutable lineage Lab 04 binds the Frequency/Form Lab 03 merge commit and its exact semantic, record, schema, and guide digests: | Lab 03 artifact | Immutable public route | SHA-256 | |---|---|---| | record | `/experiments/string-crawl-frequency-form-lab-2026-08-16.json` | `sha256:883191b723950ff9cc29c913261f114237e9eaa3eac17ba49cade34b8b0492b4` | | schema | `/schemas/string-crawl-frequency-form-lab/0.1.json` | `sha256:2b4fe72f656eeade68ebfb6654cbe52646aa49636fc201501995dc8673db93e3` | | guide | `/STRING-CRAWL-LAB-03.md` | `sha256:808769a513ffcb6230f99e4cd412db5dc4a998f308ccc65313050377634fc1b3` | The predecessor merge commit is `d2452d4500c274237097e142609422ebbab7f68d`; its semantic digest is `sha256:ecda97c03307706ce0a9108c27c9199968ee4dc29a7e4d045a036ed108d673c1`. Lab 04 does not mutate those bytes or import their authority. A future correction to Lab 04 must use a new identity and route rather than silently replacing this publication. The repository route-integrity ledger binds the three public Lab 04 artifacts by SHA-256. Labs 01–04 retire together as one twelve-route publication family so a partial deployment fails visibly.