1. Starting point — ArXe extends what counts as an “axiomatic choice”
Unlike how the term is used in standard physics (theoretical postulates: general relativity vs. loop quantum gravity), ArXe counts as an axiomatic choice any decision, even a non-theoretical one — a measurement protocol, which instrument was used, what tolerance convention was adopted, even a decision made for cost or availability reasons. Each of those decisions leaves its mark on a distinct ALO reading, as legitimate as any other within its own map. This is already developed, though not closed, in axiomatic_archaeology_unified_theory_s_en.md: “physical constants are negotiated records of axiomatic decisions — not objective laws, but stabilization points in the space of possible choices.” And in ALO_measurement_illusion_en.md: what gets called “ruling out an alternative” is almost never empirical refutation — it is, almost always, simply never having measured under those axioms at all.
Consequence for today’s work: when the grammar filter couldn’t distinguish between 273/125, 286/147, and 169/77, the right question wasn’t “which one survives?” — it was “which practical measurement choice is each one native to?”
2. The archaeology — each candidate is exact against a different target
| Candidate | Value | Closest target | Δ | Associated practical choice |
|---|---|---|---|---|
| 273/125 | 65.3981° | 65.4° | 0.0019° | Legacy/assumed estimate, the one the corpus originally used before recent LHCb measurements existed |
| 286/147 | 62.7975° | 62.8° (LHCb direct) | 0.0025° | Direct measurement (a specific experimental technique, with its own systematics) |
| 169/77 | 65.5050° | 65.5° (PDG, global unitarity fit) | 0.0050° | Indirect fit via full unitarity-triangle consistency (a different analysis technique, with its own assumptions) |
None of the three comes close to the other two targets (all three have Δ>0.7° against any target other than their own). This isn’t a partial coincidence — it’s a near-exact correspondence of each candidate to a single measurement choice, and a large discrepancy with the rest. This is exactly the pattern axiomatic archaeology would predict: there isn’t “noise” around three numbers competing for the same target — there are three distinct targets, each with its own sharpshooter.
3. Why this isn’t the same as “all three are valid, pick any one”
That would be too quick a reading, and ALO_measurement_illusion_en.md itself warns against it: the choice among the three isn’t arbitrary once one decides which measurement of the experimental data itself is accepted as the relevant one — and that is a decision that can be argued for, not a blind tie. The three data options have different standing today:
- 65.4° (legacy): no longer represents current best knowledge — a value the corpus inherited from an earlier stage, not a standing measurement.
- 62.8° (direct, LHCb): the measurement with the lowest relative precision (±2.6°) of the three.
- 65.5° (PDG, global fit): the synthesis of the entire experimental program available to date, not an isolated technique — in that sense, the least arbitrary of the three choices if the criterion is “what the experimental community accepts as its best joint estimate today.”
This favors 169/77 over 273/125 and 286/147 — not by winning a grammar filter, but by being native to the least arbitrary data choice available. This is a decision that must be made and declared as such — “we choose to accept the PDG global fit as our reference target” — not one that emerges “discovered” from the numerical or grammatical filter.
4. Consequence for δ’s classification
With this reframing, the question left open in arxe_CKM_epistemic_status_v9.md §2i (“no criterion to prefer 273/125”) has a different answer from the one being sought: no tie-breaking grammatical criterion is needed — what’s needed is an explicit declaration of which experimental data choice ArXe adopts as its own, and that declaration determines which of the three candidates is “the” native of the map ArXe chooses to inhabit. If the PDG global fit is adopted (§3, the least arbitrary option), the native candidate is 169/77, not 273/125 — a real change, not a cosmetic one, from what the corpus has used since the origin.
This isn’t a defeat for today’s work — it’s its logical continuation. The grammar filter did its job (it excluded 98/45 and 3993/1820 on valid grounds); what remained unresolved wasn’t a shortcoming of the filter — it was a question of a different kind, about data choice, not structure — one the axiomatic archaeology program already had the tools to formulate, it simply hadn’t closed the loop by applying them to a concrete case until now.
5. Pending — not decided in this document
This document draws the map; it does not choose for Diego Tentor which of the three targets to adopt as ArXe’s official reference. That is a corpus policy decision, not a result derived from the filter — and declaring it as a choice, not a finding, is exactly the point of this whole exercise.
Update — declared choice (August 2026): Diego Tentor adopted the PDG global fit (65.5°) as ArXe’s official target for δ_CKM, for being the synthesis of the complete experimental program. The official formula becomes 169/77, not 273/125. See arxe_CKM_epistemic_status_v10.md §2j for the full resolution, including the grammatical reading of the new official formula. 273/125 is not retired — it remains documented on this map as the candidate native to the legacy estimate.
ArXe Research — August 2026
Diego Luis Tentor
Axiomatic archaeology assisted by Claude.ai (Anthropic)