PROTIUM — Verification

PROTIUM's central claim is that its quantities are independently verifiable — bridge constants are measured agreements, not assumed identities. A claim like that is only as good as its evidence, so this page carries the evidence: the issues found and the practices they established (below), and the standing checks that re-confirm the framework every time the tools run. Findings are recorded by what they teach, not reconstructed in full — the corrected values live in the Parameters and the Legend.

Findings & practices

Each finding is grouped by the framework's own two error classes — tier errors (a stray factor of 10¹⁰) and c²/K☉ errors (mass↔energy crossed without the bridge) — plus the notation practices that keep results legible. Every correction was made by recomputation against physical constants, never by assertion.

Tier errors — a stray 10¹⁰

The named tier is uniformly 10¹⁰ × the base tier. An equation that combines axes can silently keep or drop that factor.

Unit definition · tooling

The decay tool once defined the named energy and mass units off-scale — energy as the base quantum (short by 10¹⁰) and mass by a circular energy-derived route (off by many orders). A tempting “elegant identity” between two quantities turned out to be an artifact of that circularity.

Practice: define every named unit as exactly 10¹⁰ × its base unit, independently per axis; derive nothing in a way that lets one definition lean on another. An identity that looks too clean is a prompt to check, not to celebrate. Count the tier factors top and bottom before collapsing any expression — equal count cancels, unequal count leaves a 10¹⁰ to carry.

Tier-label mismatch · docs

A worked example labeled named-tier magnitudes with base-tier symbols — correct numbers, wrong names, an invisible 10¹⁰ mislabel.

Practice: the case of the interstitial letter (Ht☉ vs HT☉) is the tier and is the 10¹⁰ jump — never case-fold or normalize unit tokens; treat them as case-sensitive everywhere.

c² / K☉ errors — the bridge skipped

PROTIUM's c = 1 is kinematic only. The instant it is used to cross mass and energy, a real factor goes missing.

Bridge value · docs

The bridge constant K☉ was cited as 1.5974 × 10¹⁴ across several documents; direct computation gives 1.5972 × 10¹⁴. The wrong digit had propagated from a single retired derivation file.

Practice: compute, never transcribe. A value copied between documents carries any error with it; a value recomputed from m_p·c²/E(H) at each point of use cannot. The now-retired source file is gone; the Bridge Constant document is the single authority.

Prefix error · docs

The named mass unit’s SI size was once written with the wrong metric prefix — a kilogram/gram slip in the conversion. The correct value is ≈ 16.73 fg = 1.67262 × 10⁻¹⁷ kg.

Practice: carry the unambiguous SI form (× 10ⁿ kg) alongside any prefixed display, so a prefix slip has a built-in cross-check that doesn’t depend on remembering which prefix means what.

Notation & presentation practices

Not arithmetic errors — legibility findings, where a defensible notation choice was creating avoidable confusion or risk.

Exponent placement

Writing exponents on named-tier units invited a recurring confusion between a PROTIUM scale exponent and an ordinary coefficient.

Practice: exponents belong to the axis, multipliers to the units — write 153 CLIP, not CLIPⁿ. This single rule removed a whole category of misreadings; the full error-trap reasoning is kept as an exploration rather than carried inline.

Computation order

Calculating directly in named units reintroduces 10¹⁰ bookkeeping at every step, where it can be dropped.

Practice — lower to base first: lower named symbols to base, compute where c = 1 and h = 1 with no tier factors, then raise the result to named units for presentation — a single ±10 shift at the very end.

Standing checks

These are not historical — they re-run every time the tools execute, and must hold. Where two independent routes compute the same quantity, their agreement is the check. Values shown are current.

Check	What it confirms	Margin
Bridge identity	K☉ computed natively (`CHIP·c²/QUIP`) and in SI form (`c²·m_p/E(H)`) are the same object.	bit-exact
Bridge chain	Across every decay entry, the mass deficit via the native bridge and via SI `Q/c²` agree end-to-end — a check on the whole computation pipeline, not just the constant. (This is the stronger of the two: separate operation chains accumulate independent rounding, so agreement here means the pipelines match, not merely the definition.)	≤ 2 × 10⁻¹⁶
Tritium checkpoint	The decay tool reproduces the Framework Primer’s canonical worked value: `0.3165 QUIP / 1.9814 × 10⁻¹⁵ CHIP = K☉`.	exact to 4 sig figs
CMB landmark	The Message Cost tool’s temperature axis places the CMB (2.725 K) at `Hf☉^1.60`, independently reproducing the value stated in the Temperature Note.	match

Why this page exists. A documented finding-and-resolution trail is more persuasive than flawless-looking work, because flawless-looking work is indistinguishable from work that was never tested. Each finding above became a rule; each standing check keeps firing. That a finding reasoned in the framework’s own categories — a tier error, a skipped bridge — and was resolved by recomputation against ground truth is the verification loop closing.

Corrected values: Parameters. Symbol conventions: Legend. The bridge in use: Decay Workbook.