# Calculation notes
New Eruditions • printed source values • checked 30 September 2026

The executable notebook and standard-library script reproduce 42 calculation records. Each result in calculation-results.csv/.json has an ID, formula, source inputs, assumption, status and display rounding. Extra decimal places there are computation traces, not source precision.

## Inputs and units

| Input | Printed value | Origin | Basis |
|---|---:|---|---|
| S, Synergy Q4 2025 | 119.1 billion | S1 | Printed $ interpreted as USD; quarterly service estimate |
| O, Omdia Q4 2025 | 110.9 billion | S2 | Explicit US$; quarterly service estimate |
| Synergy growth | 30% | S1 | Major currency effects backed out; not a nominal growth input |
| Omdia growth | 29% | S2 | Year-on-year; detailed FX policy not disclosed |
| Synergy older Q4 2024 release | 90.6 billion | S8 | Historical printed vintage, not a proven same-vintage baseline |
| AWS Q4 company segment sales | 35,579 million | S9 | Company disclosure, not a proven analyst numerator |

## Core calculations

| IDs | Formula | Reader result | Assumption / limit |
|---|---|---|---|
| C01 | S − O | $8.2bn | Difference between printed rounded estimates |
| C02 | (S − O) / O × 100 | About 7.4% | Omdia denominator |
| C03 | (S − O) / S × 100 | About 6.9% | Synergy denominator |
| C04 | (S − O) / ((S + O)/2) × 100 | About 7.1% | Symmetric descriptive difference; mean is not a recommended estimate |
| C05a,b | (S±0.05) − (O∓0.05) | Approximately $8.1–8.3bn boundaries | Assumed nearest $0.1bn display rounding only |
| C06 | O / 1.29 | About $86.0bn | Conditional same-basis prior; not directly observed |
| C07a,b | 110.85 / 1.295; 110.95 / 1.285 | About $85.6–86.3bn | Additionally assume nearest whole-point growth rounding |
| C08 | S / 1.30 | $91.6bn mechanically | **Rejected** nominal baseline: FX-adjusted growth and printed level are not established as same-basis |
| C09 | S − 29 | About $90.1bn | Rounded increment in S1; not an exact reconstructed/revised prior |
| C10 | (119.1 / 90.6 − 1) × 100 | About 31.5% | Cross-vintage dollar arithmetic; not a contradiction of FX-adjusted 30% |
| C11 | 119.1 − 90.6 | $28.5bn | Older printed baseline; cannot prove historical revision |
| C12 | 419 / 4 | About $104.8bn | Annual average quarter, not Q4 |
| C13 | 119.1 × 4 | $476.4bn annualized | Illustrative constant-Q4 pace, not annual revenue or forecast |
| C17 | 35,579 / 1,000 | $35.579bn | Million-to-billion unit conversion |
| C18S,O | 35.579 − (total × Amazon share) | About $2.2bn / $0.1bn | Scope diagnostics; not missing revenue, bias or error |
| C19S,O | 28+21+14; 32+22+12 | About 63% / 66% | Rounded full-scope shares; do not substitute Synergy's separate 68% public-only statement |
| C20 | 26 March − 5 February 2026 | 49 days | Publication spacing, not evidence of causal revision |

## Vendor-share diagnostic

**Formula:** implied eligible vendor amount = release total × release share / 100.

| IDs | Vendor | Synergy share | Omdia share | Synergy implied amount | Omdia implied amount |
|---|---|---:|---:|---:|---:|
| C14S,O | Amazon / AWS | 28% | 32% | About $33.3bn | About $35.5bn |
| C15S,O | Microsoft / Azure | 21% | 22% | About $25.0bn | About $24.4bn |
| C16S,O | Google / Google Cloud | 14% | 12% | About $16.7bn | About $13.3bn |

These inferred amounts are not vendor disclosures. Eligible services, treatment of group names and category allocations are precisely what needs reconciliation.

**Counterfactual:** If the Omdia numerator remained identical and only the denominator grew to Synergy's total, predicted Synergy share = 110.9 × Omdia share / 119.1. This gives about 29.8% for Amazon, 20.5% for Microsoft and 11.2% for Google (C14P–C16P). Published Synergy shares are 28%, 21%, 14%. A single extra category outside these unchanged vendor numerators does not reconcile the printed pattern.

**Sensitivity:** Under nearest $0.1bn total and nearest whole-percent share rounding, each amount lies between (total−0.05)×(share−0.5)/100 and (total+0.05)×(share+0.5)/100. Boundary inclusivity depends on rounding convention; that does not affect the non-overlap conclusion.

| Vendor | Synergy interval boundaries | Omdia interval boundaries | Result under assumption |
|---|---:|---:|---|
| Amazon | $32.74–33.96bn | $34.92–36.06bn | No overlap |
| Microsoft | $24.41–25.62bn | $23.83–24.96bn | Overlap |
| Google | $16.07–17.28bn | $12.75–13.87bn | No overlap |

The notebook keeps exact decimal boundaries for verification. These are rounding sensitivity ranges, not statistical confidence intervals or estimates of analyst error.

## How much would a category bridge need to explain?
Under the **unverified** premise that both estimates otherwise measure the same market, an added net category would need to contribute approximately $8.2bn in Q4, equivalent to 7.4% of Omdia's total. This restates C01/C02; it is not a measured hosted-private, SaaS or neocloud segment. Product overlaps and changes within vendor numerators prevent assigning the difference to a named category from these releases alone.

## Verification
All decimal arithmetic was rerun with Python's Decimal module. Checks cover the total difference, inferred vendor amounts, unit conversion, unique calculation IDs and Amazon/Google interval non-overlap. This verifies our calculations only. The saved notebook includes actual execution output. No calculation averages the two totals into a “correct” market estimate.