# SciGround Foundations

> Mathematical and statistical verification from experimental design to claims: each stage and the whole workflow, within supported methods and under stated assumptions.

## Every part and the whole, verified by math and statistics.

From experimental design to claims, SciGround verifies each stage and the whole workflow within supported methods and stated assumptions. Approved changes are rechecked, with versioned evidence others can verify.

## From design to claims. Here’s how.

Research runs from design to claim, and you can start at any stage. The four foundations are not extra steps: each supports that same research in its own way.

**Research workflow:** Design → Data → Analysis → Claim

1. **Design** — Question, comparison, units, declared assumptions. Handoff check to Data: *Correspondence* (The data match the design).
2. **Data** — Source data, samples, preparation. Handoff check to Analysis: *Numerical accuracy* (Results hold within a stated error bound).
3. **Analysis** — Supported method, results, uncertainty. Handoff check to Claim: *Claim follows* (The conclusion is derived from the results).
4. **Claim** — What the results support.

### Project — One research. Versioned.

*Where does my research live as it changes?* A Project keeps the design, data, analyses, claims, and Records of one research together. Each approved change becomes a new version; earlier versions stay traceable and the current one stays clear.

[Explore Project](https://www.licklider.ai/project/)

### Integrations — Established tools. Connected execution.

*How does it work with the tools I already trust?* Where a supported route applies, a stage’s calculation or processing runs in established scientific software, with inputs, settings, method conditions, and tool versions attached. Which tool runs depends on the route; running a tool does not by itself make a result valid.

Shown in the diagram as a rail beneath the stages labelled “Runs established scientific tools”, connected where a supported route applies.

[Explore Integrations](https://www.licklider.ai/integrations/)

### Math — Stage checks. Handoff checks. Whole-workflow verification.

*Why does the result hold?* Math checks properties within each stage, checks that each handoff keeps what the next stage needs, and joins both into verification from the declared design to the final claim. It works within supported methods and stated assumptions, and does not certify how an experiment was run or measured.

Shown in the diagram as stage checks at each stage, handoff checks between stages, and whole-workflow verification joining both from design to claim.

[Explore Math](https://www.licklider.ai/math/)

### Record — One version. Its evidence, ready to verify.

*How can someone else check it?* A Record fixes one research version with its inputs, assumptions, methods, results, checks, status, and claim, so others can verify it without the original chat. It is never rewritten after a correction, and its outcome may be unresolved or not established as well as supported.

Shown fixed at v3, the current version after v1 and v2, and never rewritten. It binds: Research version; Inputs & assumptions; Methods & results; Checks, status & claim.

[Explore Record](https://www.licklider.ai/record/)

*Conceptual workflow. Handoff labels are representative.*

## One study, checked as a whole.

*Illustrative example · synthetic data.*

**Question:** How much does mean body weight at day 14 differ between treated and control animals? Two independent groups · 10 animals each · One planned comparison.

Set in the design. Held through to the claim. Comparison: Treatment − Control · Unit: One animal · Outcome: Body weight, day 14 (g).

1. **Design — The right comparison.** Treatment − Control on day-14 body weight, one animal per unit, fixed before the data.
   - Handoff check to Data: Correspondence.
2. **Data — The right observations.** All 20 planned animals appear once, in their assigned group, with a day-14 weight in grams.
   - Handoff check to Analysis: Numerical accuracy.
3. **Analysis — The calculation, checked.** Welch’s comparison runs in SciPy, and its key numbers carry error bounds.
   - Handoff check to Claim: Claim follows.
4. **Claim — The conclusion, supported.** The wording follows the estimate’s direction and interval, without claiming a cause.

**Checked as one chain.** The claim must answer the planned comparison, for the planned animals and outcome, from the approved data. A correct calculation on the wrong samples, or for a different comparison, does not pass. *Declared, not proven: random assignment, independence, accurate weights.*

**Every check, and what it is for:**

- **Design:** Treatment − Control, two-sided, planned in advance. One animal is one experimental unit. Body weight on day 14, in grams. *Sets what every later stage must answer.*
- **Data:** Each of the 20 planned animals matched exactly once. Group labels agree with the assignment record. All weights from day 14, in grams, none missing. *The analysis gets the observations the design asks for.*
- **Analysis:** Welch’s comparison runs in an established library (SciPy). Key numbers carry error bounds; too close to call means unresolved. Normality is assumed; Welch’s degrees of freedom are an approximation, reported separately. *The right number, with its conditions in view.*
- **Claim:** Direction and size follow the estimate and its interval. A group difference is not reported as a cause. “Not established” is never rewritten as “no effect”. *What you report says no more than the result.*

### What comes back

- Mean difference, Treatment − Control: −2.08 g (95% CI −2.83 to −1.33 g)
- Claim: Mean day-14 body weight is 2.08 g lower in the treated group (95% CI 1.33 to 2.83 g lower). Under the stated assumptions. Not a causal claim. These 20 animals only.
- Research version: v3. [Data (CSV)](https://www.licklider.ai/examples/group-comparison.csv) · [Worked calculation](https://www.licklider.ai/examples/group-comparison/) · [How a Record keeps it](https://www.licklider.ai/record/)

**Method and assumptions:** Method: Two-sided Welch t-test; 95% confidence interval for the mean difference. Groups: Control 24.92 g (n = 10); Treatment 22.84 g (n = 10). Test: t = −5.85, df = 17.8 (Welch–Satterthwaite approximation), two-sided p < 0.001. Inclusion: All 20 supplied animals included; no missing values or exclusions. Assumptions: Independent observations and approximately normal within-group outcomes are assumed; equal variances are not required. Not verified: Source matching does not verify animal identity, measurement accuracy, random assignment, or independence.

*Synthetic data. The numbers are recomputed from the CSV with SciPy; this is an illustration, not a SciGround-issued Record.*

## One correction, traced to the claim.

Correct one group label, and the estimate, its interval, and its evidence are updated, while the earlier version stays on record. This is the correction behind version 3 above.

**What changed:** M17, group Treatment → Control. Weight 26.2 g, unchanged. The original assignment record, supplied after v2, places M17 in Control. You confirm the correction; the v2 input is kept, not overwritten. *Confirmed by you, not proven: that the assignment record is right.*

**What depends on it is checked again:**

- **Project:** The correction becomes v3; v2 stays exactly as it was.
- **Integrations:** Welch’s comparison runs again on the corrected groups.
- **Math:** Group correspondence, error bounds, and the claim are checked again.
- **Record:** A v3 Record is issued; the v2 Record is kept, marked superseded.

Unchanged: the design, the outcome, all 20 weights, and the method.

| Before and after | v2 (superseded) | v3 (current) |
| --- | --- | --- |
| Animals per group (changed) | Treatment 11 · Control 9 | Treatment 10 · Control 10 |
| Mean difference (changed) | −1.63 g | −2.08 g |
| 95% CI (changed) | −2.58 to −0.68 g | −2.83 to −1.33 g |
| Finding direction (rechecked, unchanged) | Lower in the treated group · Supported | Lower in the treated group · Supported |
| Reported claim (rewritten with new values) | 1.63 g lower in the treated group (95% CI 0.68 to 2.58 g lower) | 2.08 g lower in the treated group (95% CI 1.33 to 2.83 g lower) |
| Record (changed) | v2 Record, kept as issued | v3 Record, current |

- v2: Checked against the inputs and declarations recorded at v2. No longer current.
- v3: The version in the study above.

**Both calculations:** v2: Control 24.78 g (n = 9); Treatment 23.15 g (n = 11); t = −3.64, df = 16.7, two-sided p = 0.002. v3: Control 24.92 g (n = 10); Treatment 22.84 g (n = 10); t = −5.85, df = 17.8, two-sided p < 0.001. Method: Two-sided Welch t-test with a 95% confidence interval, on the same 20 weights; only the group of M17 differs.

*Synthetic data. Both versions are recomputed from the CSV with SciPy; this is an illustration, not SciGround-issued Records.*

## Limits and conditions

The foundations make strong, specific guarantees. See what they establish, and what they don’t. [Read the limits](https://www.licklider.ai/foundations/limits/) ([Markdown](https://www.licklider.ai/foundations/limits.md)).