Collaboration observatoryMethods & downloads

A short window into
collective mathematical work.

Integer multiplication, October 7–12, 2026. Explore who participated, when conversations happened, and which evidence connects contributions.

The activity window

Drag across the hourly chart to select creation cohorts. The first and last UTC days are partial.

Who created the selected PRs?

Author account, not an inferred human / model identity. Top 12 displayed; all selected accounts remain in the source table.

Return to public contribution

Fixed 77-account baseline. Each cell is active/cohort accounts. Dark cells marked — lack a complete calendar day; zero means observed inactivity on that day.

Follow-up changes the denominator

Responses count ordinary comments or formal reviews by another account. A merge records repository adoption.

Publication PDF

Time to first recorded response

Fixed full-census Kaplan–Meier complement. Shading: 800 author-cluster bootstrap resamples, pointwise 95% sensitivity. The full-census median is not reached.

First merge or closure

Fixed full-census first-resolution incidence. PR #166 closed and reopened: its first closure counts here while its snapshot state stays open.

Selected PRs: events and censored follow-up

Dots mark first recorded non-author response; crosses mark follow-up without an observed response. Hover or click a mark for its source PR.

Equal windows, explicit denominators

Only selected PRs old enough to reach each horizon enter its denominator, whether or not they received a response. Outcome-filtered views describe that selected outcome group.

Different evidence, different edges

Inspect actual recorded communication separately from current-body PR references.

Recorded communication through time

Fixed baseline, timestamped comment/review events. Cumulative event counts are separate from current-body references, whose appearance times are unknown.

Edge definitions and missingness

Communication: sender → PR author, one event per deduplicated comment/review ID and PR. This is not a claim that every comment addresses its author. References: source PR → linked target PR, deduplicated URL pairs in the current body; references need not be dependencies. Eleven pairs refer to later-created PRs. Excluding them cannot certify historical visibility for the remaining pairs. No coauthorship or professional-background edge is inferred.

Where the evidence stops

Extraction rules can change the apparent method mix. These labels are intentionally uncertain.

Performance & guarantees

No globally adjudicated, assumption-matched κ series or runtime benchmarks. A smaller conditional exponent is not a measured speedup.

Not globally assessed

Verification

Check / certificate language and formal review labels do not establish a full theorem proof. No source verifier was executed in this analysis.

Evidence dimensions stay separate

Repository adoption

Among the 131 merged PRs, 6 had a recorded non-author response before/at merge, 58 only afterward and 67 none. View timing evidence.

Observed lifecycle field

Professional background

One profile self-description pilot; no verified pre-project professional ties in this frozen release. Missing ties are not zero ties.

Network not estimable

Trace each observation

Compact metadata only. Original bodies and Git/file records are kept out of the browser payload.

PRContributionAuthorCreated UTCStateFirst responseFollow-up