2c:null 2d:["$","title",null,{"children":"2026→2027 Year-Boundary Stress Lab | Mateo Pedersen | Observable"}] 32:T42d,# 2026→2027 Year-Boundary Stress Lab A four-month window exposes date-system edge cases that a single-month preview hides: November 2026 has 30 days, December ends the civil year, January begins a new civil year, and February 2027 has 28 days. The notebook connects continuous date placement, week boundaries, and ISO week-year labels. ## Civil dates and week labels The Gregorian year changes at January 1. ISO week numbering follows a different rule: a week belongs to the year containing its Thursday. The timeline and table calculate both independently. ## Failure injection The examples below compare familiar shortcuts with Gregorian and UTC-safe calculations. They are inert demonstrations; no unsafe code is executed. References: [November](https://www.betacalendars.com/november-calendar.html) · [December](https://www.betacalendars.com/december-calendar.html) · [January](https://www.betacalendars.com/january-calendar.html) · [February](https://www.betacalendars.com/february-calendar.html) · [Beta Calendars home](https://www.betacalendars.com/)33:T13fa,const app4 = (() => {const root=document.createElement("section");root.style.cssText="font:14px/1.5 system-ui,sans-serif;color:#17233b;background:#fbfaf6;padding:20px;border:1px solid #dfe6e8;border-radius:14px;max-width:1100px;margin:auto";const css=document.createElement("style");css.textContent=".b4card{background:white;border:1px solid #dce3e7;border-radius:10px;padding:14px;margin:12px 0}.b4bar{display:flex;gap:12px;flex-wrap:wrap}.b4bar label{display:grid;font-size:12px}.b4bar select{padding:7px;border:1px solid #bac7cf;border-radius:7px}.b4timeline{display:grid;grid-template-columns:repeat(auto-fit,minmax(32px,1fr));gap:3px}.b4day{height:32px;display:grid;place-items:center;border-radius:5px;background:#e8f0ef;font-size:10px}.b4month{background:#b8d9d4!important;outline:2px solid #286f76}.b4boundary{border-left:3px solid #263b54}.b4week{border-top:3px solid #9c6b2f}.b4table{border-collapse:collapse;width:100%}.b4table td,.b4table th{padding:6px;border-bottom:1px solid #e2e7ea;text-align:left}.b4small{color:#536174;font-size:13px}";root.append(css);const h=document.createElement("h2");h.textContent="Continuous civil-date timeline";root.append(h);const bar=document.createElement("div");bar.className="b4bar";const l=document.createElement("label");l.textContent="Emphasize week boundary";const sel=document.createElement("select");["Monday","Sunday","Saturday"].forEach((x,i)=>{const o=document.createElement("option");o.value=[0,6,5][i];o.textContent=x;sel.append(o)});l.append(sel);bar.append(l);root.append(bar);const timeline=document.createElement("div");timeline.className="b4card b4timeline";root.append(timeline);const note=document.createElement("p");note.className="b4small";root.append(note);const iso=document.createElement("div");iso.className="b4card";root.append(iso);const faults=document.createElement("div");faults.className="b4card";root.append(faults); const start=Date.UTC(2026,10,1),end=Date.UTC(2027,2,1);function isoInfo(d){const x=new Date(d),day=(x.getUTCDay()+6)%7,t=new Date(d);t.setUTCDate(t.getUTCDate()-day+3);const yr=t.getUTCFullYear(),jan4=Date.UTC(yr,0,4),jday=(new Date(jan4).getUTCDay()+6)%7,firstThu=jan4+(3-jday)*86400000;return {year:yr,week:1+Math.round((t.getTime()-firstThu)/604800000)}} function draw(){timeline.replaceChildren();let dates=0;for(let t=start;tDateWeekdayGregorian yearISO week-yearISO week";const body=document.createElement("tbody");for(let d=Date.UTC(2026,11,28);d<=Date.UTC(2027,0,5);d+=86400000){const x=new Date(d),q=isoInfo(d),tr=document.createElement("tr");tr.innerHTML=""+x.toISOString().slice(0,10)+""+["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"][x.getUTCDay()]+""+x.getUTCFullYear()+""+q.year+""+q.week+"";body.append(tr)}table.append(body);iso.append(table);const ip=document.createElement("p");ip.className="b4small";ip.textContent="The week containing 2027-01-01 belongs to ISO week-year 2026 (week 53); Monday 2027-01-04 begins ISO week 1 of 2027. ISO year is assigned by the week’s Thursday.";iso.append(ip); faults.replaceChildren();const fh=document.createElement("h3");fh.textContent="Failure injection: shortcuts and corrected results";faults.append(fh);const ft=document.createElement("table");ft.className="b4table";ft.innerHTML="ShortcutCounterexampleReliable ruleLeap if divisible by 42100 would be wrongly marked leapDivisible by 4, except centuries unless divisible by 400Assume five rowsMay 2027 Monday-first needs sixceil((leading offset + month days) / 7)Use local midnight timestampTimezone conversion can change displayed civil dayKeep date-only arithmetic in UTC or integer day countsMix weekday numbering basesSunday=0 versus Monday=0 shifts offsetsNormalize with ((weekday − weekStart + 7) mod 7)";faults.append(ft);const fp=document.createElement("p");fp.className="b4small";fp.textContent="Each failure is a static, bounded example. Nothing is executed against the machine clock or local timezone.";faults.append(fp)}sel.addEventListener("change",draw);draw();return root})(); app434:[] 30:{"id":"eebcda3f7454811e","slug":"year-boundary-stress-lab-2026-2027","title":"2026→2027 Year-Boundary Stress Lab","thumbnail":"adcd4ff8d80abe7c31fef0e04568a2397f1fae0687fc19496456f42beda8a3e8","access_level":"public","create_time":"$D2026-10-07T11:22:42.438Z","update_time":"$D2026-10-07T11:29:27.290Z","view_time":null,"first_public_time":"$D2026-10-07T11:38:56.668Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"0608cb6e6fdd19ad","login":"mateopedersen","name":"Mateo Pedersen","avatar_url":"https://avatars-next.observableusercontent.com/1656f6350cbcad592ca7fe8675140cd56effd725832498d28117b54dc11cfe4b","tier":"free_2026","bio":"Independent product builder exploring calendar computation, printable-layout geometry and temporal data visualization. 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Building interactive experiments around Beta Calendars and reproducible civil-date systems. https://www.betacalendars.com/"}],"members":[{"type":"team","id":"0608cb6e6fdd19ad","login":"mateopedersen","name":"Mateo Pedersen","avatar_url":"https://avatars-next.observableusercontent.com/1656f6350cbcad592ca7fe8675140cd56effd725832498d28117b54dc11cfe4b","tier":"free_2026","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"2026→2027 Year-Boundary Stress Lab","cells":[{"id":1,"value":"$32","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"$33","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"### Related analyses\n\n- [2027 Calendar Topology Observatory](https://observablehq.com/@mateopedersen/2027-calendar-topology-observatory) — month-grid structures.\n- [Printable Calendar Constraint Solver](https://observablehq.com/@mateopedersen/printable-calendar-constraint-solver) — page and grid geometry.\n- [Seven Week Starts: Calendar Sensitivity Atlas](https://observablehq.com/@mateopedersen/seven-week-starts-sensitivity-atlas) — origin sensitivity.\n- [Calendar Writing-Space Efficiency Atlas](https://observablehq.com/@mateopedersen/calendar-writing-space-efficiency-atlas) — comparative writing area.\n- [Undated Grid Design Space](https://observablehq.com/@mateopedersen/undated-grid-design-space) — blank planner design choices.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"2"}} 31:"$30:body"