7 files changed, 280 insertions, 2 deletions
diff --git a/docs/research/140-spec-suite.md b/docs/research/140-spec-suite.md
index 4a8d9f8..1da8f4b 100644
--- a/docs/research/140-spec-suite.md
+++ b/docs/research/140-spec-suite.md
@@ -56,7 +56,7 @@
 | 7 | 텍스트 편집 | UI 개념 | text, 커서 | 편집기의 참조 모델 대조(aup `make check`) | 된다 | 된다 |
 | 8 | 상자 배치(flex 같은) | UI 개념 | 중첩, 재귀 | 기존 배치 구현(Yoga, Taffy)의 결과와 대조 | 못 쓴다(중첩, 재귀) | 중첩과 재귀는 핸들러에서 된다. 보기에서 재귀 fn을 부르지 못한다(탐침). 쓰지 않음 |
 | 9 | HTTP/1.1 요청을 패킷마다(RFC 9112) | 스트림의 상태 기계 | 바이트, 이벤트를 넘는 상태 | 경계를 아무 데서나 자른 요청 모음 | 못 쓴다(바이트). 지금은 `serve/`의 C다 | 썼다: 스트림 200개를 어디서 잘라도 h11과 같다. 우회 하나(리스트 값의 대입), 줄 1.9배, C의 83배(아래) |
-| 10 | 재시도, 물러서기, 시간 제한 | 시간 | 시각, 한 번의 타이머 | 시각을 준 시뮬레이션 | 우회(주기 틱 `every`와 `now`) | 다시 보지 않음 |
+| 10 | 재시도, 물러서기, 시간 제한 | 시간 | 시각, 한 번의 타이머 | 시각을 준 시뮬레이션 | 우회(주기 틱 `every`와 `now`) | 썼다(RFC 6298): 사건 241,612개가 같은 규칙의 모델과 같다. 우회 하나(주기 틱: 10 ms면 타임아웃 하나에 틱 2,796개), 줄 1.9배(아래) |
 | 11 | X25519, ChaCha20-Poly1305 | 상수 시간 암호 | 데이터에 따라 달라지지 않는 시간 | RFC 7748, RFC 8439의 벡터 | aup 밖(설계상, 아래) | 그대로(설계상 aup 밖) |
 
 **11은 핵의 원시 연산으로 둔다(가설).** 실행기의 시간은 데이터에 따라 달라진다. 묶음 실행기도 결함이 나면 묶음을 처음부터 실행기로
@@ -784,6 +784,64 @@
   자기에게 메시지를 걸어 두는 단발 타이머는 핵의 원시(호스트의 일정, 저장, 재생의 결정성)이고, 명세 하나(10)가 닿는다. 쌓임을
   막는 규칙대로 적어 두고 만들지 않는다.
 
+## 묶음의 10: 재시도 타이머 (RFC 6298, 2026-10-19)
+
+보내는 쪽의 재전송 타이머를 썼다(aup의 `examples/rto.aup`). 새 명령도 코어의 C도 없다.
+- **규칙.** 확인된 세그먼트 가운데 다시 보낸 적 없는 것의 왕복 시간(Karn)으로 SRTT, RTTVAR, RTO를 고친다(2.2–2.5: 1초 이상, 60초
+  이하). 타이머는 5.1–5.6대로 돈다. 보낼 때 돌지 않으면 걸고, 다 확인되면 멈추고, 새 데이터가 확인되면 다시 건다. 만료하면 가장 이른
+  것을 다시 보내고(앱은 다시 보냄을 기록한다) RTO를 두 배로 한다.
+- **시간.** 타이머는 상태의 마감(`deadline`)이다. 앱은 주기 틱(`input tick = every 10 ms`)마다 `now`와 견준다. 140이 처음 적은
+  우회 그대로다. 시계의 단위 G는 틱의 주기다.
+- **알려진 구현은 대조하지 않았다.** 운영체제의 TCP는 사건을 줄 수 없다. 오라클은 같은 규칙의 파이썬 모델(`rto.py`)이다.
+  `rto_check.py`가 닫힌 고리의 망을 만든다: 세그먼트를 무작위 간격으로 보내고, 처음 보낸 것은 다섯에 하나를 잃는다. 받는 쪽은 틈
+  없이 가진 데까지 곧바로 누적 확인하고, 확인은 왕복의 나머지 반 뒤에 닿는다. 다시 보낸 것은 닿는다. 사건마다 시각을 준다(pure-run의
+  `time MS`).
+
+**맞음.**
+- 시드 10개 × 주기 둘(10, 100 ms) = 시나리오 20개, 사건 241,612개(타임아웃 156번). 사건마다 SRTT, RTTVAR, RTO, 마감, 남은 세그먼트,
+  다시 보냄의 수가 모델과 같다. 세 실행 길에서 모두 맞고, 세 길이 같다.
+- Pure의 `make check`(`module_specs`)에 들어갔다. 시나리오 하나(시드 2, 세그먼트 20, 타임아웃 다섯)를 주기 둘로 `tests/specs/rto`에
+  두었다(사건 2,297개). RTO를 세 배로 하는 앱은 그 검사에서 떨어진다.
+
+**막대.**
+
+| 막대 | 잰 것 | |
+|---|---|---|
+| 쓸 수 있다 | aup와 Pure만. 새 명령 없음 | 지남 |
+| 우회가 없다 | 주기 틱으로 마감을 본다(아래) | **우회 하나** |
+| 줄 수 ≤ 파이썬 참조 | aup 56줄(닫는 괄호만인 줄 11) 대 파이썬 30줄 | **못 미침**(1.9배) |
+| C 대비 시간 | 시간의 일이 아니다. 셈한 명령으로 적는다: 쉬는 틱 25, 보냄 12, 확인 112–247(평균 193) | 기록(막대 없음) |
+| 견고하다 | 위의 맞음, 세 길이 같음. 세 기계는 아직 | 일부 |
+
+**틱의 값.** 주기 틱은 타이머가 돌지 않을 때도 사건이다.
+
+| 주기 | 틱 | 타임아웃 하나에 틱 | 만료를 본 늦음(평균, 최대) | 검사 시나리오에서 틱이 쓴 명령 |
+|---|---|---|---|---|
+| 10 ms | 218,070 | 2,795.8 | 4.27 ms, 9.875 ms | 54,201 가운데 50,300(93%) |
+| 100 ms | 21,968 | 281.6 | 49.23 ms, 99.0 ms | 9,106 가운데 5,175(57%) |
+
+- 주기를 줄이면 늦음은 준다. 대신 틱이 그만큼 는다. 늦음은 주기 아래이고, 틱의 수는 주기에 반비례한다. 둘을 같이 줄이는 주기는 없다.
+- `serve`는 때가 된 틱을 돌린 뒤 저장한다(`run_timers`). 쉬는 틱도 사건이므로, 저장과 재생의 기록도 틱만큼 는다.
+- 쉬는 틱과 만료한 틱이 같은 25다. 셈은 블록을 쓴 대로 센다(`charge`). 갈래가 어느 쪽으로 가든 같다.
+
+**마찰 셋.**
+1. 앱이 자기 입력의 주기를 읽지 못한다. G(2.4의 `max(G, 4·RTTVAR)`)가 틱의 주기인데, `every 10 ms`와 `fn PERIOD = 10`에 두 번 쓴다.
+2. `abs`가 없다. `|SRTT − R|`을 `max(srtt - r, r - srtt)`로 썼다.
+3. `send`는 출력의 낱말이라 입력의 이름으로 쓸 수 없다(`transmit`으로 썼다).
+
+**줄을 길게 한 것.** 56 대 30이다. 닫는 괄호의 줄을 빼면 45다.
+- 레코드 둘(`Segment`, `Retransmit`)이 9줄이다. 파이썬은 리스트와 튜플이다.
+- 상태와 입력의 선언이 10줄이다. 파이썬은 생성자의 두 줄이다.
+- 확인된 것을 고르는 고리가 6줄이다. 파이썬은 리스트 내포 두 줄이다(`[s for s in … if s[0] <= seq]`).
+
+**결정점: 단발 타이머.** 주기 틱을 걷어 낼 꼴은 이렇다.
+- 앱이 "T에 깨워라"를 건다. 상태의 마감을 호스트가 읽는 꼴이 될 수도, 효과(`after`, `at`)가 될 수도 있다.
+- 호스트는 그 시각을 저장소에 두고, T가 되면 핸들러를 `now = T`(또는 그 뒤)로 한 번 돌린다. 저장하고, 재생에서 같은 차례로 돈다.
+- 그러면 쉬는 틱(10 ms면 타임아웃 하나에 2,796개)이 없어지고, 만료를 늦음 없이 본다.
+- 그러나 지금 그것이 필요한 명세는 이것 하나다. 140의 규칙(핵은 두 명세가 필요로 하는 것만 받는다)대로 적어 두고 만들지 않는다. 두
+  번째 후보: HTTP의 유휴 연결 시간 제한, DNS 질의의 재시도. 둘 다 아직 묶음의 명세가 다루지 않는다.
+- 원본: `rto.py`(모델), `rto_check.py`(맞음, 틱의 값, 줄 수), `2026-10-19-rto.jsonl`.
+
 ## 착수 기준 (다음 일)
 
 - **바꿀 결정.** 계산의 핵을 설계한다(027). 위 표의 여덟 후보 가운데 무엇을 어떤 모양으로 받을지 정한다.
diff --git a/research/experiments/044-specs/2026-10-19-rto.jsonl b/research/experiments/044-specs/2026-10-19-rto.jsonl
new file mode 100644
index 0000000..71d73d7
--- /dev/null
+++ b/research/experiments/044-specs/2026-10-19-rto.jsonl
@@ -0,0 +1 @@
+{"scenarios": 20, "events": 241612, "timeouts": 156, "right": {"batches": 241612, "rounds": 241612, "all": 241612}, "paths_same": true, "costs": {"10": {"ticks": 218070, "timeouts": 78, "ticks_a_timeout": 2795.8, "late_mean_ms": 4.27, "late_most_ms": 9.875}, "100": {"ticks": 21968, "timeouts": 78, "ticks_a_timeout": 281.6, "late_mean_ms": 49.23, "late_most_ms": 99.0}}, "aup_lines": 56, "aup_brace_lines": 11, "python_lines": 30}
diff --git a/research/experiments/044-specs/rto.py b/research/experiments/044-specs/rto.py
new file mode 100644
index 0000000..e4a4a57
--- /dev/null
+++ b/research/experiments/044-specs/rto.py
@@ -0,0 +1,40 @@
+# RFC 6298's retransmission timer in plain Python: the reference 140 counts aup's lines against. A sender's segments
+# are sent and acknowledged (cumulatively) at given times; the round-trip time of each acknowledged segment that was
+# never sent again (Karn) updates SRTT, RTTVAR and RTO (2.2-2.5: 1 s at least, 60 s at most), and the timer runs as
+# 5.1-5.6 say: started when one is sent and none runs, stopped when all are acknowledged, restarted when new data is,
+# and on expiry the earliest is sent again and RTO doubles. The timer is seen at ticks of period P, as an app sees time.
+LOWEST, HIGHEST = 1000, 60000  # milliseconds; the clock's granularity G is the tick's period
+
+
+class Sender:
+    def __init__(self, period):
+        self.period, self.srtt, self.rttvar, self.rto, self.measured = period, 0.0, 0.0, 1000.0, False
+        self.deadline, self.outstanding, self.retransmits = -1.0, [], []  # outstanding: [seq, sent, again]
+
+    def send(self, now, seq):
+        self.outstanding.append([seq, now, False])
+        if self.deadline < 0:
+            self.deadline = now + self.rto  # 5.1
+
+    def ack(self, now, seq):
+        acked = [s for s in self.outstanding if s[0] <= seq]
+        if not acked:
+            return
+        self.outstanding = [s for s in self.outstanding if s[0] > seq]
+        last = acked[-1]
+        if not last[2]:  # Karn: no sample from a segment sent again
+            r = now - last[1]
+            if not self.measured:
+                self.srtt, self.rttvar, self.measured = r, r / 2, True  # 2.2
+            else:
+                self.rttvar = 0.75 * self.rttvar + 0.25 * abs(self.srtt - r)  # 2.3
+                self.srtt = 0.875 * self.srtt + 0.125 * r
+            self.rto = min(max(self.srtt + max(self.period, 4 * self.rttvar), LOWEST), HIGHEST)  # 2.4, 2.5
+        self.deadline = now + self.rto if self.outstanding else -1.0  # 5.3, 5.2
+
+    def tick(self, now):
+        if self.deadline >= 0 and now >= self.deadline:  # 5.4-5.6
+            self.outstanding[0][2] = True
+            self.retransmits.append((self.outstanding[0][0], now))
+            self.rto = min(self.rto * 2, HIGHEST)
+            self.deadline = now + self.rto
diff --git a/research/experiments/044-specs/rto_check.py b/research/experiments/044-specs/rto_check.py
new file mode 100644
index 0000000..be41ffb
--- /dev/null
+++ b/research/experiments/044-specs/rto_check.py
@@ -0,0 +1,145 @@
+#!/usr/bin/env python3
+"""Research 140: RFC 6298's retransmission timer written in aup (aup's examples/rto.aup), with periodic ticks.
+
+Each scenario (a seed and a tick period P) is made closed-loop by rto.py's model and a receiver: segments sent at random
+gaps, each arriving half a random round trip later unless its first sending is lost (one in five), the receiver
+acknowledging cumulatively all it holds without a gap, the acknowledgement arriving after the other half; a segment the
+timer sends again arrives. The events (sends, acknowledgements, ticks every P ms) are then given to the app
+through pure-run (time MS before each), on Pure's three paths: after every event its SRTT, RTTVAR, RTO, deadline, the
+segments outstanding and the retransmissions must be the model's, the paths the same. No known implementation is
+compared: the oracle is the model of the same rules. What the ticks cost is measured: ticks a timeout (a one-shot timer
+would be one event), and how late a timeout is seen (below P). Then counts lines of rto.aup and of rto.py's model. One
+JSON line."""
+import json, os, random, struct, subprocess, sys, tempfile
+
+here = os.path.dirname(os.path.abspath(__file__))
+pure = os.path.normpath(os.path.join(here, '../../..'))
+aup = os.environ.get('AUP', os.path.join(pure, '..', 'aup'))
+sys.path.insert(0, here)
+import rto  # noqa: E402
+
+START = 1_000_000  # the first event's time (ms since 1970, as now is)
+
+
+def lines(path, stop=None):
+    code = braces = 0
+    for line in open(path):
+        if stop and line.startswith(stop): break
+        text = line.strip()
+        if not text or text.startswith('#'): continue
+        code += 1
+        braces += text == '}'
+    return code, braces
+
+
+def scenario(seed, period, segments=40):
+    """The events the app is given (time, kind, seq), the model's state after each, and the timeouts' lateness. The
+    network: a sending arrives half a random round trip later unless it is lost (a first sending, one in five), and the
+    receiver acknowledges at once, cumulatively, all it holds without a gap; the acknowledgement arrives after the other
+    half."""
+    chooser = random.Random(seed)
+    sender = rto.Sender(period)
+    pending, t = [], START + period  # (time, order, kind, seq): arrivals, then acknowledgements, sends, then ticks
+    for seq in range(1, segments + 1):
+        t += chooser.choice([0, 0, 5, 40, 120, 300, 900])
+        pending.append((t, 2, 'transmit', seq))
+    held, through = set(), 0  # the receiver's segments, and the last one it holds every one up to
+
+    def sent(time, seq, first):
+        if not first or chooser.random() > 0.2:
+            half = chooser.randrange(20, 350)
+            pending.append((time + half, 0, 'arrive', seq * 1000 + half))
+
+    events, states, late = [], [], []
+    tick = START
+    while pending or sender.outstanding:
+        pending.sort()
+        if pending and pending[0][0] < tick + period:  # the host ticks every P, the timer running or not
+            time, _, kind, seq = pending.pop(0)
+        else:
+            time, kind, seq = tick + period, 'tick', 0
+            tick = time
+        if kind == 'arrive':  # the receiver's: not the app's
+            seq, half = divmod(seq, 1000)
+            held.add(seq)
+            while through + 1 in held:
+                through += 1
+            if through:
+                pending.append((time + half, 1, 'ack', through))
+            continue
+        if kind == 'transmit':
+            sender.send(time, seq)
+            sent(time, seq, True)
+        elif kind == 'ack':
+            sender.ack(time, seq)
+        else:
+            before, deadline = len(sender.retransmits), sender.deadline
+            sender.tick(time)
+            if len(sender.retransmits) > before:
+                late.append(time - deadline)
+                sent(time, sender.retransmits[-1][0], False)
+        events.append((time, kind, seq))
+        states.append((sender.srtt, sender.rttvar, sender.rto, sender.deadline, len(sender.outstanding), len(sender.retransmits)))
+        if len(events) > 200000:
+            raise RuntimeError('a scenario without end')
+    return events, states, late
+
+
+def run(module, events, env, work):
+    commands = os.path.join(work, 'rto.commands')
+    with open(commands, 'w') as f:
+        for time, kind, seq in events:
+            f.write(f'time {time}\n')
+            f.write('tick tick\n' if kind == 'tick' else f"message {kind} {struct.pack('<I', seq).hex()}\n")
+    got = []
+    with open(commands) as stdin:
+        process = subprocess.Popen([os.path.join(pure, 'build', 'pure-run'), module], stdin=stdin, stdout=subprocess.PIPE,
+                                   text=True, env=dict(os.environ, **env))
+        for k, line in enumerate(process.stdout):
+            if k % 2 == 0: continue  # a time command's
+            state = json.loads(line)
+            s = state['states']
+            got.append((state['fault'], s['srtt'], s['rttvar'], s['rto'], s['deadline'], len(s['outstanding']),
+                        len(s['retransmits'])))
+        process.wait()
+    return got
+
+
+if __name__ == '__main__':
+    report = {'scenarios': 0, 'events': 0, 'timeouts': 0, 'right': {}, 'paths_same': True}
+    costs = {}
+    seeds = int(sys.argv[1]) if len(sys.argv) > 1 else 10
+    with tempfile.TemporaryDirectory() as work:
+        source = open(os.path.join(aup, 'examples', 'rto.aup')).read()
+        for period in (10, 100):
+            module = os.path.join(work, f'rto-{period}.pmod')  # its tick and its G the scenario's period
+            with open(os.path.join(work, f'rto-{period}.aup'), 'w') as f:
+                f.write(source.replace('every 10 ms', f'every {period} ms').replace('fn PERIOD = 10 ', f'fn PERIOD = {period} '))
+            subprocess.run([os.path.join(aup, 'build', 'aup'), 'build', os.path.join(work, f'rto-{period}.aup'), '-o', module], check=True)
+            ticks = timeouts = 0
+            lateness = []
+            for seed in range(seeds):
+                events, states, late = scenario(seed, period)
+                outputs = {}
+                for name, env in (('batches', {'PURE_JIT': '0'}), ('rounds', {'PURE_JIT': '0', 'PURE_BATCH': '0'}),
+                                  ('all', {'PURE_JIT': 'all'})):
+                    got = run(module, events, env, work)
+                    want = [('none',) + s for s in states]
+                    report['right'][name] = report['right'].get(name, 0) + sum(g == w for g, w in zip(got, want))
+                    outputs[name] = got
+                report['paths_same'] = report['paths_same'] and outputs['rounds'] == outputs['batches'] == outputs['all']
+                report['scenarios'] += 1
+                report['events'] += len(events)
+                ticks += sum(kind == 'tick' for _, kind, _ in events)
+                timeouts += len(late)
+                lateness += late
+            report['timeouts'] += timeouts
+            costs[period] = {'ticks': ticks, 'timeouts': timeouts, 'ticks_a_timeout': round(ticks / max(timeouts, 1), 1),
+                             'late_mean_ms': round(sum(lateness) / max(len(lateness), 1), 2), 'late_most_ms': max(lateness, default=0)}
+    report['costs'] = costs
+    aup_code, aup_braces = lines(os.path.join(aup, 'examples', 'rto.aup'))
+    python_code, _ = lines(os.path.join(here, 'rto.py'))
+    report.update({'aup_lines': aup_code, 'aup_brace_lines': aup_braces, 'python_lines': python_code})
+    ok = all(n == report['events'] for n in report['right'].values()) and report['paths_same']
+    print(json.dumps(report))
+    sys.exit(0 if ok else 1)
diff --git a/tests/check.py b/tests/check.py
index 7a5f50e..5574b80 100644
--- a/tests/check.py
+++ b/tests/check.py
@@ -1736,7 +1736,9 @@ def module_specs(aup, pure, work):
     written back by its view to the same records, cut ones refused; HTTP/1.1
     request streams (tests/specs/http) read by its examples/http.aup a packet
     at a time, cut anywhere, to the same requests; line breaking (UAX #14) by its
-    examples/linebreak.aup on LineBreakTest.txt's lines (tests/specs/linebreak)."""
+    examples/linebreak.aup on LineBreakTest.txt's lines (tests/specs/linebreak);
+    RFC 6298's retransmission timer by its examples/rto.aup on a scenario's
+    events (tests/specs/rto), the model's state after each."""
     import hashlib
     import os
     import random
@@ -1962,6 +1964,30 @@ def module_specs(aup, pure, work):
         state = json.loads(line)
         assert state['fault'] == 'none' and [b != 0 for b in bytes.fromhex(state['views']['boundaries'])] == want, codes
     runs['linebreak'] = {'lines': len(lines), 'code_points': sum(len(c) for c, _ in lines)}
+    # RFC 6298's retransmission timer (its examples/rto.aup, ticked): a scenario's sends, acknowledgements and ticks
+    # (tests/specs/rto, at periods of 10 and 100 ms), after each the model's SRTT, RTTVAR, RTO, deadline and counts.
+    source, events = (EXAMPLES / 'rto.aup').read_text(), 0
+    for scenario in json.loads((pure / 'tests/specs/rto/scenarios.json').read_text()):
+        period = scenario['period']
+        (work / 'rto.aup').write_text(source.replace('every 10 ms', f'every {period} ms').replace('fn PERIOD = 10 ', f'fn PERIOD = {period} '))
+        program = work / 'rto.pmod'
+        compile_module(aup, work / 'rto.aup', program)
+        given = ''.join(f'time {t}\n' + ('tick tick\n' if kind == 'tick' else f"message {kind} {struct.pack('<I', seq).hex()}\n")
+                        for t, kind, seq in scenario['events'])
+        shown = {name: subprocess.run([str(pure / 'build/pure-run'), str(program)], input=given, capture_output=True, text=True,
+                                      timeout=120, env=dict(os.environ, **env)).stdout
+                 for name, env in (('batches', {'PURE_JIT': '0'}), ('rounds', {'PURE_JIT': '0', 'PURE_BATCH': '0'}), ('all', {'PURE_JIT': 'all'}))}
+        for name in ('rounds', 'all'):
+            assert shown[name] == shown['batches'], ('rto', period, name)
+        out = shown['batches'].splitlines()[1::2]
+        assert len(out) == len(scenario['states']), ('rto', period, len(out))
+        for line, want in zip(out, scenario['states']):
+            state = json.loads(line)
+            s = state['states']
+            assert state['fault'] == 'none' and [s['srtt'], s['rttvar'], s['rto'], s['deadline'], len(s['outstanding']),
+                                                 len(s['retransmits'])] == want, ('rto', period, want)
+        events += len(out)
+    runs['rto'] = {'scenarios': 2, 'events': events}
     return runs
 
 
diff --git a/tests/specs/rto/README.md b/tests/specs/rto/README.md
new file mode 100644
index 0000000..e090586
--- /dev/null
+++ b/tests/specs/rto/README.md
@@ -0,0 +1,7 @@
+# RFC 6298's retransmission timer: two scenarios
+
+`scenarios.json` holds one scenario (seed 2, 20 segments, five timeouts) of `research/experiments/044-specs/rto_check.py`
+at tick periods of 10 and 100 ms: the events an app is given (time in ms, kind, segment) and, after each, the state the
+model of the same rules (`rto.py`) has (SRTT, RTTVAR, RTO, deadline, segments outstanding, retransmissions).
+`tests/check.py`'s `module_specs` gives the events to aup's `examples/rto.aup` (its tick and G made the period's) on
+Pure's three paths.
diff --git a/tests/specs/rto/scenarios.json b/tests/specs/rto/scenarios.json
new file mode 100644
index 0000000..b0e4846
--- /dev/null
+++ b/tests/specs/rto/scenarios.json
@@ -0,0 +1 @@
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+\ No newline at end of file