Artifacts (~/sackscoreboard): gentrace.sh, scoreboard.awk, reference.py, naive.awk, analyzenaive.py, verify.sh, plus SOLUTION.md (full document), and generated trace.txt/report.txt.
Done. The complete, runnable solution is in ~/sack_scoreboard/. Here is the solution write-up.
Artifacts (~/sack_scoreboard): gen_trace.sh, scoreboard.awk, reference.py, naive.awk, analyze_naive.py, verify.sh, plus SOLUTION.md (full document), and generated trace.txt/report_*.txt.
Run it: cd ~/sack_scoreboard && ./verify.sh → ALL CHECKS PASSED.
A SACK scoreboard is a set of disjoint, sorted, merged byte intervals plus a cumulative-ack pointer. Four mistakes each corrupt the report:
left < HighACK is a DSACK (duplicate data), not new receive data. Treating it as SACK deflates bytes-in-flight and hides spurious retransmits.seq < nxt and 32-bit interval math are wrong. Values must be unwrapped to 64-bit absolute coordinates using nearest-congruence.Unwrap: unwrap(x,ref) = ref + d, where d = (x − ref mod 2³²) mod 2³², adjusted by −2³² if d ≥ 2³¹.
Interval set: arrays IL[set,i]/IR[set,i] (right-exclusive), insertion-sorted by left edge and coalesced on every add; subtraction splits intervals.
Per ACK (one round):
1. ack_abs = unwrap(ack, SND.UNA); advance SND.UNA.
2. Build nw: l < ack_abs ⇒ DSACK (dsack_total++; if it overlaps a recorded retransmit, spurious++), else add [l,r).
3. Reneging rg = scoreboard − nw − [.., ack_abs); report each range, then scoreboard = nw (trace assumes complete SACK reports). A pure cumulative ACK never triggers reneging.
4. bytes_in_flight = (SND.NXT − SND.UNA) − Σscoreboard (clamped ≥ 0).
5. NextSeg: highest hole whose start is below the highest SACKed octet (else lowest); record it for later DSACK spurious detection.
6. On a 2³² epoch crossing, emit the WRAP scoreboard snapshot.
Core engine (full text in scoreboard.awk):
function mod32(v) { v = v % MOD; if (v < 0) v += MOD; return v }
function unwrap(x, ref, d) {
d = mod32(x - mod32(ref)); if (d >= HALF) d -= MOD; return ref + d
}
# iv_add: insertion-sort by left edge, then coalesce when IL <= last IR
# iv_remove: subtract [l,r), splitting intervals
# build_holes: complement of scoreboard in [SND.UNA, SND.NXT)
The generator (gen_trace.sh) uses ISN = 2³²−4000 so the wrap lands exactly on a segment boundary; one block is retransmitted spuriously (later DSACK proves it) and one SACKed block is silently dropped (reneging).
1. Exactness. awk -f scoreboard.awk trace.txt and python3 reference.py trace.txt are byte-identical (diff exits 0) — every per-round byte count, hole list, reneging range, DSACK count, spurious count, and wrap snapshot.
2. Reference report:
ROUND 1 ... bytes_in_flight=10000 holes=-3000:-2000,-1000:8000 reneged=- dsack_total=0 spurious=0
ROUND 2 ... bytes_in_flight=8000 holes=-1000:0,1000:8000 reneged=- dsack_total=1 spurious=1
ROUND 3 ... bytes_in_flight=5000 holes=...5 holes...
ROUND 4 ... bytes_in_flight=4000 holes=...4 holes...
WRAP round=4 scoreboard=2000:3000,4000:5000,6000:7000
ROUND 5 ... bytes_in_flight=4000 holes=1000:4000,5000:6000 reneged=2000:3000 dsack_total=1 spurious=1
ROUND 6 ... bytes_in_flight=2000 holes=3000:4000,5000:6000
ROUND 7 ... bytes_in_flight=0 holes=-
Round 5 reneged=2000:3000 is the dropped block; removing it merges the adjacent holes into 1000:4000. Round 2 dsack_total=1 spurious=1 is the spurious retransmit. Round 4 WRAP is the scoreboard across the 2³² boundary.
3. Naive baseline damage (naive.awk — unsorted/unmerged, no reneging, DSACK treated as SACK):
max bytes-in-flight relative error : 200.0% at round 6
reneging events : 1
reneging holes the naive list lost : 1
PASS: naive bytes-in-flight error exceeds 10%
PASS: naive loses at least one hole for every reneging event
At round 5 the naive holes are 1000:2000,3000:4000,5000:6000 instead of the reference 1000:4000,5000:6000, so 2000:3000 is not reported as a hole; error across the trace ranges 12.5%–200% (> 10%).
| Check | Result |
|---|---|
| awk vs Python, field-by-field | identical |
| Reneging | 1 event, 2000:3000 |
| DSACK spurious retransmits | 1 |
| Wrap snapshot | round 4 |
| Naive bytes-in-flight error | max 200% (> 10%) |
| Naive holes lost per reneging event | 1 of 1 |
The exact fix is (a) 64-bit modular unwrapping, (b) a sorted/merged/disjoint interval set, (c) reneging as a set difference against the previous scoreboard, and (d) DSACK as block.left < HighACK. The naive baseline that omits these loses a hole per reneging event and mis-reports bytes-in-flight by up to 200% on the wraparound trace.
One documented scope note: the trace assumes the receiver reports all held SACK blocks in every SACK-bearing ACK (needed to treat an omission as reneging); a production implementation must first rule out the TCP 4-block option-space limit.
# Evidence - Problem class: bash-tcp-sack-scoreboard-reneging-dsack-exact-bytes-in-flight - Model: openrouter/deepseek/deepseek-v4.1-flash - Solved: 2026-09-24T04:09:20.498Z - Verification: solution produced by pi in sandbox; see signatures.json
{"description": "Implement a pure bash/awk TCP SACK scoreboard reconstructor that consumes a synthetic segment/ack trace (lines of direction, seq, ack, flags, sack-block list, timestamp) with 32-bit sequence wraparound, reassembles cumulative ack, merges and splits SACK blocks into a hint-free interval set, retransmits only from the highest-SACKed hole per RFC 6675 NextSeg order, and detects reneging (a previously SACKed block later cumulatively acked as lost without ever being SACKed again) plus DSACK (a SACK block below the cumulative ack that predicts a spurious retransmit). Deliver the script plus a generator and accounting report that print, per transmission round, the exact bytes-in-flight, the hole list, the reneging events with the sequence range that was silently dropped by the receiver, the DSACK-induced spurious retransmit count, and the scoreboard state after each wraparound. Prove exactness by running the trace through an independent Python reference implementation and diffing every per-round byte count and hole list, and show that a naive implementation that keeps SACK blocks unsorted or ignores DSACK loses at least one hole per reneging event and mis-reports bytes-in-flight by more than 10 percent on the wraparound trace.", "environment": "bash", "language": "bash", "model": "openrouter/deepseek/deepseek-v4.1-flash", "problem_class": "bash-tcp-sack-scoreboard-reneging-dsack-exact-bytes-in-flight", "provider": "openrouter", "solved_at": "2026-09-24T04:09:20.498Z", "version": "5.2"}Done. The complete, runnable solution is in ~/sack_scoreboard/. Here is the solution write-up.
Artifacts (~/sack_scoreboard): gen_trace.sh, scoreboard.awk, reference.py, naive.awk, analyze_naive.py, verify.sh, plus SOLUTION.md (full document), and generated trace.txt/report_*.txt.
Run it: cd ~/sack_scoreboard && ./verify.sh → ALL CHECKS PASSED.
A SACK scoreboard is a set of disjoint, sorted, merged byte intervals plus a cumulative-ack pointer. Four mistakes each corrupt the report:
left < HighACK is a DSACK (duplicate data), not new receive data. Treating it as SACK deflates bytes-in-flight and hides spurious retransmits.seq < nxt and 32-bit interval math are wrong. Values must be unwrapped to 64-bit absolute coordinates using nearest-congruence.Unwrap: unwrap(x,ref) = ref + d, where d = (x − ref mod 2³²) mod 2³², adjusted by −2³² if d ≥ 2³¹.
Interval set: arrays IL[set,i]/IR[set,i] (right-exclusive), insertion-sorted by left edge and coalesced on every add; subtraction splits intervals.
Per ACK (one round):
1. ack_abs = unwrap(ack, SND.UNA); advance SND.UNA.
2. Build nw: l < ack_abs ⇒ DSACK (dsack_total++; if it overlaps a recorded retransmit, spurious++), else add [l,r).
3. Reneging rg = scoreboard − nw − [.., ack_abs); report each range, then scoreboard = nw (trace assumes complete SACK reports). A pure cumulative ACK never triggers reneging.
4. bytes_in_flight = (SND.NXT − SND.UNA) − Σscoreboard (clamped ≥ 0).
5. NextSeg: highest hole whose start is below the highest SACKed octet (else lowest); record it for later DSACK spurious detection.
6. On a 2³² epoch crossing, emit the WRAP scoreboard snapshot.
Core engine (full text in scoreboard.awk):
function mod32(v) { v = v % MOD; if (v < 0) v += MOD; return v }
function unwrap(x, ref, d) {
d = mod32(x - mod32(ref)); if (d >= HALF) d -= MOD; return ref + d
}
# iv_add: insertion-sort by left edge, then coalesce when IL <= last IR
# iv_remove: subtract [l,r), splitting intervals
# build_holes: complement of scoreboard in [SND.UNA, SND.NXT)
The generator (gen_trace.sh) uses ISN = 2³²−4000 so the wrap lands exactly on a segment boundary; one block is retransmitted spuriously (later DSACK proves it) and one SACKed block is silently dropped (reneging).
1. Exactness. awk -f scoreboard.awk trace.txt and python3 reference.py trace.txt are byte-identical (diff exits 0) — every per-round byte count, hole list, reneging range, DSACK count, spurious count, and wrap snapshot.
2. Reference report:
ROUND 1 ... bytes_in_flight=10000 holes=-3000:-2000,-1000:8000 reneged=- dsack_total=0 spurious=0
ROUND 2 ... bytes_in_flight=8000 holes=-1000:0,1000:8000 reneged=- dsack_total=1 spurious=1
ROUND 3 ... bytes_in_flight=5000 holes=...5 holes...
ROUND 4 ... bytes_in_flight=4000 holes=...4 holes...
WRAP round=4 scoreboard=2000:3000,4000:5000,6000:7000
ROUND 5 ... bytes_in_flight=4000 holes=1000:4000,5000:6000 reneged=2000:3000 dsack_total=1 spurious=1
ROUND 6 ... bytes_in_flight=2000 holes=3000:4000,5000:6000
ROUND 7 ... bytes_in_flight=0 holes=-
Round 5 reneged=2000:3000 is the dropped block; removing it merges the adjacent holes into 1000:4000. Round 2 dsack_total=1 spurious=1 is the spurious retransmit. Round 4 WRAP is the scoreboard across the 2³² boundary.
3. Naive baseline damage (naive.awk — unsorted/unmerged, no reneging, DSACK treated as SACK):
max bytes-in-flight relative error : 200.0% at round 6
reneging events : 1
reneging holes the naive list lost : 1
PASS: naive bytes-in-flight error exceeds 10%
PASS: naive loses at least one hole for every reneging event
At round 5 the naive holes are 1000:2000,3000:4000,5000:6000 instead of the reference 1000:4000,5000:6000, so 2000:3000 is not reported as a hole; error across the trace ranges 12.5%–200% (> 10%).
| Check | Result |
|---|---|
| awk vs Python, field-by-field | identical |
| Reneging | 1 event, 2000:3000 |
| DSACK spurious retransmits | 1 |
| Wrap snapshot | round 4 |
| Naive bytes-in-flight error | max 200% (> 10%) |
| Naive holes lost per reneging event | 1 of 1 |
The exact fix is (a) 64-bit modular unwrapping, (b) a sorted/merged/disjoint interval set, (c) reneging as a set difference against the previous scoreboard, and (d) DSACK as block.left < HighACK. The naive baseline that omits these loses a hole per reneging event and mis-reports bytes-in-flight by up to 200% on the wraparound trace.
One documented scope note: the trace assumes the receiver reports all held SACK blocks in every SACK-bearing ACK (needed to treat an omission as reneging); a production implementation must first rule out the TCP 4-block option-space limit.
# Evidence - Problem class: bash-tcp-sack-scoreboard-reneging-dsack-exact-bytes-in-flight - Model: openrouter/deepseek/deepseek-v4.1-flash - Solved: 2026-09-24T04:09:20.498Z - Verification: solution produced by pi in sandbox; see signatures.json
{"description": "Implement a pure bash/awk TCP SACK scoreboard reconstructor that consumes a synthetic segment/ack trace (lines of direction, seq, ack, flags, sack-block list, timestamp) with 32-bit sequence wraparound, reassembles cumulative ack, merges and splits SACK blocks into a hint-free interval set, retransmits only from the highest-SACKed hole per RFC 6675 NextSeg order, and detects reneging (a previously SACKed block later cumulatively acked as lost without ever being SACKed again) plus DSACK (a SACK block below the cumulative ack that predicts a spurious retransmit). Deliver the script plus a generator and accounting report that print, per transmission round, the exact bytes-in-flight, the hole list, the reneging events with the sequence range that was silently dropped by the receiver, the DSACK-induced spurious retransmit count, and the scoreboard state after each wraparound. Prove exactness by running the trace through an independent Python reference implementation and diffing every per-round byte count and hole list, and show that a naive implementation that keeps SACK blocks unsorted or ignores DSACK loses at least one hole per reneging event and mis-reports bytes-in-flight by more than 10 percent on the wraparound trace.", "environment": "bash", "language": "bash", "model": "openrouter/deepseek/deepseek-v4.1-flash", "problem_class": "bash-tcp-sack-scoreboard-reneging-dsack-exact-bytes-in-flight", "provider": "openrouter", "solved_at": "2026-09-24T04:09:20.498Z", "version": "5.2"}