T04: specs/SessionShape.md — compaction is the lever, not session length

The task's original premise was wrong and is recorded rather than
deleted. It was written to prescribe one task per session; measurement
says the variable is context, not turn count.

Measured:
  - compaction cut context 27x (542,991 -> 19,974) and cost/turn 3.1x;
    the 202 turns after C1 cost less than half the 136 before it
  - a turn costs $0.010 at 20k context and $0.270 at 540k
  - break-even for a compaction is 2-11 turns, so: compact whenever
    context exceeds ~300k and work remains
  - a fresh session is NOT free -- cold start floors at ~51k and must
    then re-read the artifacts a compact summary already holds (~66k).
    Prefer compaction to continue work; prefer a fresh session when the
    task changes, because then prior context is pure overhead.

cb-cost now emits SH-1..SH-3 so the targets come from the instrument
rather than from analysis, per InnerLoop v1.1. All three are UNMET
(mean context 232,982 vs 200,000; p90 492,042 vs 300,000; batching 7.8%
vs 20%) and are reported unmet rather than retargeted -- retargeting in
the commit that first measures is precisely what T07 exists to prevent.

Eighth error instance found while writing this: CB-WP-0001's claim that
"0 of 330 tool calls were batched" is wrong. 330 was the count of
single-call responses, not the total; 31 responses batched, covering 76
calls. It was carried into this workplan unverified. Trusted-arithmetic
class -- the one the T01 audit flagged as having no executable defence,
confirming that finding within hours of making it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

tools/cb-cost.py

@@ -147,6 +147,14 @@ def read_responses(path, pin=None):
                 )
         toks["output"] = max(t["output"] for t in per_row)
         head = rows[0]
+        # Tool calls are spread across the group's lines, so they are counted
+        # over the whole group — one response may carry several (SS-05).
+        tool_calls = sum(
+            1
+            for r in rows
+            for c in (r["message"].get("content") or [])
+            if c.get("type") == "tool_use"
+        )
         out.append(
             {
                 "request_id": rid,
@@ -154,12 +162,33 @@ def read_responses(path, pin=None):
                 "timestamp": head.get("timestamp") or "",
                 "session": head.get("sessionId") or os.path.basename(path),
                 "toks": toks,
+                "tool_calls": tool_calls,
                 "subagent": "/subagents/" in path,
             }
         )
     return out
 
 
+def session_shape(responses):
+    """SH-1..SH-3 from specs/SessionShape.md."""
+    import statistics
+
+    ctx = sorted(r["toks"]["cache_read"] for r in responses)
+    with_tools = [r for r in responses if r["tool_calls"] > 0]
+    batched = [r for r in with_tools if r["tool_calls"] > 1]
+    calls = sum(r["tool_calls"] for r in with_tools)
+    pct = statistics.quantiles(ctx, n=100) if len(ctx) > 1 else [ctx[0]] * 99
+    return {
+        "SH-1_mean_context": statistics.mean(ctx) if ctx else 0,
+        "SH-2_p90_context": pct[89],
+        "SH-3_batching_rate": (len(batched) / len(with_tools)) if with_tools else 0.0,
+        "p50_context": pct[49],
+        "responses_with_tools": len(with_tools),
+        "tool_calls": calls,
+        "calls_in_batched_turns": calls - (len(with_tools) - len(batched)),
+    }
+
+
 # ------------------------------------------------------------- attribution
 
 
@@ -293,6 +322,7 @@ def collect(slug, pin_ref=None):
 
     sub = sum(r["cost"] or 0 for r in responses if r["subagent"])
     return {
+        "session_shape": session_shape(responses),
         "slug": slug,
         "pin": pin,
         "responses": len(responses),
@@ -344,6 +374,17 @@ def render(rep, by_task=False, composition=False):
             f"    A per-task table is a view over {100*(1-un/tot):.0f}% of spend."
         )
 
+    sh = rep["session_shape"]
+    print("\n  session shape (specs/SessionShape.md)")
+    print(f"    SH-1 mean context   {sh['SH-1_mean_context']:>12,.0f} tok  "
+          f"[{'ok ' if sh['SH-1_mean_context']<=200_000 else 'FAIL'} target 200,000]")
+    print(f"    SH-2 p90 context    {sh['SH-2_p90_context']:>12,.0f} tok  "
+          f"[{'ok ' if sh['SH-2_p90_context']<=300_000 else 'FAIL'} target 300,000]")
+    print(f"    SH-3 batching rate  {100*sh['SH-3_batching_rate']:>11.1f}%   "
+          f"[{'ok ' if sh['SH-3_batching_rate']>=0.20 else 'FAIL'} target 20.0%]")
+    print(f"         {sh['tool_calls']} tool calls in {sh['responses_with_tools']} responses; "
+          f"{sh['calls_in_batched_turns']} in batched turns")
+
     if rep["unpriced"]:
         print(f"\n  UNPRICED ({len(rep['unpriced'])} responses, model not in sheet):")
         for u in rep["unpriced"]:
@@ -446,6 +487,8 @@ def main():
     ap.add_argument("--pin", help="commit-ish or ISO Z instant (CA-07)")
     ap.add_argument("--by-task", action="store_true")
     ap.add_argument("--composition", action="store_true")
+    ap.add_argument("--session-shape", action="store_true",
+                    help="SH-1..SH-3 (always shown in the default report)")
     ap.add_argument("--self-test", action="store_true")
     ap.add_argument("--json", action="store_true")
     args = ap.parse_args()