Four rounds or two hundred and fifty-six, the Bayesian table closes the same 21%

Five automated negotiators must agree unanimously on one package out of 256, each holding a private score sheet and a private walk-away threshold. The published all_rational lineup seats five copies of the project's Bayesian agent; all_oracle is the same decision machinery shown every sheet, and is the ceiling. This sweep changes exactly one thing — the deadline, from 4 rounds to 256 — on the same frozen 24-parameter-set bank and the same 24 × 5 = 120-episode grid per cell. It is the control that decides whether the rational table's closure failure is a clock problem.

It is not a clock problem. Quadrupling the deadline and then quadrupling it again leaves the Bayesian table where it started: deal rate 0.233 [0.142, 0.325] at four rounds and 0.250 [0.158, 0.350] at sixty-four, with essentially every episode — successful or not — running to its forced final vote. The omniscient lineup closes every game at every deadline. Time is not the scarce resource; the agreement rule and the information the agents hold are.

The Bayesian table across the horizon

cell	deadline (rounds)	episodes	deal rate	normalized score	rounds to agreement	utilitarian welfare	belief accuracy accept-set F1, time-mean	episode pages
`all_rational_r4`	4	120	0.233 [0.142, 0.325]	0.195 [0.116, 0.279]	4.96 [4.86, 5.00]	45.4 [25.7, 67.2]	0.210 [0.191, 0.230]	10 pages
`all_rational_r8`	8	120	0.267 [0.150, 0.383]	0.230 [0.127, 0.343]	8.97 [8.90, 9.00]	55.6 [28.5, 87.9]	0.228 [0.206, 0.252]	no per-episode viewer published
`all_rational_r16`	16	120	0.208 [0.117, 0.317]	0.182 [0.097, 0.274]	17.00 [17.00, 17.00]	44.0 [21.7, 71.1]	0.241 [0.217, 0.266]	no per-episode viewer published
`all_rational_r32`	32	120	0.208 [0.117, 0.317]	0.178 [0.094, 0.268]	32.96 [32.84, 33.00]	43.3 [20.5, 70.4]	0.244 [0.220, 0.269]	1 page
`all_rational_r64`	64	120	0.250 [0.158, 0.350]	0.207 [0.127, 0.287]	64.97 [64.88, 65.00]	48.0 [27.9, 71.3]	0.241 [0.218, 0.264]	no per-episode viewer published

Intervals are 95% instance-clustered bootstraps over the 24 parameter sets, each set's five seeds resampled together. Rounds to agreement is defined only on episodes that closed, so its denominator is the deal count rather than 120. A no-deal scores zero in normalized score. The belief accuracy column is the mechanism: how well a seat's posterior predicts which packages its opponents would sign, time-averaged so it is comparable across horizons. It improves out to about sixteen rounds and is then flat, which is why the extra rounds deliver nothing — the posterior stops learning long before the deadline arrives, and without identification there is nothing to concede to.

The omniscient ceiling across the same horizon

cell	deadline (rounds)	episodes	deal rate	normalized score	rounds to agreement	utilitarian welfare	belief accuracy accept-set F1, time-mean	episode pages
`all_oracle_r4`	4	120	1.000 [1.000, 1.000]	0.888 [0.867, 0.910]	1.40 [1.20, 1.63]	193.3 [178.3, 209.3]	1.000 [1.000, 1.000]	6 pages
`all_oracle_r8`	8	120	1.000 [1.000, 1.000]	0.884 [0.860, 0.906]	1.62 [1.27, 2.00]	192.1 [177.8, 207.4]	1.000 [1.000, 1.000]	no per-episode viewer published
`all_oracle_r16`	16	120	1.000 [1.000, 1.000]	0.877 [0.851, 0.903]	1.00 [1.00, 1.00]	191.9 [176.7, 207.9]	1.000 [1.000, 1.000]	no per-episode viewer published
`all_oracle_r32`	32	120	1.000 [1.000, 1.000]	0.899 [0.880, 0.920]	3.42 [2.07, 5.00]	194.6 [179.9, 209.9]	1.000 [1.000, 1.000]	6 pages
`all_oracle_r64`	64	120	1.000 [1.000, 1.000]	0.890 [0.868, 0.912]	5.80 [3.13, 9.00]	193.7 [178.5, 210.0]	1.000 [1.000, 1.000]	no per-episode viewer published
`all_oracle_r128`	128	120	1.000 [1.000, 1.000]	0.884 [0.860, 0.906]	10.62 [5.27, 17.00]	192.1 [177.8, 207.4]	1.000 [1.000, 1.000]	no per-episode viewer published
`all_oracle_r256`	256	120	1.000 [1.000, 1.000]	0.877 [0.851, 0.903]	1.00 [1.00, 1.00]	191.9 [176.7, 207.9]	1.000 [1.000, 1.000]	6 pages

Why the oracle's closing round is not flat, and what that does and does not mean

Deal rate is 1.000 at every deadline, but rounds to agreement is not flat and the outcome aggregates wobble in the third decimal. Neither is noise and neither is a defect: the structure is periodic mod 5. With five rotating proposers, (deadline + 1) mod 5 fixes which seat holds the forced final vote, and that seat's identity decides whether a game closes in round 1 or is rationally ridden to the deadline. Cells sharing a residue therefore land on the same outcomes — two of the three pairs here agree to sixteen digits — and the spread between residues (0.0218 on normalized score) is an order of magnitude larger than the spread within one.

(deadline + 1) mod 5	cells	normalized score	agreement
0	r4, r64	0.888210 / 0.890121	differ by 0.0019
2	r16, r256	0.877028 / 0.877028	identical to 16 digits
3	r32	0.898837	—
4	r8, r128	0.883569 / 0.883569	identical to 16 digits

Residue 2 — where the terminal-node holder supports round-1 agreement in all 120 games — is the residue with no straggler tail at all; the other residues leave 9–12 games per 120 in which the oracle rides to the forced final and strikes the same deal, later, which is why rounds to agreement can differ inside a residue pair whose scores are identical. One such episode is published: this all_oracle_r32 game runs 165 turns before closing, against the five turns a round-1 agreement takes.

The oracle arm is a flat control for aggregates only. Per episode it lands on materially different deals at different deadlines, so it licenses "the ceiling does not move with the horizon" and not "the omniscient table plays the same game at every deadline." The same distinction applies to the anchor: the four-round cells are statistically indistinguishable from the frozen campaign's corresponding arm, never episode-for-episode identical — roughly 3–6% of episodes flip deal/no-deal between machines (7 of 120 in this arm) because near-ties in the seats' dynamic program resolve differently under different float summation orders.

What is not here yet

The sweep is published while its two longest rational cells are being re-run, because the finding does not depend on them — the deal rate is flat from 4 rounds to 64. Their numbers appear here only when the refill lands; a stale cell record is not a result.

all_rational_r128 — preemption destroyed the original run; being re-run by a fill-missing job.
all_rational_r256 — preemption destroyed the original run; being re-run by a fill-missing job, and the cell record on disk predates that refill (its summary is empty).

What is not published here. Every deadline's numbers above are the full 120 episodes, but the per-episode viewers are a representative set, thinned in a size review because this site is at its serving ceiling: the four-round anchor cell, one long-horizon exemplar (all_rational_r32, which still dies at its deadline), and for the omniscient arm one cell per behaviour (r4, the r32 straggler tail, and r256 as the residue-2 cell that closes in round 1 everywhere). Retired as redundant: the all_rational_r8 and all_rational_r16 viewers, which show what r4 and r32 already show, and the all_oracle_r16 viewer, whose cell is digit-identical to the published r256. The complete corpus — every episode of all twelve cells, every turn, every conditioned view — is public in 2026.RA.Pure-Rounds-Sweep.

Everything behind the page

Per-cell summaries and per-episode rows (analysis/)Launcher cell records, one per sweep cell Dataset: 2026.RA.Pure-Rounds-Sweep The W&B grid sweep behind these cells The quorum sweep — the rule, not the clock The agent variants — telling them what you want Dataset: 2026.RA.Quorum-Rounds-Sweep

This sweep is research note 0061 in the ii_mats repository; the mechanism behind the flat line is note 0057 (the Bayesian arm's no-deal rate is a silent information channel) and the two levers that do move closure are notes 0058 and 0059. Provenance: all 12 published cells ran from one code vintage — parent repo 96d83e00, interlens 2a286d8e (interlens 0.1.60), recorded against working trees marked dirty because several lanes were active. Episode pages are rationed against the pages repo's size ceiling — a 64-round episode renders to roughly 40 MB — so the long-horizon cells are represented by their full 120-episode numbers and, where a page was affordable, a handful of exemplars.