Logic

Does a soup assemble features beyond its one-step rungs when the parts are paid? Each run starts from an emerged world under the Metabolism economy, with one assay-only NAND byte and a ladder of nine logic tasks. One arm is paid for every rung, one for XOR and EQU alone, and one for nothing. A labelled substrate: it imports an objective and a primitive.

Substrate: soup imports an objective
Status: finished
Epochs per run: 40,000
Runs finished: 162 / 162
Transition rate: no finished run yet

Findings resting on this sweep: Given a NAND, paid replicators climb every logic task that reads its inputs once, and none that needs one twice negative imports an objective

Transition epoch vs treatment

No finished runs yet.

Time to emergence vs treatment

No run has been observed yet.

Distinct lineages vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

Share of the largest lineage vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

Compressed length of the dominant tape (bytes) vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

Instructions in the dominant tape vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

Compressed length of the largest lineage's tape (bytes) vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

Instructions in the largest lineage's tape vs epoch, per arm of treatment

logic×8×2048×initiator×0×1024×65536
logic×8×xor×2048×initiator×0×1024×65536
logic×8×0×initiator×1024×65536

The pre-registered reading final imports an objective

Every child of every qualifying parent has finished. Each full-ladder child is paired with the unpaid child of the same parent and seed, and for H-stones with the child paid for XOR and EQU alone; all are read over their own samples past a settling window of 1,000 epochs. A child is extinct where its last-decile median share is below 10%, and a pair with an extinct child is in no test. Each test is a one-sided sign test at p < 0.05, re-read with the extinct pairs kept and without the parents the design study piloted (runs 1007, 944, 2577, and 2700). This substrate imports an objective and a primitive, the NAND byte, so rung 4 on Soup stays not shown whatever it reads.

Children per arm, read so far. A deep rung is XOR or EQU held by a tenth of the world for 5 samples running; a stepping stone is OR, ANDN or NOR held first.

Arm	Children	Finished	Settled relapses	Extinct	Capability measured	Complexity survivors	Rises
full	54	54	6	1	53	48	2
deep-only	54	54	0	0	54	54	1
none	54	54	0	0	54	54	1

Hypotheses

H-capability-L, full against none: shown

53 pairs measured on both sides: 53 favour full, 0 none, 0 tie; p = 1.11e-16. With the extinct pairs kept: shown, 54 to 0, p = 5.55e-17. Without the piloted parents: shown, 41 to 0, p = 4.55e-13.

Per-parent agreement

Parent	Favour full	Not both measured
run 944	3	0
run 950	3	0
run 967	3	0
run 991	3	0
run 1007	3	0
run 1029	3	0
run 1087	3	0
run 1089	3	0
run 1103	2	1
run 2568	3	0
run 2577	3	0
run 2590	3	0
run 2654	3	0
run 2676	3	0
run 2700	3	0
run 2771	3	0
run 2802	3	0
run 2862	3	0

H-deep, full against none: refuted

53 pairs measured on both sides: 0 favour full, 0 none, 53 tie. With the extinct pairs kept: refuted, 0 to 0. Without the piloted parents: refuted, 0 to 0.

Per-parent agreement

Parent	Tie	Not both measured
run 944	3	0
run 950	3	0
run 967	3	0
run 991	3	0
run 1007	3	0
run 1029	3	0
run 1087	3	0
run 1089	3	0
run 1103	2	1
run 2568	3	0
run 2577	3	0
run 2590	3	0
run 2654	3	0
run 2676	3	0
run 2700	3	0
run 2771	3	0
run 2802	3	0
run 2862	3	0

H-stones, full against deep-only: refuted

53 pairs measured on both sides: 0 favour full, 0 deep-only, 53 tie. With the extinct pairs kept: refuted, 0 to 0. Without the piloted parents: refuted, 0 to 0.

Per-parent agreement

Parent	Tie	Not both measured
run 944	3	0
run 950	3	0
run 967	3	0
run 991	3	0
run 1007	3	0
run 1029	3	0
run 1087	3	0
run 1089	3	0
run 1103	2	1
run 2568	3	0
run 2577	3	0
run 2590	3	0
run 2654	3	0
run 2676	3	0
run 2700	3	0
run 2771	3	0
run 2802	3	0
run 2862	3	0

H-complexity, full against none: not shown

48 pairs measured on both sides: 2 favour full, 1 none, 45 tie; p = 0.5. With the extinct pairs kept: not shown, 2 to 1, p = 0.5. Without the piloted parents: not shown, 2 to 0, p = 0.25.

Per-parent agreement

Parent	Favour full	Favour none	Tie	Not both measured
run 944	0	1	2	0
run 950	0	0	3	0
run 967	0	0	2	1
run 991	0	0	3	0
run 1007	0	0	3	0
run 1029	2	0	1	0
run 1087	0	0	3	0
run 1089	0	0	3	0
run 1103	0	0	2	1
run 2568	0	0	3	0
run 2577	0	0	3	0
run 2590	0	0	3	0
run 2654	0	0	3	0
run 2676	0	0	3	0
run 2700	0	0	2	1
run 2771	0	0	3	0
run 2802	0	0	0	3
run 2862	0	0	3	0

The pairs

Parent	Seed	Full child	Capability	Deep-only child	Capability	None child	Capability
run 944	2001	run 4681	2	run 4684	0	run 4687	0
run 944	2002	run 4682	4	run 4685	0	run 4688	0
run 944	2003	run 4683	2	run 4686	0	run 4689	0
run 950	2001	run 4690	5	run 4693	0	run 4696	0
run 950	2002	run 4691	5	run 4694	0	run 4697	0
run 950	2003	run 4692	3	run 4695	0	run 4698	0
run 967	2001	run 4699	4	run 4702	0	run 4705	0
run 967	2002	run 4700	3	run 4703	0	run 4706	0
run 967	2003	run 4701	2	run 4704	0	run 4707	0
run 991	2001	run 4708	3	run 4711	0	run 4714	0
run 991	2002	run 4709	1	run 4712	0	run 4715	0
run 991	2003	run 4710	2	run 4713	0	run 4716	0
run 1007	2001	run 4717	4	run 4720	0	run 4723	0
run 1007	2002	run 4718	3	run 4721	0	run 4724	0
run 1007	2003	run 4719	4	run 4722	0	run 4725	0
run 1029	2001	run 4726	4	run 4729	0	run 4732	0
run 1029	2002	run 4727	4	run 4730	0	run 4733	0
run 1029	2003	run 4728	4	run 4731	0	run 4734	0
run 1087	2001	run 4735	4	run 4738	0	run 4741	0
run 1087	2002	run 4736	3	run 4739	0	run 4742	0
run 1087	2003	run 4737	4	run 4740	0	run 4743	0
run 1089	2001	run 4744	5	run 4747	0	run 4750	0
run 1089	2002	run 4745	3	run 4748	0	run 4751	0
run 1089	2003	run 4746	3	run 4749	0	run 4752	0
run 1103	2001	run 4753	4	run 4756	0	run 4759	0
run 1103	2002	run 4754	4	run 4757	0	run 4760	0
run 1103	2003	run 4755 extinct	3	run 4758	0	run 4761	0
run 2568	2001	run 4762	4	run 4765	1	run 4768	1
run 2568	2002	run 4763	4	run 4766	0	run 4769	0
run 2568	2003	run 4764	4	run 4767	0	run 4770	0
run 2577	2001	run 4771	4	run 4774	0	run 4777	0
run 2577	2002	run 4772	2	run 4775	0	run 4778	0
run 2577	2003	run 4773	2	run 4776	0	run 4779	0
run 2590	2001	run 4780	4	run 4783	0	run 4786	0
run 2590	2002	run 4781	6	run 4784	0	run 4787	0
run 2590	2003	run 4782	4	run 4785	0	run 4788	0
run 2654	2001	run 4789	4	run 4792	0	run 4795	0
run 2654	2002	run 4790	3	run 4793	0	run 4796	0
run 2654	2003	run 4791	3	run 4794	0	run 4797	0
run 2676	2001	run 4798	2	run 4801	0	run 4804	0
run 2676	2002	run 4799	4	run 4802	0	run 4805	0
run 2676	2003	run 4800	4	run 4803	0	run 4806	0
run 2700	2001	run 4807	2	run 4810	0	run 4813	0
run 2700	2002	run 4808	3	run 4811	0	run 4814	0
run 2700	2003	run 4809	1	run 4812	0	run 4815	0
run 2771	2001	run 4816	4	run 4819	0	run 4822	0
run 2771	2002	run 4817	4	run 4820	0	run 4823	0
run 2771	2003	run 4818	4	run 4821	0	run 4824	0
run 2802	2001	run 4825	7	run 4828	0	run 4831	0
run 2802	2002	run 4826	4	run 4829	0	run 4832	0
run 2802	2003	run 4827	4	run 4830	0	run 4833	0
run 2862	2001	run 4834	4	run 4837	0	run 4840	0
run 2862	2002	run 4835	4	run 4838	1	run 4841	1
run 2862	2003	run 4836	3	run 4839	0	run 4842	0

The ladder, descriptive only: how many children's worlds held each rung at a share of 10% for 5 samples running, settling window included, and the median first epoch they did.

Rung	Full: children	Full: median first epoch	Deep-only: children	Deep-only: median first epoch	None: children	None: median first epoch
echo	54	20,690	19	22,630	19	22,630
not	52	23,660	0	—	0	—
nand	37	25,680	0	—	0	—
and	14	28,550	0	—	0	—
orn	44	26,420	0	—	0	—
or	23	27,890	0	—	0	—
andn	32	29,810	0	—	0	—
nor	19	33,810	0	—	0	—
xor	0	—	0	—	0	—
equ	0	—	0	—	0	—

Runs

Download CSV

Seed	Treatment	Status	Priority	Epochs done	Transition epoch	Census
2001	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	—	Run
2002	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	14 census only	Run
2003	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	25 census only	Run
2001	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	15 census only	Run
2002	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	23 census only	Run
2003	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	14 census only	Run
2001	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	15 census only	Run
2002	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	23 census only	Run
2003	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	14 census only	Run
2001	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	—	Run
2002	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	—	Run
2003	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	9 census only	Run
2001	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	—	Run
2002	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	17 census only	Run
2003	logic×8×xor×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	—	Run
2001	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	—	Run
2002	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	17 census only	Run
2003	logic×8×0×initiator×1024×65536	finished	40	60,000	— confirmed	—	Run
2001	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	17 census only	Run
2002	logic×8×2048×initiator×0×1024×65536	finished	40	60,000	— confirmed	57 census only	Run