paper/README.md

paper

Universal Construction and Exact Self-Reproduction in Ternary McCulloch–Pitts Networks. The manuscript and the records of the runs it reports.

universal_construction_ternary.tex    source
universal_construction_ternary.pdf    typeset
runs/                                 the record written by each command

What each command establishes

Each command is python src/<file>.py <command> and writes its record to runs/; paper.py rocq needs Rocq 9.1 with the opam packages coq-coquelicot and coq-interval, and ocamlfind, on the PATH; the development was checked on OCaml 4.14.2 with these versions:

opam install rocq-core.9.1.1 rocq-stdlib.9.2.0 coq-coquelicot.3.4.5 coq-interval.4.11.4 \
  rocq-mathcomp-ssreflect.2.4.0 coq-flocq.4.2.2 rocq-bignums.9.0.0+rocq9.1 ocamlfind.1.9.8

Command	Record	Establishes
host.py	—	the host family H_A, the serialization sigma and its inverse, the device, the constructor P and the program P*, and the evaluators
paper.py host-family	paper_host_family.json	one step of H_A against SUBLEQ_A for A = 3 to 12, on the evaluator in C
paper.py host-fold	paper_host_fold.json	the folded host family, depth 11, against SUBLEQ_A for A = 3 to 12
paper.py stats	paper_stats.json	unit counts, levelization sizes, fan-in
paper.py verify	paper_verify.json	codec, framing, serialization, datapath, levelization
paper.py runs	paper_runs_*.json	self-description, three generations, lockstep
paper.py codec	paper_codec.json	the recipe codec at every boundary of the token format
paper.py optimal	paper_optimal.json	the length bound is optimal on run-free strings
paper.py steps	paper_steps.json	the closed forms for the step counts
paper.py device	paper_device.json	the device against its definition
paper.py host	paper_host.json	the reference machine against its definition
paper.py lev	paper_lev.json	the levelization against gate-by-gate evaluation
paper.py framing	paper_framing.json	ser injective, inst partial and inverse
paper.py ternarity	paper_ternarity.json	no ternary unit computes the branch predicate
paper.py environment	paper_environment.json	the cost of the environment against the cost of the network
paper.py sigma	—	sigma is a function, injective, and inverted by the parser
paper.py family	paper_runs_family.json	the constructor emits all 29 machines
paper.py family-gate	paper_runs_family_gate.json	four of them on the netlist of sigma
paper.py c	paper_c_evaluator.json	the host on the evaluator in C, src/netlist_eval.c
paper.py throughput	paper_throughput.json	the rate of each evaluator
paper.py rocq	paper_rocq.json	the Rocq development of rocq/, its assumptions, the host family extracted from it for A = 8, 9, 10 against sigma(N_host) and the generator, the stored host extracted for A = 8, 9 against the image twohead.py stored builds, the memory images of P and P*, and the ring netlist extracted for three members
twohead.py organism	paper_twohead.json	the organism on the ring machine M_{3,160,3200}, six generations with the copies and the period (organism run --generations 6 --S 160 --L 3200); organism rocq writes rocq/Organism.v
twohead.py net	paper_twohead_net.json	the netlist N_{K,S,L} against the machine on random states of three members (net check), one generation of the organism on it in C beside the machine (net lockstep), the netlists extracted from Rocq (net extract), and the rows of its levelization with the noise a generation of the stored host survives (net lev)
twohead.py stored	paper_stored_host.json	the host compiled into records of the ring machine: one pass against the host's step and its device on random states (stored check), the startup, step, device and hand-over records on decision diagrams (stored symbolic), and six generations in C in a ring of three banks (stored run 6); --width A checks H_A in place of H_8, and stored widths tabulates A = 8 to 12
noise.py host	paper_noise_*.json	the margin, the profile bound in sum and product form, read noise, the deviation curve, the exact Poisson intervals of the measured rates (host intervals), weight error with leakage, the active-input counts of the orbit certificate, and the steps in which some row fails against the product form b' with the fraction the state masks (host masked)
noise.py amplified	paper_redundant_*.json	the amplified host N_3: one step on replicated states, the margin 3/2, exact self-reproduction in C, the run under noise, the deviation curve and its bound by layer, the failure rate of the state read by majority and the restoration bound, computed by src/restore_bound.c
independent.py	independent_*.json	code written from the paper's definitions alone: H_A rebuilt from Construction 5.8 for A = 3 to 12, Lev(N_host) from sigma and the measurements of Section 8.1 and Appendix E with the noise simulator src/nsim.c

Rebuild the typeset paper with any TeX installation:

tectonic -X compile universal_construction_ternary.tex