New Arithmetic Regularities of the Standard Genetic Code

The genetic code has been proposed as a place where a sender could leave a message, and three studies have reported exact arithmetic relations in the nucleon numbers of the amino acids it groups (Jestin and Soulé, 2007; shCherbak and Makukov, 2013; Panov and Filatov, 2024). We continue from their leads. If carrying a message was an equal or even the primary function of the code, its design should give up some chemical optimality to carry it, and a sender who wanted the text read would leave a signal in plain sight, as a non-optimality that evolution would otherwise remove. The clearest such place is arginine. Every exchange of two amino acids that would make the code more robust to point mutations breaks at least one published regularity, the six most profitable all move arginine, and seven published regularities together leave only the standard code and its Ile ↔ Leu twin. Arginine is also the only latecomer among the eight amino acids of the strong octet, the other seven being prebiotic; it closes the four-fold sum 333; and its side chain weighs 10² nucleons. We report new findings, each pointing to counting in tens: arginine's side chain of 10 hydrogen atoms and 10² nucleons; the numeral 111 in base 3q − 2 implied by q letters read in triplets, which is base 10 for the four letters of the code; five side chains that are the numeral 111 in the consecutive bases 5 to 9, one step short of base 10; and the synthetase-class grid, whose binary reading with the grid's own signs, 1 and −1, gives five −1, five 1, five −1, five 1, words of five worth −31 and 31, the outer column sums, sign included. A further observation is the approximation 1/α ≈ 3700/27. Under the hypothesis of design the findings read as two signals, the abundance of 37 and arginine, that are themselves pointers to counting in tens and lead to three more, the last a calligram with check sums, together with a key, the proline correction; each pointer uses a different kind of mathematics, in the order of the messages humans have composed for other civilizations. All statistics are collected at the end. Given the freedoms of our search, random codes match the standard code's excess of multiples of 37 in about 1 in 17,000 in partitions defined by the structure of the code; in 630 arbitrary partitions by letter position the standard code shows no excess; repeated in every base from 2 to 80, the same census ranks base 10 first. The grid of synthetase classes, with its three zero middle columns, binary reading, outer sums of 31 and odd-column sums of 37, occurs in about 1 in 12 million random codes, independently of the octets; the chemical pointer to base 10, the ladder of bases together with arginine's side chain of 10 hydrogens and 10² nucleons, in about 1 in 21,000 alphabets of plausible side chains (1 in 420 to 1 in 1050 after allowing for the choice of pattern); and 3700/27 in about 1 in 210 after correction. The three independent tests, of the signal, the side chains and the grid, multiply to about 1 in 9 × 10¹³ to 1 in 2 × 10¹⁴, without correction for the choice of findings reported. Tests outside the code table were negative. Files: the preprint (PDF), its detached signature (.sig) and a reproduction package (scripts, protocols and outputs for every number in the paper). Authorship: the author publishes anonymously. The PDF is signed with an Ed25519 key (OpenSSH format); public key fingerprint SHA256:xtJKKOe1xIP4y+7i1Qhq2SfWtfi+5BdeY3reuAKl0u8. The public key is printed in the preprint.