diff --git a/experiments/ramanujan_28/submission/NOTATION_AND_BORROWED_TERMINOLOGY.md b/experiments/ramanujan_28/submission/NOTATION_AND_BORROWED_TERMINOLOGY.md new file mode 100644 index 0000000..f4ea030 --- /dev/null +++ b/experiments/ramanujan_28/submission/NOTATION_AND_BORROWED_TERMINOLOGY.md @@ -0,0 +1,98 @@ +# Notation, invented terminology, and borrowed words + +## Why this document exists + +This work crosses several fields, and its vocabulary was assembled accordingly. +Some names are invented; others are borrowed from unrelated disciplines because +they were short and evocative, and then given a purely mathematical meaning. + +That borrowing creates a specific hazard. A reader who knows the source field +may read a term as a claim about that field. **Several terms used across this +programme are borrowed from molecular biology and genetics. No claim about +biology, genetics, or any physical or biochemical system is made anywhere in +this work.** Every object named below is defined entirely by its equations, and +those equations are the only content. + +If a term looks like it is asserting something about the natural world, it is +not. Read the definition, not the word. + +--- + +## Part 1 — Terms used in this submission + +These are grounded in `solution.tex` and the certificate scripts, and are the +ones an evaluator of Problem 2.8 will actually meet. + +| Term | Meaning here | Ordinary meaning it may collide with | +|---|---|---| +| **seed**, **seed row** | The two official integer initial-condition rows `A_0`, `A_1` of the recurrence. Nothing grows; "seed" only marks where the iteration starts. | Botany; also "seed" in cryptography/RNG, which is closer but still not this. | +| **jet** | Truncated local expansion data of a function at a point — the standard differential-geometry sense (an equivalence class of functions agreeing to finite order). | Aviation; fluid jets; the physics "jet" of particles. None apply. | +| **carrier** | The vector space or module on which an operator or representation acts — the object that *carries* the structure. Standard representation-theory usage. | **Genetics: a carrier of an allele.** Not intended, not implied. | +| **mutation**, **mutant** | Software *mutation testing*: deliberately corrupting a constant to confirm a passing check is capable of failing. E.g. changing `64R-44` to `64R-43` must produce an `AssertionError`. | **Genetic mutation.** Entirely unrelated. The "mutant" is a modified copy of a Python file. | +| **deformation**, **deformed family** | Replacing the constant `R` by a free variable `r = 1/x`, giving a one-parameter analytic family that specialises to the official matrix at `x_0 = 1/R`. Standard deformation-theory usage. | Materials science. | +| **compact form** | A short generating expression (Pascal rows `b_0..b_3`, the row `C(x)`, constants `A, B, S`) that reproduces the large official integer data exactly. A re-encoding, not an approximation. | "Compact" in topology — unrelated here. | +| **certificate** | An executable script whose assertions, if they all pass, witness a stated mathematical fact. | Cryptographic certificates; academic certificates. | +| **red case**, **negative control** | A deliberately false input included to prove the check can fail. Borrowed from experimental science, and used in the same spirit. | — | +| **authority tag** | A per-claim label recording *how* a statement is known: `EXACT` (integer/rational arithmetic), `NUMERICAL WITNESS` (high-precision identification, not proof), `LITERATURE` (cited, not re-proved). | — | + +### On `EXACT` versus `NUMERICAL WITNESS` + +This distinction is load-bearing and is not merely stylistic. `EXACT` means the +statement is closed under exact arithmetic with no floating point anywhere. +`NUMERICAL WITNESS` means a quantity was *identified* to some number of digits — +strong evidence, **not** a proof. The submission's main claim rests only on +`EXACT` and `LITERATURE` items; numerical enclosures appear as corroboration and +are never used as premises. + +--- + +## Part 2 — Borrowed words from biology, used in the wider programme + +These do **not** appear in the Problem 2.8 submission, but they appear in +adjacent repositories that an evaluator may encounter. They are the terms most +likely to be misread as biological claims. + +> **Reconstructed from working notes — the author should confirm each definition +> before this document is circulated.** + +| Term | Meaning in this work | Source field | Explicitly NOT a claim about | +|---|---|---|---| +| **hachimoji** | A base-8 encoding/decoding scheme (a codec) used to render algebraic invariants as short strings. The name was taken purely because the source system has eight symbols. | Benner et al.'s *hachimoji DNA*, a synthetic 8-letter genetic alphabet (Japanese 八文字, "eight letters"). | DNA, nucleotides, synthetic biology, base pairing, or any biochemical system. It is an integer-encoding convention and nothing else. | +| **scar** (as in `SCAR-013`) | A registry entry recording a route that has been *proved impossible*, together with its witness and a redirect to a live route. A permanent mark left by a closed-off attempt. | **CRISPR / molecular cloning:** a "scar" is residual sequence left after an editing or ligation step. | Gene editing, CRISPR, recombination, or any laboratory procedure. | +| **scar-map** | A tabulated collection of such exclusion records (e.g. the `Δ₇` scar-map). | as above | as above | +| **strand**, **braid** | Strands of a mathematical *braid group* `B_n` — topological curves in a cylinder, and their linear representations (Burau, Lawrence–Krammer–Bigelow). | DNA strands, double helix. | DNA, chromosomes, or any molecular structure. The braid group is a purely topological/algebraic object. | +| **chirality**, **chiral** | Handedness — the orientation or sign convention of a basis or lookup table. | Chemistry (stereochemistry), particle physics. | Molecular handedness or any chemical claim. | +| **codebook** | An information-theoretic dictionary mapping objects to short canonical labels. | Coding theory (correct source); also espionage. | — | + +### The general rule + +Where a borrowed word could be read as a claim about a natural system, it is +being used **metaphorically for structure only**. The mathematics is defined by +its equations; the name is a label chosen for brevity, and carries none of the +source field's content, mechanisms, or empirical commitments. + +--- + +## Part 3 — Why the vocabulary is like this, stated plainly + +The programme spans modular forms, hypergeometric series, braid representations, +formal verification, and computational infrastructure. Working across that range +produces a lot of objects that need names faster than the literature supplies +them. Borrowing a short, memorable word from an unrelated field is efficient for +a solo author and costly for a reader — the cost only becomes visible when the +work is read by someone fluent in the source field. + +This document is the correction. It is not an apology for the naming; it is a +key, so that no reader has to guess whether a biological word implies a +biological claim. It does not. + +## Part 4 — Reading rule for evaluators + +1. Every mathematical object is defined by displayed equations. If a name and an + equation disagree, the equation governs. +2. No statement in this work is a claim about genetics, molecular biology, + chemistry, or any physical system. +3. Where a term is borrowed, Part 1 or Part 2 gives the intended meaning and the + collision it may cause. +4. The distinction between `EXACT`, `NUMERICAL WITNESS`, and `LITERATURE` is + substantive; see Part 1.