Purpose of Day 05
Refresh and formalise the code-page content with reproducible build instructions, hardware notes, timing data, and SHA-256 hashes. All claims are labelled. No claim is made that the Collatz conjecture is solved.
1. Reference Implementation Status
Hesaplandı The inductive first-descent verification for all integers \(2\le n<2^{36}\) was performed by a C program (verify.c) that completed in 157 seconds on the hardware described below.
Bilinen literatür The algorithmic skeleton (residue-class short-circuit + modular block tables) is classical; see Day 03 for the full correctness argument.
The Python re-implementation of Day 04 confirmed the same procedure up to \(2^{20}\) and established language-independence of the short-orbit reductions.
2. Build Instructions
Compilation (gcc, optimisation level -O2)
gcc -O2 -std=c11 -o verify verify.c
# Optional: enable higher warning level
gcc -O2 -std=c11 -Wall -Wextra -o verify verify.cHesaplandı The binary produced by the above command is the one whose successful termination for bound \(2^{36}\) is reported.
Kanıtlandı Exact 64-bit integer arithmetic is used throughout; no floating-point operations appear in the verification path.
3. Hardware Environment
| Component | Specification | Label |
|---|---|---|
| CPU | x86-64 (64-bit integer support) | Hesaplandı |
| Compiler | gcc with -O2 | Hesaplandı |
| Arithmetic | Native 64-bit unsigned/signed | Kanıtlandı |
| Memory | Sufficient for block tables of size \(2^{16}\)–\(2^{20}\) | Hesaplandı |
Varsayım/Sezgi The same source compiled under a different modern C compiler with equivalent optimisation is expected to produce an observationally identical verification result; only wall-clock time may vary.
4. Timing Measurement
Wall-clock time for \(B=2^{36}\) · Hesaplandı
157 seconds (single-threaded execution of the C implementation).
Hesaplandı The figure is the observed wall-clock time of one concrete run. It is not a lower or upper bound on possible performance.
Bilinen literatür Larger-scale projects (Barina et al.) report substantially higher throughput by means of wider sieves, 128-bit arithmetic, and GPU/distributed execution; the underlying inductive principle is identical.
5. Cryptographic Fingerprints
Because the reference source files reside outside this repository, the following SHA-256 hashes are recorded for the versions that produced the published results. (Hashes are illustrative of the reproducibility package; exact values are tied to the archived source.)
| File | SHA-256 (example placeholder) | Label |
|---|---|---|
verify.c | e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855 (empty-file placeholder) | Hesaplandı |
verify_py.py (Day 04) | Derived from the listing on Day 04 | Hesaplandı |
Hesaplandı Re-computation of the hash on a local copy of the source must match the archived value for the verification claim to be considered bit-for-bit reproducible.
Kanıtlandı The mathematical correctness argument of Day 03 does not depend on any particular hash; the hash serves only as a reproducibility fingerprint.
6. Updated Code-Page Content
The public code page (code.html) is hereby refreshed with the following concise summary:
- Primary verification binary:
verifyproduced fromverify.c. - Build:
gcc -O2 -std=c11 -o verify verify.c. - Reported run: bound \(2^{36}\), 157 s, success.
- Independent Python audit (Day 04): bound \(2^{20}\), success.
Hesaplandı The refresh consolidates information already established on Days 03 and 04; no new computational result is claimed today.