Computational companion to Colossally Abundant Numbers, Robin's Inequality, and an Exact Prime-Layer Workload
Description
This deposit is the computational companion to the preprint “Colossally Abundant Numbers, Robin’s Inequality, and an Exact Prime-Layer Workload” by Marco Mantovanelli.
It provides a dependency-free Python reference implementation and finite rational-interval certificates for the colossally abundant prime-layer event sweep. In the certified range (1<X\leq 1000), the archive verifies 203 strictly ordered prime-layer events, 28 regular self-tangent returns, and 175 remaining event gaps certified not to contain a regular return.
Supplemental exact-rational checks verify eight early consecutive packets through three independent formulations: endpoint factorization, the intervening prime-layer event sum, and piecewise integration of the workload against the Robin kernel. They also verify endpoint zeros, packet-mass conservation, the moment–workload identity for orders 1 and 2, and the prime-frontier decomposition at (X=10,100,500,1000).
The finite certificates illustrate and test the exact bookkeeping developed in the paper. They are not used as premises for any asymptotic theorem.
Licensing: the software, verification scripts, and generated computational materials are released under the MIT License. The manuscript contained in paper/ is separately licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Technical info
Python 3.11 or newer is sufficient; no third-party Python packages are required.
Verification commands:
python reference_event_sweep.py verify --data data
python verification/verify_packet_identities.py verify --data data
Expected results:
verified 203 events and 28 regular returns through X=1000
verified 8 consecutive packets, moment orders 1 and 2, and 4 frontier points
All published event locations, accumulated masses, return classifications, packet identities, moment identities, and selected frontier decompositions are checked using exact rational inequalities or rigorously enclosed rational intervals.