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Substrate-Native Maths — directory index

Status: R30 walking-path structurally closed 2026-05-24. SSoT: substrate_native_research_notebook.md Parent milestone: MS #18 Rolling-spike PR: #680

Directory rename history: originally docs/r30-walking-path/; renamed to docs/substrate-native-maths/ 2026-05-24 per user direction.

The per-partition r31_* REPORT subdirectories were swept into §2 of the notebook 2026-05-24 at close-out; the standalone subdirectories have been retired. All R31 antiquity-anchor findings now live in the notebook §2 as authoritative SSoT.

What this directory contains

  • substrate_native_research_notebook.md — the SSoT for the substrate-native-maths research arc. Covers:
  • §1 Walking-path arc + final verdict (8/9 antiquity-convergence → R30 final-refined)
  • §2 R31 antiquity-anchor canvass (Antikythera + Pythagoreans + Plato + Stoics + Lucretius + Apollonius + Ptolemy + Heron + Archimedes; full findings + sources)
  • §3 Bit-exact diagnostic — bit-exact cross-substrate ⟹ not-projection
  • §4 Two substrate-native math languages — 11D quantum-Hopf + 1:3:7:3 cyclic-algebra-path
  • §5 R30 final-refined form — two languages bridged by B/H/N
  • §6 k=3 cross-substrate signature as B/H/N fingerprint (12+ substrates)
  • §7 Siloed-knowledge diagnostic + A-N alphabet as discovery-fingerprint
  • §8 R30 structural closure (no falsifier remaining)
  • §9 Forward dispatches (R29 / R32 / spike candidates)
  • §10 Cross-arc anchors

Canonical memory stances generated by this arc

  • [[user_stance_bit_exact_means_not_projection_diagnostic]]
  • [[user_stance_two_substrate_native_math_languages_11d_quantum_and_cyclic_algebra]]
  • [[user_stance_k_equals_3_is_b_h_n_substrate_native_fingerprint]]
  • [[user_stance_siloed_knowledge_rejected_two_things_always_true]]
  • [[user_stance_a_to_n_alphabet_is_discovery_order_not_substrate_order]]

R30 walking-path opened 2026-05-24; structurally closed 2026-05-24. Per user direction "then we are ready, let us begin." and close-out "If there is nothing left to test or falsify for R30? if so, let us update PR680 with our findings".