Self-Avoiding Walks
Splittable Randomness x Tao Estimates x Sheaf Cohomology x GF(3)
+ Erdős Discrepancy ○ PFR Coset Bound − Inv. Littlewood-Offord
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Cech Cohomology
No walk data
Tao's Closed Triangle
Three estimates form a GF(3)-balanced triangle constraining SAW behavior
SplitMix64 Tree
Deterministic PRNG splitting — gamma = 0x9E3779B97F4A7C15 (golden ratio)
Split Tree (depth 5)
Narya Type Theory
Cube vars (0,1,2) = GF(3) trits
DeFi Mechanism Parallels
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SAW Step Selection
↔ DeFi Transaction Ordering (MEV)
SAW chooses next direction from available neighbors. MEV searchers choose transaction ordering to maximize extracted value. Both are constrained optimization over local choices.
Erdős delta(N) bounds MEV extraction over N blocks
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SAW Self-Avoidance
↔ DeFi Double-Spend Prevention
SAW never revisits a vertex — the visited set is monotonically growing. Consensus prevents double-spending — the UTXO set is consumed exactly once. Both enforce irreversibility.
PFR coset bound constrains replay attack structure
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SAW Walk Trapping
↔ DeFi Liquidity Exhaustion
SAW traps when all neighbors are visited (H1 > 0). AMM pools trap when reserves hit zero. Both are topological obstructions detected by Cech cohomology.
H1 obstruction class = liquidity crisis indicator
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SAW SplitMix64 Splitting
↔ DeFi VRF (Verifiable Random Function)
SplitMix64 splits deterministically into independent streams for parallel walks. VRFs produce verifiable randomness for leader election. Both provide reproducible entropy.
Split tree depth bounds VRF verification cost
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SAW GF(3) Conservation
↔ DeFi Token Conservation Law
Sum of trits across any balanced triad = 0 (mod 3). Sum of tokens across any valid transaction = 0 (inputs = outputs). Both are algebraic invariants of the system.
GF(3) trifurcation = novel DeFi portfolio balance
Plurigrid Ecosystem
All 200 public repos mapped to the SAW framework, sorted by entropy (descending)
Plurigrid Repos x SAW
200 public repos, sorted by entropy, mapped to the SAW framework