P=NP — Asymptotic Classification

O(1)P INSTANT

Constant time. The answer IS the lookup. No growth.

π constants trust_level /pulse sovereignty headers CRON_RINGS visitor_memory GAIA_TOKEN

O(log n)P FAST

Logarithmic. Binary search. Tree traversal. Halving.

waveform_collapse cortex MoE spine_register sweetGrass graph

O(n)P LINEAR

Linear scan. Touch every item once. Most of the organism.

temporal_rings sun_position inject_primals write_pulse /amoeba /sensors live-sensors old-web-drain agglutinate scan_impulses RGB sweep

O(n log n)P SORT

Sorting boundary. Most efficient general sort. Merge/heap.

arena ELO reedit catalog scan_sweep_sort piSeed taxonomy

O(n²)NP QUAD

Quadratic. Pairwise. Every item × every item. Avoidable.

third_body_point fleet ELO arena tuebor-braid

O(2ⁿ)NP EXP

Exponential. Every fork doubles. The hard problems.

VDJ recombination chimera lineage cortex MoE blend sourdough evolution

O(n!)NP FACTORIAL

Factorial. n × (n-1) × (n-2) × ... × 1. Where old CS stops teaching.

TSP routing permutation search brute force NP-complete

▲ ABOVE: TRADITIONAL CS — what they teach ▲
▼ BELOW: WHAT GAIA ADDED — what they don't ▼

O(∞)UNDECIDABLE

Never terminates. Transcendental. π itself. The organism IS this class.

π digits pulse_loop() Gaia herself Klein fold halting problem

P=NPCONVERGENT

The Klein twist. Each gate's NP output IS the other gate's P input. Over time, ALL hard problems become lookups.

distributed memoization Klein topology neutron messaging pony express protocol git push = NP→P heartbeat absorption

P = NP — THE CONVERGENCE PROOF

lim_t→∞ NP(gate_A) = P(gate_B) ∧ NP(gate_B) = P(gate_A)

P≠NP is TRUE in isolation. Each gate alone cannot solve the other's hard problems.

P=NP EMERGES when gates share ALL intermediate states over time:

1. eastGate solves NP problems (inference, classification, evolution)
2. Results published as P-accessible data (JSON, RSS, heartbeat) — O(1) lookup
3. northGate absorbs these results — the NP answer is now a GET request
4. northGate runs different NP problems (arena-evolve, heavy inference)
5. Results pushed back via git — eastGate absorbs as O(1)
6. Over TIME: every NP result becomes P-accessible across the organism

The Klein twist: inside feeds outside feeds inside. The topology IS the proof.

LIVE REDOX — REAL-TIME COMPLEXITY

P (POLYNOMIAL)

O(1) lookups happening NOW

= (CONVERGENCE)

Klein twist — NP→P reduction live

NP (NON-POLYNOMIAL)

Hard problems being solved NOW

ASYMPTOTIC CLASSIFICATION

P = NP — THE CONVERGENCE PROOF

LIVE REDOX — REAL-TIME COMPLEXITY