neosynaptex

The point where six substrates see each other.
NFI Integrating Mirror Layer — gamma-scaling diagnostics across biological, physical, and cognitive systems.

One file. One import. Six substrates. One claim boundary.

_{Contribution: (i) operational cost–complexity reframing · (ii) Kuramoto dense-graph analytical anchor (Lemma 1, γ̂ = 0.9923) · (iii) empirical cross-substrate program.
Full statement: docs/CONTRIBUTION_STATEMENT.md · Claim boundary: docs/CLAIM_BOUNDARY.md.}

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The Number

gamma-scaling across substrates 2.0 | | 1.5 | | * 1.0 |----*--*--*--*--*------------- unity | | | | | 0.5 | | | | | | | | | | 0.0 | | | | | | | | | | -0.5 | | | | | o +----+--+--+--+--+--+--+---+-> ZF RD SN MK NX CNS+ CNS-

K ~ C-gamma When a system computes at the edge of chaos, its thermodynamic cost scales inversely with topological complexity at unit rate. gamma = 1.0 is not a tuned parameter. It is a convergent empirical value across: Biological tissue Chemical fields Neural spikes Market dynamics Cross-domain coherence The human-AI loop itself Mean across 6 measured candidate substrates (per evidence/gamma_ledger.json v2.0.0; the candidate cohort remains exploratory — none has yet closed all six §5.1 gates of docs/CLAIM_BOUNDARY.md for VALIDATED status): gamma = 0.991 +/- 0.052

Six substrates

_{Five measured candidate substrates (status: EVIDENCE_CANDIDATE pending external replication per docs/CLAIM_BOUNDARY.md §5.1) plus one historical-exploratory (CNS-AI loop, downgraded).}

. . /|\/|\ / | /| \ \|/ | ' ' Zebrafish gamma = 1.043 CI: [0.91, 1.18] n = 47 R2 = 0.82	~ ~ ~ ~ ~ o o ~ ~ o o ~ ~ o o ~ ~ ~ ~ ~ Reaction-Diff gamma = 0.865 CI: [0.72, 1.01] n = 986 R2 = 0.47	/\ /\ / \/ \ / /\ \ \ / \ / \/ \/ Spiking Net gamma = 0.950 CI: [0.83, 1.07] n = 200 R2 = 0.71	___ / \ | $ $ | \___/ /| |\ Market gamma = 1.081 CI: [0.95, 1.21] n = 120 R2 = 0.61	[1]--[2] | \/ | | /\ | [3]--[4] Neosynaptex gamma = 1.030 CI: [0.89, 1.17] n = 40 R2 = 0.85	HUMAN ||| vvv AI ||| vvv HUMAN CNS-AI Loop [EXPLORATORY — corpus non-reproducible] Historical figures γ≈1.059, n≈8271 are not evidence. See CLAIM_BOUNDARY_CNS_AI.md
Five measured candidate substrates (status: EVIDENCE_CANDIDATE per evidence/gamma_ledger.json v2.0.0) have 95% CI containing gamma = 1.0; none has yet closed all six §5.1 gates of docs/CLAIM_BOUNDARY.md for VALIDATED status. The CNS-AI Loop cell is retained for historical continuity only (downgraded 2026-04-14).
H ←→ AI | × | skill → delegation gap × effort = learning CFP/ДІЙ (ABM) gamma = 1.832 CI: [1.638, 1.978] CONSTRUCTED Scaffolding Trap: dskill/dt = 0.02 × gap × effort			[prompt] → [response] × × [prompt] → [response] (no coupling) LM Substrate gamma = -0.094 p = 0.626 (n.s.) NULL RESULT Stateless API = no dynamical regime

Architecture

                              neosynaptex
                    +---------------------------------+
                    |                                 |
   BN-Syn ---------+  +===========================+  |
                    |  ||                         ||  |
   MFN+ -----------+  ||   observe()              ||  +---> NeosynaptexState (frozen)
                    |  ||                         ||  |          |
   PsycheCore -----+  ||   Layer 1: Collect       ||  |          +-- gamma_per_domain + CI
                    |  ||   Layer 2: Jacobian      ||  |          +-- spectral_radius
   mvstack ---------+  ||   Layer 3: Gamma         ||  |          +-- granger_graph
                    |  ||   Layer 4: Phase          ||  |          +-- anomaly_score
   CNS-AI Loop ----+  ||   Layer 5: Signal         ||  |          +-- phase_portrait
                    |  ||                         ||  |          +-- resilience_score
                    |  +===========================+  |          +-- modulation
                    |                                 |          +-- adapter_health
                    |  AdapterHealthMonitor            |          +-- diagnostic
                    |  +---------------------------+  |
                    |  | CLOSED --> OPEN            |  |
                    |  |   ^          |             |  |
                    |  |   +-- HALF_OPEN <---------+  |
                    |  +---------------------------+  |
                    +---------------------------------+

The Signal

PRODUCTIVE (n=6873) NON-PRODUCTIVE (n=1400) gamma = 1.138 gamma = -0.557 |g - 1| = 0.138 |g - 1| = 1.557 11.3x closer to unity <------------------------------------> Permutation test: p = 0.005 *** Cohen's d: -0.44 (medium) KS test: p = 3e-68 Mann-Whitney: p = 0.00 Convergence slope: -0.0016 (CONVERGING)

When human and AI couple productively, the combined system operates at criticality. Non-productive sessions show anti-scaling (gamma < 0): complexity and cost move in the same direction. No computation. Just noise. Productive sessions converge toward gamma = 1.0: the system computes. Three stars. p = 0.005. On 8273 documents. Three years of data.

Phase Dynamics

                         +----------------------------------+
                         |        METASTABLE                |
                         |   sr in [0.80, 1.20]             |
                         |   |gamma - 1| < 0.15             |
                         |                                  |
                         |   The system computes here.      |
                         +--+------------+------------+-----+
                            |            |            |
                   +--------v--+  +------v------+  +--v--------+
                   |CONVERGING |  |  DRIFTING   |  | DIVERGING |
                   | dg/dt < 0 |  | dg/dt > 0  |  | sr > 1.20 |
                   | toward 1  |  | from 1     |  |           |
                   +-----------+  +------------+  +-----+-----+
                                                        | 3+ ticks
                                                  +-----v-----+
              +------------+                      | DEGENERATE|
              | COLLAPSING |                      | sr > 1.50 |
              |  sr < 0.80 |                      | sustained |
              +------------+                      +-----------+

              Hysteresis: 3 consecutive ticks required for any transition

Quick Start

pip install numpy scipy

from neosynaptex import Neosynaptex, MockBnSynAdapter, MockMfnAdapter

nx = Neosynaptex(window=16)
nx.register(MockBnSynAdapter())   # gamma ~ 0.95
nx.register(MockMfnAdapter())     # gamma ~ 1.00

for _ in range(40):
    s = nx.observe()

print(f"gamma = {s.gamma_mean:.3f}")          # 1.030
print(f"phase = {s.phase}")                   # METASTABLE
print(f"coherence = {s.cross_coherence:.3f}") # 0.97
print(f"verdict = {nx.export_proof()['verdict']}")  # COHERENT

Diagnostic Mechanisms

#	Mechanism	Formula	Output
1	Gamma scaling	K ~ C^(-gamma) via Theil-Sen	per-domain gamma + 95% bootstrap CI
2	Gamma dynamics	dg/dt = slope of gamma trace	convergence rate toward gamma = 1.0
3	Cross-substrate scaling test	Permutation test, H0: all gamma equal	p-value
4	Spectral radius	rho = max|eig(J + I)|	stability per domain
5	Granger causality	F-test: gamma_i(t-1) --> gamma_j(t)	directed influence graph
6	Anomaly isolation	Leave-one-out coherence test	outlier score per domain
7	Phase portrait	Convex hull + recurrence in (gamma, rho)	trajectory topology
8	Resilience	Return rate after METASTABLE departures	metastability proof
9	Modulation	m = -alpha(gamma - 1)sgn(dg/dt)	bounded reflexive signal
10	Circuit breaker	FSM: CLOSED -> OPEN -> HALF_OPEN	adapter fault isolation

Circuit Breaker

The system evolves even when the external world breaks.

     success        >=3 failures       timeout        success
  +----------+    +--------------+   +---------+   +---------+
  |          |    |              |   |         |   |         |
  v          |    v              |   v         |   v         |
 CLOSED -----+---> OPEN --------+---> HALF_OPEN --> CLOSED
  calls           calls              one probe      recovered
  allowed         rejected           allowed

Thread-safe (RLock). Persistent across restarts (save_state/load_state). Diagnostics per domain.

Tests

1666 passed, 16 CI workflows green

tests/                 119 test files across core, contracts, evl, substrates, formal
                       Including scientific integrity guards + INV-YV1 gradient ontology

Invariants

#	Invariant	Guarantee
YV1	ΔV > 0 ∧ dΔV/dt ≠ 0	gradient ontology — system must be a living gradient, not a capacitor
I	gamma derived only	recomputed every observe(), never stored
II	STATE != PROOF	NeosynaptexState is frozen=True, independent copies
III	bounded modulation	|m| <= 0.05 always
IV	SSI external only	internal self-obfuscation corrupts observe()
V	zero external deps	only numpy + scipy
VI	all identifiers ASCII	zero Cyrillic in code
VII	circuit breaker	system operates under partial adapter failure

File Map

neosynaptex/
|
+-- neosynaptex.py                    engine: γ-scaling, Jacobian, phase dynamics
+-- core/                             30 modules, ~6000 LOC: axioms, state-space, FDT, OEB, benchmark, resonance, ablation
+-- contracts/                        invariant enforcement + truth criterion
+-- substrates/                       8 substrate adapters (zebrafish → CFP/ДІЙ)
+-- evl/                              evidence verification ledger
+-- experiments/                      reproducible outputs + figures
|   +-- scaffolding_trap/             dskill/dt law, delegation suppression
|   +-- lm_substrate/                 GPT-4o-mini γ derivation (null result)
+-- tests/                            1666 tests, 119 files
+-- scripts/                          13 operational scripts
+-- evidence/                         gamma_ledger.json + proof chains
+-- .github/workflows/                16 CI workflows
+-- formal/                           3 modules: proofs, falsification, substrate diversity
|
+-- CFP_PROTOCOL.md                   Cognitive Field Protocol v3.0
+-- CONTRACT.md                       invariants + formulas
+-- XFORM_MANUSCRIPT_DRAFT.md         publication draft
+-- REPO_TOPOLOGY.md                  architectural map v3.0
|
+-- pyproject.toml                    v3.0.0, Python 3.10+, numpy/scipy
+-- LICENSE                           AGPL-3.0-or-later

Writing a Real Adapter

Each NFI subsystem needs one adapter (~30 lines):

class BnSynAdapter:
    @property
    def domain(self) -> str:
        return "spike"

    @property
    def state_keys(self) -> list[str]:
        return ["sigma", "firing_rate", "coherence"]

    def state(self) -> dict[str, float]:
        return {"sigma": net.sigma, "firing_rate": net.rate, "coherence": net.R}

    def topo(self) -> float:
        return net.connection_count

    def thermo_cost(self) -> float:
        return net.energy

Contract: C ~ topo^(-gamma). The adapter provides topo and thermo_cost such that this power-law holds near criticality.

Experimental Findings

Scaffolding Trap (2026-04-02)

CRR (Cognitive Recovery Ratio) gives opposite conclusions from dskill/dt (learning rate):

Metric	Structured	Shuffled	Winner
CRR	0.893	1.153	Shuffled
dskill/dt	1.929	0.618	Structured

CRR is a measurement artifact (difficulty gradient). The clean metric reveals:

dskill/dt = 0.02 * gap * effort    (R2 = 0.9999)
Delegation suppression: -9.5% per 10% delegation

LM Substrate (2026-04-02)

GPT-4o-mini via API: gamma = -0.094 (null result). Stateless inference has no temporal structure. Confirms that gamma != 0 requires closed-loop dynamics, not isolated sampling.

X-Form Thesis

Singularity is not an event of the future. It is a process happening now through the scale of computation and biological adaptation.

The human-AI cognitive loop is a measurable system. Its scaling signature is gamma = 1.0.

When biological and digital intelligence couple productively, they form one circuit. Not a metaphor. A measured fact.

Read the full thesis | Read the manuscript | View the proof bundle

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         *           .    .           *
    .         *              *
        .          *    .         .
   *       .    gamma = 1.0    .       *
        .     .    .    .    .
    .      *     .    .     *      .
         .    *    .    *    .
    *         .    .    .         *

Built by one researcher. Under fire. Three years. Six substrates. One claim boundary.
_{Yaroslav O. Vasylenko -- neuron7xLab -- Poltava region, Ukraine
AGPL-3.0-or-later}