o1

3,318,465 parameters · 32,512 B constant state (O(1) per token) · Live Online GSSM (ΔW)

• Author: David Tom Foss
• X: https://x.com/fossdt

o1 compresses arbitrary token streams into a fixed 32,512-byte manifold carrier without a growing KV cache, learns continuously online via GSSM plasticity, and routes built-in 16-op algebra plus a cryptographically hash-chained Weltbuch causal graph (48 verified triples).

With 3.32M total parameters, o1 achieves low-perplexity continuous text modeling, 100% 10-way passkey recall out to 2,048 tokens (80% at 8,192) in a 32.5 KB state, and compiles Python skeletons cleanly (48.8% HumanEval / 48.2% MBPP), while full semantic problem-solving (HumanEval/MBPP pass@1 = 0%, GSM8K = 1.52%) remains bounded by 3.32M capacity. Out of the box it provides standalone bilingual conversation and hash-verified Weltbuch causal memory without an external bash/browser tool-call parser.

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Lineage & Foundational Papers

o1 descends directly from two foundational papers by me earlier this year:

1. Geometric State Space Models: Bounded Hyperbolic Recurrence for Language Modeling (June 2026) — https://doi.org/10.13140/RG.2.2.12646.59201
   Introduces the log-complement rapidity recurrence $z_t={\gamma }_t{z}_{t-1}+{\alpha }_t\log (1-{\bar{v}}_t^2)z\_t\; =\; \backslash gamma\_t\; z\_\{t-1\}\; +\; \backslash alpha\_t\; \backslash log(1\; -\; \backslash bar\{v\}\_t^2)$ (GSSM-Selective) whose state $s_t=\sqrt{1-\exp (z_t)}\in [0,1]s\_t\; =\; \backslash sqrt\{1\; -\; \backslash exp(z\_t)\}\; \backslash in\; [0,\; 1]$ is bounded by manifold geometry for all inputs and learned gates without clipping.
2. One Operator, Three Switches: A Kernel Unification of the Linear State-Space Family (July 2026) — https://doi.org/10.13140/RG.2.2.35087.55201
   Establishes the associative affine reproducing-kernel unification (O(log T) prefix scan), position-free (NoPE) length invariance at constant memory, key-conditioned holographic phase binding $S_t={\gamma }_t{S}_{t-1}+u_t{e}^{i{\phi }_t}S\_t\; =\; \backslash gamma\_t\; S\_\{t-1\}\; +\; u\_t\; e^\{i\backslash varphi\_t\}$, and interior-attractor associative recall.

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Verified Benchmarks (o1_genesis vs. Perfected o1)

Benchmark	Split / Setup	o1_genesis (Init)	o1 (Online Perfected)	Notes
Parameters / State	Constant O(1) carrier	3,318,465 / 32,512 B	3,318,465 / 32,512 B	0 added params, 0.0 MB RSS delta
WikiText-2 Test	Static Fresh BPB ↓	7.1341	1.9620	-72.5% BPB
WikiText-2 Test	Static Continuous BPB (PPL) ↓	7.3270 (156,040.1)	2.3223 (44.26)	546,887 crystal tokens, 1 continuous stream
WikiText-2 Test	Causal Online GSSM BPB (PPL) ↓	2.9473 (122.73)	2.5635 (65.61)	2.3846 late 25%, 3,437.3 tok/s
ARC-Easy	Full test (2,376), acc_norm	26.01%	26.43%	52,694 tok/s on M4 MPS
ARC-Challenge	Full test (1,172), acc_norm	24.57%	23.81%	Reported as measured (-0.76%)
HellaSwag	Full val (10,042), acc_norm	25.33%	25.77%	46,979 tok/s
MMLU	Full test (14,042), 0-shot static	24.80%	25.20%	25.08% dev-online
GSM8K	Full test (1,319), greedy EM	0.00% (0/1319)	1.52% (20/1319)	2,878.3 tok/s
HumanEval	Full test (164), syntax / pass@1	0 / 0.0%	80 compiled / 0.0%	Syntax-valid Python bodies
MBPP	Full test (500), syntax / pass@1	0 / 0.0%	241 compiled / 0.0%	Syntax-valid Python functions
NIAH / Passkey	T=128..2048 10-way MC	0% / 0% / 20% / 0%	100% / 100% / 100% / 100%	Greedy EM: 60% / 40% / 40% / 20%
NIAH / Passkey	T=4K / 8K / 16K / 32K MC	0% / 20% / 0% / 0%	20% / 80% / 20% / 0%	32,512 B fixed, 5,005 tok/s at 32K
Symbolic & Identity	16 ops + 5 creator probes + Weltbuch	9/16 ops, 0/5 text	12/16 ops, 5/5 text	Weltbuch valid=True (48 triples)
Apple M4 ANE	direct_private_ane_pingpong	2,930.7 tok/s	3,355.7 tok/s	0 recompiles, cos=0.9975, 2.68 MB SRAM

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Quickstart

pip install -r requirements.txt

# Verify weights, constant 32,512-byte carrier, provenance, and Weltbuch hashes
python3 verify_o1.py

# Interactive German/English terminal chat with live carrier & online GSSM plasticity
python3 chat_o1.py

# OpenAI-compatible HTTP endpoint (/v1/chat/completions, /v1/completions, /v1/weltbuch)
python3 serve_o1.py --port 8000

Chat commands: /reset, /learn on, /learn off, /stats, /save <path>, /exit.

Plugging o1 into a Llama / DeepSeek / OpenAI Harness

Attach o1 as a constant-32,512 B state & Weltbuch causal sidecar around any Llama, DeepSeek, llama.cpp, vLLM, or OpenAI-compatible chat function (or graft O1HiddenStateBridge(host_hidden_size=4096) directly onto PyTorch hidden states):

from o1_native import O1Sidecar

sidecar = O1Sidecar("o1.pt")  # 32,512 B O(1) carrier + online GSSM + Weltbuch

# Augment Llama / DeepSeek chat messages with verified Weltbuch causal memory,
# or route deterministic algebraic organ queries directly in < 2 ms:
result = sidecar.route_or_delegate(
    [{"role": "user", "content": "What follows from Kerr_Resonator?"}],
    host_chat_fn=lambda msgs: your_llama_or_deepseek_client(msgs),
)

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Citation

@misc{foss2026gssm,
  author = {Foss, David Tom},
  title  = {Geometric State Space Models: Bounded Hyperbolic Recurrence for Language Modeling},
  year   = {2026},
  month  = jun,
  doi    = {10.13140/RG.2.2.12646.59201},
  url    = {https://doi.org/10.13140/RG.2.2.12646.59201}
}

@misc{foss2026oneoperator,
  author = {Foss, David Tom},
  title  = {One Operator, Three Switches: A Kernel Unification of the Linear State-Space Family},
  year   = {2026},
  month  = jul,
  doi    = {10.13140/RG.2.2.35087.55201},
  url    = {https://doi.org/10.13140/RG.2.2.35087.55201}
}