Invarians

PATTERN REFERENCE

A complementary analytical reference to the panel API: 32 execution contexts (L1 regime × L2 regime × bridge state) anchored to documented historical events. Frequency data derived from backtest and calibration. Not part of the live signed payload (the three primitives are Attestation, Regime, Drift Signal).

The grid below shows the legacy 4-state regimes (S1D1, S1D2, S2D1, S2D2). Since 2026-04-29, the panel API also emits signed regime codes on chains with calibrated lower bounds: S1D2+, S1D2-, S1D2±, S2+D1, S2-D1, S2+D2+, S2+D2-, S2+D2±, S2-D2+, S2-D2-, S2-D2±. The legacy 4 codes remain valid as aliases on chains without lower bounds yet calibrated. See the signed regime codes entry in the glossary for the full grid.

01 Regime Frequency by Chain

Proportion of time each chain spends in each regime, derived from multi-year backtest and calibration data. Calibration status as of April 2026.

S1D1, structural nominal · demand nominal
S1D2, structural nominal · demand elevated
S2D1, structural stress · demand nominal
S2D2, structural stress · demand elevated
pending calibration
Ethereum
95.4%
1.7%
3.0%
backtest 2020–2024
n = 34,697 windows
Polygon
~93%
~2%
~5%
backtest 2020–2023
n = 25,906 windows
Solana
~90%
~5%
~5%
backtest 2021–2024
π partial, pending
Arbitrum
86.1%
13.9%
S2, τ dormant
237 windows · 12 days
π: size+tx only (σ bug)
Base
84.9%
15.1%
S2, 0% nominal
238 windows · 11 days
baselines converging
Optimism
80.7%
19.3%
S2, 0% nominal
238 windows · 11 days
baselines converging
Avalanche
calibration confidence LOW, no BigQuery backtest available
thresholds empirical
backtest pending
02 Pattern Reference, L1 regime × L2 regime × bridge state

Each row is an execution context, a specific combination of L1 regime, L2 regime, and bridge state. Patterns with documented historical events are marked. Frequencies are estimates based on the reference pair Ethereum × Base.

Pattern Frequency Documented events
L1 S1D1× L2 S1D1× BS1
ETH 95.4%  ·  Base 92.4%
joint ≈ 88% (ETH × Base)
— no event documented
L1 S1D1× L2 S1D2× BS1
joint ≈ 7.3% (ETH × Base)
— no event documented
L1 S1D2× L2 S1D1× BS1
ETH 1.7%
joint ≈ 1.6% (ETH × Base)
DeFi Summer  Jun–Sep 2020 NFT Mania  Mar–May 2021
L1 S2D1× L2 S1D1× BS1
ETH 3.0%  ·  Polygon ~5%
joint ≈ 2.8% (ETH × Base)
Ethereum Merge  15 Sep 2022  +18.3h detection Ethereum Shanghai  12 Apr 2023  +22.8h detection Solana outage ×4  Sep 2021 · Jan 2022 · May 2022 · Oct 2022 Polygon Reorg Storm  Feb 2023  157 blocks  +20.1h detection
L1 S1D2× L2 S1D2× BS1
joint ≈ 0.1% (ETH × Base)
Polygon Gas Crisis  May 2021  +3.5h  σ = 1.896
L1 S2D1× L2 S1D2× BS1
joint ≈ 0.2% (ETH × Base)
— no event documented
L1 S2D2× L2 S1D1× BS1
ETH 0.2%
— no event documented
L1 S2D2× L2 S1D2× BS1
≈ 0.015% (ETH × Base)
— no event documented
Pending calibration
L1 any× L2 S2D1× BS1
freq = 0% observed · 237–238 windows Base / Optimism: τ = 1.0000 in all 238 windows of nominal production data (FPR≈0%). A genuine sequencer incident causing block timing anomaly WOULD trigger S2. Failure modes NOT covered by τ (submission delays with regular blocks) are detected by the adapter (publish_latency) and the variable-latency bridge surface (CCTP attestation latency, CCIP sequence advance).
Arbitrum: τ dormant in nominal conditions (max rhythm_ratio 1.03 in 237 windows, threshold 1.15).
L1 any× L2 S2D2× BS1
freq = 0% observed · 237–238 windows Same constraint as S2D1. Requires L2 τ stress, not observed for any current L2 chain.
Structural stress on L2 detected via adapter publish_latency (Phase C), not τ.
L1 any× L2 any× BS2
Q3 2026 Bridge classification on the variable-latency surface (CCIP, CCTP). Both protocols captured per message: CCTP carries the Circle ECDSA signature; CCIP matches source send and destination execute by bytes32 messageId.
Signed regime codes, live since 2026-04-29

The patterns above use the legacy 4-state grid. Since 2026-04-29, chains with calibrated lower bounds also emit signed regime codes that distinguish elevated, depressed, and asymmetric demand, plus signed structure direction:

  • S1D2+, elevated demand (legacy S1D2 alias)
  • S1D2-, depressed demand (sequencer slowing the user side, censorship effect, mempool gel)
  • S1D2±, composition asymmetric (size up + tx down, or vice versa), agentic concentration signature
  • S2+D1, S2-D1, rhythm direction without demand signal
  • S2±D2±, combined structural and demand signed states (12 codes total on L1, 9 on L2)

Signed codes active as of 2026-04-29: ETH, POL on L1 (event-based + statistical lows), ARB, BASE, OP on L2 (multi-dim demand statistical). SOL and AVAX remain on the legacy 4-state grid until July 2026 calibration. See glossary and calibration_log.md Entries #029 to #032 for the full audit trail.

03 Pattern Evolution, Live Observatory

Rolling 30-day regime frequencies, computed continuously from production windows since March 2026. As AI agents adopt the execution context layer at scale, the distribution of execution contexts shifts over time — measurable evidence of agentic infrastructure behavior. We are establishing the baseline now.

loading live frequencies…
L1 frequencies: Ethereum backtest 2020–2024 (34,697 windows) · Polygon backtest 2020–2023 (25,906 windows).
L2 frequencies: production data 2026-03-15→27 (ARB 237 windows · BASE 238 windows · OP 238 windows). Bridge classification scope: variable-latency surfaces (Chainlink CCIP, Circle CCTP), both captured per message (capability_level: per_message_attested). BS1 / BS2 thresholds are preliminary on the per-message latency baseline.
OP Stack chains (Base, Optimism): τ signal structurally blind, 2s fixed block time by protocol design. S2 states unreachable via τ.
Arbitrum: σ dimension excluded from D2 classification (rho_s=0, gas capacity instrumentation). D2 = size>1.20 AND tx>1.10.
Joint frequencies assume chain independence. Reference pair: Ethereum × Base.
Invarians certifies structural regime and bridge state. Event interpretation and execution policy belong to the agent.