Receipts

Five shapes of receipt.

A receipt is more honest than a benchmark. We publish five formats — energy, epistemic mode, evidence, byte-reproducible routing checkpoint, and byte-reproducible kernel output — all of them in-tree, all of them typed.


01 · The joule receipt

Every call returns its joules.

A metered call doesn’t return a value. It returns a value and what it cost, computed at the call site against a silicon-specific cost model. You know what the pipeline cost before you ship it to a battery-powered drone.

Math-Ground AI · receipt
step 207 / 400
  • RSS safety envelope 37.2 pJ
  • DAM-VLA route 6.2 µs · 4.1 pJ
  • CAD transition (closed) 1.8 ns · 0.2 pJ
  • Diffusion step 11.4 µs · 8.7 pJ
  • Verifier (e-value · accept) 0.8 µs · 0.6 pJ
  • Per-step total 219.7 pJ
total · 400 steps 87.9 J

epistemic_mode from_retrieval
retrieved_at 2026-05-23T14:02:11Z
source example.org/page
valid_time 2026-05-23
scope particular
certainty 0.94
authority_tier 1

02 · The epistemic receipt

Every claim labels its source.

A confident answer about what was true at training cutoff is a different object than a confident answer about what is true now. The substrate enforces the distinction; the verifier rejects time-varying claims asserted from priors.

invariant I13 · mgai-epistemic


03 · The evidence receipt

Verification earns its stop.

Evidence accumulates as an e-value — a non-negative supermartingale. By Ville’s inequality, stopping at the first threshold crossing preserves the type-I error guarantee. Easy claims halt in one step. Hard ones get the full check.

Vovk-Wang 2021 · Ville 1939

E-value accumulating against an accept threshold accept · e = 20 stop 0 evidence step 1 e-value (log) type-I error bound ≤ 1/e

Matryoshka prefix-dim ladder with router-selected rung d SWAP-2C envelope 16 · MCU 32 · drone (long range) 64 · drone 128 · soldier-carried   ← router 256 · industrial robot 384 · AV (full rank)

04 · The routing receipt

Checkpoints that are byte-reproducible.

One adaptor, six SWAP-2C envelopes. The router picks the prefix dimension that meets the query’s spec within the energy budget. The teacher is the cascade replayed as an oracle. Same seed, same file, byte for byte.

dam-router · Matryoshka representation


05 · The reproducibility receipt

Kernel outputs that hash the same on every run.

The 04 receipt commits the routing to be reproducible; this one commits the kernel output. Every Primitive carries an optional output_hash: Option<u64>; consumers compare the hash against a prior run of the same primitive (name × v_class × iters) and either confirm byte-reproducibility (≡), confess divergence (≠), or stay silent (∎ — the substrate hasn’t committed yet).

Inspired by Thinking Machines Lab’s Defeating Nondeterminism in LLM Inference (Horace He, 2025): batch-size variance, not concurrent atomic adds, is the real culprit for LLM nondeterminism. Mathground publishes the hash so the gap is visible from the consumer side, not just the kernel side.

mgai_meter_web::Primitive.output_hash · Connectionism, 2025-09

Three hashed runs of one primitive — ≡ ≡ ≠ ≡ runs of fft_256 (deterministic substrate) run 1 · 0xdeadbeefcafef00d run 2 · 0xdeadbeefcafef00d run 3 · 0xdeadbeefcafef00d run 4 · 0xa1b2c3d4e5f60718 run 5 · 0xdeadbeefcafef00d ≠ at run 4 is the substrate being honest, not lying about joules.

05.5 · Pinned · mgai-meter output

The canonical receipt.

The same JSON the mgai-meter CLI emits, pinned here as what the substrate publishes. Per-tier wall-time, Landauer floor, TDP envelope, apparent impedance — and the cascade ratios that anchor the L0/L1/L2 spread on commodity silicon. The exhibit receipts on this site are produced by the same accounting.

macos/aarch64 32 vCPUs method · tdp estimate landauer floor tdp · 8 W
primitive V-class wall_ns/op E_floor/op E_tdp/op μ apparent
l0_closed::fk_rollout l0 closed 82.75 5.878e-18 J 662.020 nJ 1.13e+11×
l0_retrieved::hashmap_lookup l0 retrieved 8.11 1.469e-18 J 64.872 nJ 4.41e+10×
l0_identifiable::hdc_cleanup l0 identifiable 2793.42 4.592e-16 J 22.347 µJ 4.87e+10×
l1::cited_lookup l1 12.30 2.939e-18 J 98.387 nJ 3.35e+10×
l2::matmul_proxy l2 110991.25 1.505e-15 J 887.930 µJ 5.90e+11×

cascade ratios (wall-time)

  • l1 / l0-closed 0.149×
  • l0-identifiable / l0-closed 33.76×
  • l2 / l0-closed 1,341.24×
  • l2 / l1 9,024.87×
E_measured: null (no live counter on this substrate)
Time and inter-tier cascade ratios are MEASURED. Energy is bounded below by Landauer (kT·ln 2 × bit-op proxy, exact lower bound) and estimated above by TDP (wall_time × assumed_watts, labelled assumption). Absolute joules require a live silicon counter (RAPL, powercap, NVML, or powermetrics with root); when none is available `e_measured_j` is null. The cascade ratios themselves are real on commodity silicon.
Reproduce: download mgai-meter, run mgai-meter --json, compare cascade ratios.

The worked proof

Three solvers. One puzzle. Cryptographic hashes confirm they agree.

The sudoku exhibit runs this end-to-end — constraint-propagating CSP, brute force, and Z3, each emitting a typed receipt with wall time, ops counted, and joules spent.


05 · This session

Your receipts, from this device.

Every exhibit you open writes its receipts to localStorage on this device. Nothing is uploaded; the table below reads what your browser computed against the Landauer floor. Open the FFT, Lorenz, heat, SDF, or particle-filter exhibits in any tab to populate it. Refresh this page after a few seconds to see the totals update.

No receipts on this device yet. Open the exhibits to start.