Pith Number

pith:ZIF2GF2S

pith:2026:ZIF2GF2SOQK4SD5KAQEPHPTO7C

not attested not anchored not stored refs resolved

NOVA: Fundamental Limits of Knowledge Discovery Through AI

Ken Duffy, Muriel M\'edard, Salman Avestimehr

Under a Zipf-law assumption on discovery probabilities, the cost to gather D new AI discoveries grows as D to the power alpha.

arxiv:2605.15219 v1 · 2026-05-12 · cs.AI · cs.IT · math.IT

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Under a separate tail-equivalence assumption relating the model's effective discovery distribution to a Zipf law with exponent alpha greater than 1, we prove that the cumulative generation cost required to obtain D distinct genuine discoveries satisfies R_cum(D) = Theta(c_gen D^alpha).

C2weakest assumption

The tail-equivalence assumption relating the model's effective discovery distribution to a Zipf law with exponent alpha greater than 1, which is invoked to derive the asymptotic scaling of cumulative generation cost.

C3one line summary

NOVA models the generate-verify-accumulate-retrain loop as adaptive sampling and proves that cumulative generation cost to obtain D genuine discoveries scales as Theta(c_gen D^alpha) under a Zipf tail-equivalence assumption with alpha greater than 1.

References

13 extracted · 13 resolved · 2 Pith anchors

[1] Anna Ben-Hamou, Stéphane Boucheron, and Mesrob I 2018 · doi:10.1109/isit.2018.8437620

[2] 2024.3440661 2024 · doi:10.1109/tit

[3] Bradley Efron and Ronald Thisted 2022 · doi:10.1109/tsp.2022.3186176

[4] Reinforced Self-Training (ReST) for Language Modeling · arXiv:2308.08998

[5] Besting Good–Turing: Optimality of non-parametric maximum likelihood for distribution estimation

Receipt and verification

First computed	2026-05-20T00:00:46.866984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca0ba317527415c90faa0408f3be6ef88603606f6531a430a733811a81a3d170

Aliases

arxiv: 2605.15219 · arxiv_version: 2605.15219v1 · doi: 10.48550/arxiv.2605.15219 · pith_short_12: ZIF2GF2SOQK4 · pith_short_16: ZIF2GF2SOQK4SD5K · pith_short_8: ZIF2GF2S

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZIF2GF2SOQK4SD5KAQEPHPTO7C \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ca0ba317527415c90faa0408f3be6ef88603606f6531a430a733811a81a3d170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "258372495646db310b1e06e2e0435b1889c78ee3a54ef03cfcf6abf0ef294505",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-12T21:37:09Z",
    "title_canon_sha256": "accbcbb5ed31a9504b76f9d549e57f52d563ff8d470b62c6b2ea4880b48689eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15219",
    "kind": "arxiv",
    "version": 1
  }
}