Pith Number

pith:QU2GDMBR

pith:2026:QU2GDMBRRISEFHHMM4OPPGKISG

not attested not anchored not stored refs resolved

Distributed Statistical Zero-Knowledge Proofs via Sumcheck

Benjamin Jauregui, Masayuki Miyamoto

A distributed Sumcheck protocol verifies polynomial sums with statistical zero-knowledge in linear rounds.

arxiv:2605.14015 v1 · 2026-05-13 · cs.DC

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\pithnumber{QU2GDMBRRISEFHHMM4OPPGKISG}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Given oracle access to a polynomial F over a finite field F with N variables, we design a protocol verifying claims of the form sum_{x in F} F(x)=a using O(N) rounds of O(log |F|)-bit messages, while achieving statistical zero-knowledge and small soundness error.

C2weakest assumption

The protocol assumes oracle access to the polynomial F is available to the distributed nodes and that local computation is polynomial-time, as required for the Sumcheck lifting and simulation arguments.

C3one line summary

A distributed statistical zero-knowledge Sumcheck protocol is constructed and applied to non-k-colorability and subgraph counting with O(n) and O(k log n) rounds respectively.

References

24 extracted · 24 resolved · 1 Pith anchors

[1] Locally Verifiable Distributed SNARGs 2023

[2] Fully Local Succinct Distributed Argu- ments 2024

[3] [BKO22] Aviv Bick, Gillat Kol, and Rotem Oshman 2022

[4] Zero knowledge protocols from succinct constraint detection 2017

[5] Aurora: Transparent succinct arguments for r1cs 2019

Receipt and verification

First computed	2026-05-17T23:39:13.014395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

853461b0318a24429cec671cf7994891bcdc53ab72f7d25b882062499ddebd07

Aliases

arxiv: 2605.14015 · arxiv_version: 2605.14015v1 · doi: 10.48550/arxiv.2605.14015 · pith_short_12: QU2GDMBRRISE · pith_short_16: QU2GDMBRRISEFHHM · pith_short_8: QU2GDMBR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QU2GDMBRRISEFHHMM4OPPGKISG \
  | 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: 853461b0318a24429cec671cf7994891bcdc53ab72f7d25b882062499ddebd07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4c32b360cf03718bf1d2c54e73ccc4ce517606782f8be58d1dd8b5f4b02bd17",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DC",
    "submitted_at": "2026-05-13T18:27:32Z",
    "title_canon_sha256": "7cd60c5ec0fffb0a375dd2803339763027f0a19e184dfe1dde778dc5bea530c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14015",
    "kind": "arxiv",
    "version": 1
  }
}