Pith Number

pith:ODJK3Z44

pith:2026:ODJK3Z44TZIGZGTYZ6ZLQRZOV4

not attested not anchored not stored refs resolved

New Algorithms for Parity-SAT and Its Bounded-Occurrence Versions

Frank Stephan, Haoyun Tang, Junqiang Peng, Mingyu Xiao, Sanjay Jain

Randomized algorithms solve Parity-d-occ-SAT in O^*(2^{m(1-1/O(d))}) time for any fixed d.

arxiv:2605.14093 v1 · 2026-05-13 · cs.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ODJK3Z44TZIGZGTYZ6ZLQRZOV4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

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

We design a randomized O^*(2^{m(1-1/O(d))})-time algorithm for Parity-d-occ-SAT, thereby breaking the 2^m barrier for every fixed d. For d=2 we obtain O^*(1.1193^n) or O^*(1.3248^m), and for general Parity-SAT an O^*(1.1052^L) algorithm.

C2weakest assumption

The algorithms assume that parity can be exploited via structural reductions and branching rules that avoid the overhead of exact counting, without hidden costs that would appear only in a full proof or implementation.

C3one line summary

New randomized and branching algorithms achieve O*(2^{m(1-1/O(d))}) time for Parity-d-occ-SAT and O*(1.1052^L) time for general Parity-SAT, outperforming exact counting bounds.

References

47 extracted · 47 resolved · 0 Pith anchors

[1] Cook , title = 1971

[2] Valiant , title = 1979

[3] Proceedings of the 44th Annual Symposium on Foundations of Computer Science ( 2003

[4] Dan Roth , title =. Artif. Intell. , volume =. 1996 , doi = 1996

[5] Kautz , title =

Receipt and verification

First computed	2026-05-17T23:39:12.183097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d2ade79c9e506c9a78cfb2b8472eaf13e83d3f1058636d55a83543ea2ac714

Aliases

arxiv: 2605.14093 · arxiv_version: 2605.14093v1 · doi: 10.48550/arxiv.2605.14093 · pith_short_12: ODJK3Z44TZIG · pith_short_16: ODJK3Z44TZIGZGTY · pith_short_8: ODJK3Z44

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/ODJK3Z44TZIGZGTYZ6ZLQRZOV4 \
  | 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: 70d2ade79c9e506c9a78cfb2b8472eaf13e83d3f1058636d55a83543ea2ac714

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "043430e1da4601815e44f8c7620a44556c6bda62a048b92d18dbc31c653a853a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T20:25:11Z",
    "title_canon_sha256": "cb5a6e5da6d309bd197a4c9fada2ec41442fca5e687310c40eb77be4163c46f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14093",
    "kind": "arxiv",
    "version": 1
  }
}