Pith Number

pith:LQSTKPBB

pith:2026:LQSTKPBBWEFVMJ4JOGEAU6M5NQ

not attested not anchored not stored refs pending

Fine-Grained AC$^0$ Lower Bounds for $k$-OV, $k$-XOR, and $k$-SUM via Colored Subgraph Isomorphism

Haoxing Lin

arxiv:2608.08578 v1 · 2026-08-09 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LQSTKPBBWEFVMJ4JOGEAU6M5NQ}

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.

Receipt and verification

First computed	2026-08-11T01:23:02.803032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c25353c21b10b56278971880a799d6c128f0441847a9674ecb2a0dbc37f5cca

Aliases

arxiv: 2608.08578 · arxiv_version: 2608.08578v1 · doi: 10.48550/arxiv.2608.08578 · pith_short_12: LQSTKPBBWEFV · pith_short_16: LQSTKPBBWEFVMJ4J · pith_short_8: LQSTKPBB

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/LQSTKPBBWEFVMJ4JOGEAU6M5NQ \
  | 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: 5c25353c21b10b56278971880a799d6c128f0441847a9674ecb2a0dbc37f5cca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93ab44c860a25a4250d88e028964a4432ad3bc06f39554e42253eba8d3bf2d42",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-08-09T08:43:25Z",
    "title_canon_sha256": "dc52b2b1959565aac82017d9da079b77fb25900cdca95a689812d1e587872575"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08578",
    "kind": "arxiv",
    "version": 1
  }
}