Pith Number

pith:C4V4HJ3K

pith:2016:C4V4HJ3K5D2RHGV3Y3KOSJ4HK4

not attested not anchored not stored refs pending

Almost-Polynomial Ratio ETH-Hardness of Approximating Densest $k$-Subgraph

Pasin Manurangsi

arxiv:1611.05991 v2 · 2016-11-18 · 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{C4V4HJ3K5D2RHGV3Y3KOSJ4HK4}

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	2026-05-18T00:46:48.800774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

172bc3a76ae8f5139abbc6d4e9278757318899a9b5de166d265b62ba77b377ef

Aliases

arxiv: 1611.05991 · arxiv_version: 1611.05991v2 · doi: 10.48550/arxiv.1611.05991 · pith_short_12: C4V4HJ3K5D2R · pith_short_16: C4V4HJ3K5D2RHGV3 · pith_short_8: C4V4HJ3K

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/C4V4HJ3K5D2RHGV3Y3KOSJ4HK4 \
  | 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: 172bc3a76ae8f5139abbc6d4e9278757318899a9b5de166d265b62ba77b377ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8da14f5a16c397b34d7a106740252c9cd325bb7bcbfcbf9924b589c354f7f60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2016-11-18T07:05:00Z",
    "title_canon_sha256": "57f029812f2b2cb4a7397cace7e965b98762ff5f9648fc5af1f6c3eb0b7e9e44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05991",
    "kind": "arxiv",
    "version": 2
  }
}