Pith Number

pith:U7THNRPY

pith:2013:U7THNRPYEIZRSW2HKL43IQ42OP

not attested not anchored not stored refs pending

The densest subgraph problem in sparse random graphs

Justin Salez, Venkat Anantharam

arxiv:1312.4494 v2 · 2013-12-16 · math.PR · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U7THNRPYEIZRSW2HKL43IQ42OP}

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	2026-05-18T01:23:16.968236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7e676c5f82233195b4752f9b4439a73c295aed43d56e630eeae109c35bae736

Aliases

arxiv: 1312.4494 · arxiv_version: 1312.4494v2 · doi: 10.48550/arxiv.1312.4494 · pith_short_12: U7THNRPYEIZR · pith_short_16: U7THNRPYEIZRSW2H · pith_short_8: U7THNRPY

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/U7THNRPYEIZRSW2HKL43IQ42OP \
  | 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: a7e676c5f82233195b4752f9b4439a73c295aed43d56e630eeae109c35bae736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ed7133480b35adcf08025537c71a3149d278a9c190157d93040ca79155d13d0",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-16T20:09:35Z",
    "title_canon_sha256": "481e1148f4765d60973d603da7b2ebd8f6c0dc8485067a02029dde3ff560e6fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4494",
    "kind": "arxiv",
    "version": 2
  }
}