Pith Number

pith:EL5J22GP

pith:2013:EL5J22GPKWTE4F23JMRLZEYGFJ

not attested not anchored not stored refs pending

Beyond Log-Supermodularity: Lower Bounds and the Bethe Partition Function

Nicholas Ruozzi

arxiv:1309.6859 v1 · 2013-09-26 · 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{EL5J22GPKWTE4F23JMRLZEYGFJ}

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	2026-05-18T03:12:10.015692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22fa9d68cf55a64e175b4b22bc93062a461dbcf58ed0f514b584c48723c5df56

Aliases

arxiv: 1309.6859 · arxiv_version: 1309.6859v1 · doi: 10.48550/arxiv.1309.6859 · pith_short_12: EL5J22GPKWTE · pith_short_16: EL5J22GPKWTE4F23 · pith_short_8: EL5J22GP

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/EL5J22GPKWTE4F23JMRLZEYGFJ \
  | 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: 22fa9d68cf55a64e175b4b22bc93062a461dbcf58ed0f514b584c48723c5df56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efea1a4907496d583270c0923155d4b6dafd0d0178734ce6a2a4cde8ce53a276",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-09-26T12:49:27Z",
    "title_canon_sha256": "7562e3e7d35f5db55de447bba945d1369336f6f32eae49885f02c0d6d2a1fac3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6859",
    "kind": "arxiv",
    "version": 1
  }
}