Pith Number

pith:7GTZ2YE2

pith:2015:7GTZ2YE2DGM3IVRISQW5N7QC5B

not attested not anchored not stored refs pending

Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions

Fabian Rigterink, Marco Molinaro, Natashia Boland, Santanu S. Dey, Thomas Kalinowski

arxiv:1507.08703 v3 · 2015-07-30 · math.OC · 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{7GTZ2YE2DGM3IVRISQW5N7QC5B}

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	2026-05-18T00:50:01.957888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9a79d609a1999b45628942dd6fe02e8575a1f0c64723bbf230a0aaa68dea7cc

Aliases

arxiv: 1507.08703 · arxiv_version: 1507.08703v3 · doi: 10.48550/arxiv.1507.08703 · pith_short_12: 7GTZ2YE2DGM3 · pith_short_16: 7GTZ2YE2DGM3IVRI · pith_short_8: 7GTZ2YE2

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/7GTZ2YE2DGM3IVRISQW5N7QC5B \
  | 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: f9a79d609a1999b45628942dd6fe02e8575a1f0c64723bbf230a0aaa68dea7cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "badacdc895cddfe5746901f0e63c74c074f8cc3d5e78b8bcb9361dd6aff322eb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-07-30T22:28:02Z",
    "title_canon_sha256": "1ba38f22302f3cc44b7d1e703458df609dcfeded30f1b779b0ecfbc717c4d43f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08703",
    "kind": "arxiv",
    "version": 3
  }
}