Pith Number

pith:E7KPQFDP

pith:2012:E7KPQFDP6K2P6EPF53FMRIPG7J

not attested not anchored not stored refs pending

Crossing Minimization within Graph Embeddings

Amina Shabbeer, Cagri Ozcaglar, Kristin P. Bennett

arxiv:1210.2041 v1 · 2012-10-07 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E7KPQFDP6K2P6EPF53FMRIPG7J}

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	2026-05-18T03:43:51.285143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27d4f8146ff2b4ff11e5eecac8a1e6fa5863b1902ed96747842799395575443c

Aliases

arxiv: 1210.2041 · arxiv_version: 1210.2041v1 · doi: 10.48550/arxiv.1210.2041 · pith_short_12: E7KPQFDP6K2P · pith_short_16: E7KPQFDP6K2P6EPF · pith_short_8: E7KPQFDP

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/E7KPQFDP6K2P6EPF53FMRIPG7J \
  | 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: 27d4f8146ff2b4ff11e5eecac8a1e6fa5863b1902ed96747842799395575443c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "562a1721ff5e56246df34149e9b0614951f877065083a2c9b4964b2b0c21ce89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-10-07T10:52:53Z",
    "title_canon_sha256": "a65c9fde643805be6c72114896fc53028641cc4035322ee81bcd2f74f77d2cd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2041",
    "kind": "arxiv",
    "version": 1
  }
}