Pith Number

pith:7NV6EQYN

pith:2015:7NV6EQYNPA3QLLK3C3ZSGGOD4Y

not attested not anchored not stored refs pending

Equivalent Properties of CD Inequality on Graph

Shuang Liu, Yong Lin

arxiv:1512.02677 v1 · 2015-12-06 · math.CO · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NV6EQYNPA3QLLK3C3ZSGGOD4Y}

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	2026-05-18T01:24:43.379331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb6be2430d783705ad5b16f32319c3e62a9cc9c7aec14af2ca96d51b24a2c2d2

Aliases

arxiv: 1512.02677 · arxiv_version: 1512.02677v1 · doi: 10.48550/arxiv.1512.02677 · pith_short_12: 7NV6EQYNPA3Q · pith_short_16: 7NV6EQYNPA3QLLK3 · pith_short_8: 7NV6EQYN

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/7NV6EQYNPA3QLLK3C3ZSGGOD4Y \
  | 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: fb6be2430d783705ad5b16f32319c3e62a9cc9c7aec14af2ca96d51b24a2c2d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cce381807c6f81429c2e3584ab6b2daffc521ab563f4484847f4e05694cd56c8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-06T01:27:30Z",
    "title_canon_sha256": "e737d489a5f2f2bd80e6822cbe1d54a534956c8d122eb3b12db749a193ef51eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02677",
    "kind": "arxiv",
    "version": 1
  }
}