Pith Number

pith:5P2M4HZM

pith:2017:5P2M4HZMEAUATZ4GBQN77APNRR

not attested not anchored not stored refs pending

Hypergraph Theory: Applications in 5G Heterogeneous Ultra-Dense Networks

Geoffrey Ye Li, Hongliang Zhang, Lingyang Song, Yonghui Li

arxiv:1709.07129 v1 · 2017-09-21 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5P2M4HZMEAUATZ4GBQN77APNRR}

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	2026-05-18T00:34:36.507804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebf4ce1f2c202809e7860c1bff81ed8c7e50eb79e13ba269df4d90e8e0b88951

Aliases

arxiv: 1709.07129 · arxiv_version: 1709.07129v1 · doi: 10.48550/arxiv.1709.07129 · pith_short_12: 5P2M4HZMEAUA · pith_short_16: 5P2M4HZMEAUATZ4G · pith_short_8: 5P2M4HZM

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/5P2M4HZMEAUATZ4GBQN77APNRR \
  | 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: ebf4ce1f2c202809e7860c1bff81ed8c7e50eb79e13ba269df4d90e8e0b88951

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81cc666625e1e3552fbdd12d964e7783ac1a9b4ae5f2ae09915c577b7e1ab9eb",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2017-09-21T02:07:36Z",
    "title_canon_sha256": "4baf5649898bc01982ab5c86f946da14fcecbd53b3b73c50c3b8207a469836d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07129",
    "kind": "arxiv",
    "version": 1
  }
}