Pith Number

pith:KAJ4ER3P

pith:2015:KAJ4ER3PVQGQUR6XNCDWKA3X2M

not attested not anchored not stored refs pending

A Graph Theoretical Analysis of the Number of Edges in k-dense Graphs

Henry Escuardo, Karl R.B. Schmitt, Linda Eroh, Ralucca Gera, Samuel Prahlow

arxiv:1505.04300 v1 · 2015-05-16 · 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{KAJ4ER3PVQGQUR6XNCDWKA3X2M}

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	2026-05-18T02:07:25.805022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5013c2476fac0d0a47d76887650377d3276327d08b86fdb9a7fedb3fb6a8f046

Aliases

arxiv: 1505.04300 · arxiv_version: 1505.04300v1 · doi: 10.48550/arxiv.1505.04300 · pith_short_12: KAJ4ER3PVQGQ · pith_short_16: KAJ4ER3PVQGQUR6X · pith_short_8: KAJ4ER3P

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/KAJ4ER3PVQGQUR6XNCDWKA3X2M \
  | 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: 5013c2476fac0d0a47d76887650377d3276327d08b86fdb9a7fedb3fb6a8f046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce78b1441340c3a180889713592c369105a5c9f2ee7b6d915c2d2f51d78bdb42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-16T17:44:46Z",
    "title_canon_sha256": "0c1215aceb9431edfe01382d81419569e71bf366f34ab3cafafd4fb48d205bee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04300",
    "kind": "arxiv",
    "version": 1
  }
}