Pith Number

pith:I3RFM3KN

pith:2016:I3RFM3KNNQH6MQSQXXWJ5K3VBD

not attested not anchored not stored refs pending

A Stability Theorem for Maximal $K_{r+1}$-free Graphs

Julian Sahasrabudhe, Kamil Popielarz, Richard Snyder

arxiv:1608.04675 v3 · 2016-08-16 · 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{I3RFM3KNNQH6MQSQXXWJ5K3VBD}

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	2026-05-18T00:13:38.154076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e2566d4d6c0fe64250bdec9eab7508cc31e42a63f7ff18d825e0a8e5ed6e73

Aliases

arxiv: 1608.04675 · arxiv_version: 1608.04675v3 · doi: 10.48550/arxiv.1608.04675 · pith_short_12: I3RFM3KNNQH6 · pith_short_16: I3RFM3KNNQH6MQSQ · pith_short_8: I3RFM3KN

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/I3RFM3KNNQH6MQSQXXWJ5K3VBD \
  | 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: 46e2566d4d6c0fe64250bdec9eab7508cc31e42a63f7ff18d825e0a8e5ed6e73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c7ef7d2f42dbd5da97f401ed101454c144bb0c667b60ccc03627ddbf680405f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-16T17:12:49Z",
    "title_canon_sha256": "6f5f51f0640f27ea17d946c0cd39e2a4ac89e75b997cf9287e0f7f9f15e8aa29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04675",
    "kind": "arxiv",
    "version": 3
  }
}