Pith Number

pith:VTEKPBDZ

pith:2015:VTEKPBDZ235G7GHDXULFVHZJZ3

not attested not anchored not stored refs pending

Cycle lengths and minimum degree of graphs

Chun-Hung Liu, Jie Ma

arxiv:1508.07912 v1 · 2015-08-31 · 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{VTEKPBDZ235G7GHDXULFVHZJZ3}

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	2026-05-18T01:34:31.200666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acc8a78479d6fa6f98e3bd165a9f29cec6eb9cc9227abf4fb65ee6d33b315c3d

Aliases

arxiv: 1508.07912 · arxiv_version: 1508.07912v1 · doi: 10.48550/arxiv.1508.07912 · pith_short_12: VTEKPBDZ235G · pith_short_16: VTEKPBDZ235G7GHD · pith_short_8: VTEKPBDZ

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/VTEKPBDZ235G7GHDXULFVHZJZ3 \
  | 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: acc8a78479d6fa6f98e3bd165a9f29cec6eb9cc9227abf4fb65ee6d33b315c3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74e057415449cbb8eb64f06686cb1a1e8455f66dea4fbb42947e2138aa7cf95b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-31T16:45:53Z",
    "title_canon_sha256": "1d82ee19b2ade051c5db50f12e1411eac66d528629ab00e5d3b48c7445fdecac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07912",
    "kind": "arxiv",
    "version": 1
  }
}