Pith Number

pith:6BS2XKPS

pith:2019:6BS2XKPS42B2XQ4TPHS5B4OCVE

not attested not anchored not stored refs pending

Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs

Shuya Chiba, Tomoki Yamashita

arxiv:1904.03818 v1 · 2019-04-08 · 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{6BS2XKPS42B2XQ4TPHS5B4OCVE}

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	2026-05-17T23:49:08.053816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f065aba9f2e683abc39379e5d0f1c2a90ee1acc350968fe3d6e8cc6c7b3c3e49

Aliases

arxiv: 1904.03818 · arxiv_version: 1904.03818v1 · doi: 10.48550/arxiv.1904.03818 · pith_short_12: 6BS2XKPS42B2 · pith_short_16: 6BS2XKPS42B2XQ4T · pith_short_8: 6BS2XKPS

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/6BS2XKPS42B2XQ4TPHS5B4OCVE \
  | 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: f065aba9f2e683abc39379e5d0f1c2a90ee1acc350968fe3d6e8cc6c7b3c3e49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bd8f09d2a4e0ffccbb4e19300874385d2ae5a9d6f7e18e5a980a809fa3f9b09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-08T03:22:36Z",
    "title_canon_sha256": "26bbf4afbf1741a771313c1a3e6617bfb7e58e38b86285601f87610785d19124"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.03818",
    "kind": "arxiv",
    "version": 1
  }
}