Pith Number

pith:7A2Z7LKT

pith:2017:7A2Z7LKTYYI3SU2VGNTZITVTVH

not attested not anchored not stored refs pending

On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity

Adri\'an Pastine, Melissa Keranen

arxiv:1712.09291 v1 · 2017-12-26 · 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{7A2Z7LKTYYI3SU2VGNTZITVTVH}

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	2026-05-18T00:27:14.015854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8359fad53c611b953553367944eb3a9f7a3127a2d99af2c38813dcb8ba068ad

Aliases

arxiv: 1712.09291 · arxiv_version: 1712.09291v1 · doi: 10.48550/arxiv.1712.09291 · pith_short_12: 7A2Z7LKTYYI3 · pith_short_16: 7A2Z7LKTYYI3SU2V · pith_short_8: 7A2Z7LKT

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/7A2Z7LKTYYI3SU2VGNTZITVTVH \
  | 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: f8359fad53c611b953553367944eb3a9f7a3127a2d99af2c38813dcb8ba068ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab826825853d9315f34b8603b2b97dfa6dc70318bb35880b33c508c6fe626149",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-12-26T15:47:57Z",
    "title_canon_sha256": "b7b267e50d1a19defbbab791b6539200904a56ad09de2ca3e4a4c83c02e12fda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09291",
    "kind": "arxiv",
    "version": 1
  }
}