Pith Number

pith:IF5FYWBC

pith:2018:IF5FYWBCV6YLRX2UFO5FPGP6MU

not attested not anchored not stored refs pending

Avoiding long Berge cycles, the missing cases $k=r+1$ and $k = r+2$

Abhishek Methuku, Beka Ergemlidze, Casey Tompkins, Ervin Gy\H{o}ri, Nika Salia, Oscar Zamora

arxiv:1808.07687 v1 · 2018-08-23 · 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{IF5FYWBCV6YLRX2UFO5FPGP6MU}

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	2026-05-18T00:07:24.489911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

417a5c5822afb0b8df542bba5799fe653147ed2c39887b60521a3efb0729f632

Aliases

arxiv: 1808.07687 · arxiv_version: 1808.07687v1 · doi: 10.48550/arxiv.1808.07687 · pith_short_12: IF5FYWBCV6YL · pith_short_16: IF5FYWBCV6YLRX2U · pith_short_8: IF5FYWBC

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/IF5FYWBCV6YLRX2UFO5FPGP6MU \
  | 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: 417a5c5822afb0b8df542bba5799fe653147ed2c39887b60521a3efb0729f632

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdc91a3ccf4d2b9eb87d9b2de39c4986febc4990ad11a302b10b3e03d428861f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-23T10:12:10Z",
    "title_canon_sha256": "8af2f1d34fa41031df733f492aa59f3f8ac5dc3e3cc03d786d98319193cdcfa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.07687",
    "kind": "arxiv",
    "version": 1
  }
}